Download - Towards more efficient Praseodymium Doped Fibre Amplifiers … · Uitnodiging Tot het bijwonen van de openbare verdediging van mijn proefschrift Towards more efficient Praseodymium

Uitnodiging

Tot het bijwonen van deopenbare verdediging van

mijn proefschrift

Towards more efficientPraseodymium Doped

Fibre Amplifiers forthe O-band

op dinsdag 7 november 2006

om 16:00 uur

De promotie vindt plaats inhet Auditorium van deTechnische Universiteit

Eindhoven.

Na afloop van deze plechtigheid zal er eenreceptie plaatsvinden

waarvoor u ook van hartewordt uitgenodigd.

Ronald SchimmelVoermanstraat 601973 VL IJmuiden

0255 52 31 [email protected]

PMS Yellow 012 C + zwart ± 266 pag. = 18 mm rug GLANS-laminaat oplage: 500 stuks

Towards more efficient Praseodymium Doped Fibre Amplifiers

for the O-Band

Ronald Schimmel

Towards m

ore efficient Praseodymium

Doped Fibre A

mplifiers for the O

-Band R

onald Schim

mel

Towards more efficient

Praseodymium Doped Fibre Amplifiers

for the O-Band

Towards more efficient

Praseodymium Doped Fibre Amplifiers

for the O-Band

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de

Technische Universiteit Eindhoven, op gezag van de

Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een

commissie aangewezen door het College voor

Promoties in het openbaar te verdedigen

op dinsdag 7 november 2006 om 16.00 uur

door

Ronald Christiaan Schimmel

geboren te Veldhoven

Dit proefschrift is goedgekeurd door de promotoren:

prof.ir. G.D. Khoeenprof.dr.ir. R.G.C. Beerkens

Copromotor:dr.ir. H. de Waardt

CIP–DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

Schimmel, Ronald C.

Towards more efficient praseodymium doped fibre amplifiers for the O-band / byRonald Christiaan Schimmel. –Eindhoven : Technische Universiteit Eindhoven, 2006.Proefschrift. – ISBN-10: 90-386-1903-0ISBN-13: 978-90-386-1903-3NUR 959Trefw.: optische versterkers / glasvezels / glastechnologie / lanthaniden /chalcogenen / optische telecommunicatiesystemen.Subject headings: optical fibre amplifiers / glass fibres / optical fibre fabrication /praseodymium / chalcogenide glasses / optical communication.

The work described in this thesis was carried out at the Department of Electrical

Engineering of the Eindhoven University of Technology and was financially supportedby TNO and the COBRA Research Institute.

Druk: Printservice Technische Universiteit Eindhoven

Aan mijn Ouders& Robin

Summary

Due to their potentially high gain efficiency (i.e. high signal gain per unit pumppower), rare earth doped amplifiers are considered as suitable travelling-wave am-plifiers for optical communication systems. In order to fully exploit the transparentwindows of the installed fibre, and particularly the 1.31 µm wavelength region, apowerful amplifier technique for these wavelengths is needed in the near future.In the 1290–1340 nm wavelength range, the praseodymium doped fibre amplifier(PDFA) is commercially available since the late 1990s, however the efficiency of theseamplifiers (based on fluoride host glasses) is low. In this study, the objective is thedevelopment of a PDFA with improved efficiency, based on sulphide host glasses. Fur-thermore, the objective is to assess the performance (i.e. gain, saturation and noisecharacteristics) of PDFAs in telecommunication systems deploying the O-band (thewavelenght range between 1290 and 1340 nm) by means of modelling and measure-ment of e.g. the gain and noise figure.

Praseodymium doped germanium gallium sulphide host materials

Using the pure chemical elements as a starting material, germanium gallium sulphideglasses were prepared by melting at 1000 C in vitreous silica ampoules. Purifica-tion of the raw materials, especially sulphur, is essential to obtain highly transparenthost glasses, especially for the praseodymium doped fibre amplifiers’ pump and sig-nal wavelength ranges (i.e. 1010–1040 nm and 1290–1340 nm, respectively). Thegermanium gallium sulphide glasses are transparent in the 0.5–8.0 µm wavelengthrange. The wavelength dependency of the refractive index of the glasses was deter-mined by ellipsometry and measurement of the Brewster angle. The guiding of lightwithin a glass fibre is determined by, among others, the refractive index of the coreand cladding glasses. The refractive index of the developed glasses, in the amplifiers’pump and signal wavelength ranges, is approximately 2.07 and is slightly dependentof the composition.The radiative (absorption and emission) properties of the praseodymium in the ger-manium gallium sulphide host glass were quantitatively characterised using Judd-Ofelt theory. The Judd-Ofelt parameters, for the optical transitions within thepraseodymium ions, were used to establish the signal emission cross section and ex-cited state absorption cross sections. Besides absorption or emission of photons, theenergy state of the praseodymium ion can change by non-radiative (e.g. multi-phonon)

i

ii Towards more efficient praseodymium doped fibre amplifiers for the O-band

energy transfer to the host glass. The energy difference between the 1G4 and 3F4

state of praseodymium in the germanium gallium sulphide glasses is approximately2945 cm−1, while the effective phonon energy of the host glass is limited to 490 cm−1.The (measured) emission lifetime of the 1G4 – 3H5 transition is approximately 400 µs.The estimated multi-phonon relaxation rate of the 1G4 level is approx. 1150 s−1 (atroom temperature), which corresponds to a non-radiative lifetime of 870 µs.

Fibre drawing of chalcogenide glasses

The difference between the glass transition temperature and the crystallisation tem-perature (below this temperature no crystallisation will occur within normal timespans) is important for the stability of the germanium gallium sulphide glasses dur-ing forming processes. The glass transition temperature, of the developed glasses,is approximately 360 C and the crystallisation temperature is circa 185 C higherthan the glass transition temperature. From the measured viscosity – temperaturerelation, it is concluded that the viscosity of the glass is sufficiently low to draw fibreswell below the crystallisation temperature.The relatively simple preform technique for fibre drawing was selected in favour of thecrucible drawing process, due to the availability of glass rods, fabricated by melting insealed ampoules. In this work, the methods suitable for preparation of a germaniumgallium sulphide fibre preform, based on the rod-in-tube process, were investigated.In the rod-in-tube process, the fibre preform is constructed by inserting a (thin) rodof core sulphide glass into a cladding tube of sulphide glass with slightly differentcomposition. Prior to assembly of the preform, the quality of the surface is improvedby chemical etching.A hot deformation process for production of germanium gallium sulphide claddingglass tubes is presented. In this process, the visco-elastic properties of the glass areused. Rods of cladding glass are heated inside a mould and converted into tubes bypenetration of a needle under isothermal conditions. Selection of the working tem-perature is critical to prevent cracking of the material (at low temperature and highviscosity), crystallisation (due to high temperatures) or collapse upon removal of theneedle (at low viscosity). Thin core glass rods could be prepared by stretching of coreglass rods (as melted) to the desired diameter in the fibre drawing tower.Etching of the glass surfaces, prior to assembly of the fibre preform and fibre drawing,is needed to limit the formation of defects at the core cladding interface during fibredrawing and obtain fibres with low optical losses. Aqueous, alkaline solutions can beused to etch the surface of germanium gallium sulphide glasses. In this study, thebest etching results are obtained using diluted caustic soda (0.02 M). The etching rateof more concentrated solutions (>0.5 M) is too high for controllable etching. Due tonegligible reactivity between (concentrated) acids and germanium gallium sulphideglasses, these glasses can not be etched with acids. Hence, (concentrated) acids canbe used only to clean contaminated glass surfaces, without impairments to the glasssurface.The assembly of germanium gallium sulphide preforms (with core-cladding structure)and the fibre drawing of these preforms is rather complicated and could not be realised

Summary iii

in the course of this study, due to the limited availability of suitable glass sampleswith the required dimensions.A mathematical model is used to determine suitable process conditions for fibre draw-ing of germanium gallium sulphide glasses. This twodimensional model is based onaxi-symmetry of the preform and includes the solution of the equations of continuity,motion and heat transfer and their appropriate boundary conditions for the drawingof glass fibres from a preform was presented. Furthermore, the properties of the ger-manium gallium sulphide glass are incorporated in the model.The model was used to calculate the temperature, stresses and velocity profile inthe neckdown, for various fibre drawing velocities and furnace temperatures. Theworking range (i.e. the applicable fibre drawing rate as a function of furnace temper-ature) for fibre drawing of germanium gallium sulphide glasses is derived from thesecomputed results. The accuracy of the model results possibly can be improved bydetailed modelling of both radiative heat transfer within the glass and radiative heattransfer between the glass and the furnace. It is concluded that the fibre drawing ofgermanium gallium sulphide glasses is possible, however the narrow working area isbound by crystallisation (which limits the maximum applicable furnace temperature)and the axial stresses occurring in the fibre (which limits the applicable fibre drawingspeed).Uncladded germanium gallium sulphide fibres with a diameter between 200 and300 µm and a length of 17.5 m were obtained using a pilot scale fibre drawing tower.Based on the modelling results, it is expected that germanium gallium sulphide fibreswith a core diameter of less than 4 µm and a cladding diameter of less than 150 µmcan be drawn using this equipment by improved process control.

Optical properties of germanium gallium sulphide fibres

The attenuation losses at the amplifiers’ pump and signal wavelengths of these fibres,with composition Ge28.8Ga1.2S70.0, were determined, too. The applied praseodymiumdopant concentration is 370 ppm (mg/kg). The signal attenuation loss at 1300 nm ofthis fibre is 0.2 dB/cm. The attenuation at 1030 nm equals 0.43 dB/cm, which canbe partly contributed to pump ground state absorption at this wavelength. The peakwavelength of the spontaneous emission spectrum is located at 1335 nm, the 3 dBbandwidth is approximately 70 nm.

Performance and design of PDFAs for telecommunication systems

The system performance of a PDFA in an optical transmission system operating at1.3 µm was investigated experimentally. The PDFA, based on a fluoride glass fi-bre, was constructed using commercially available components. The performance isanalysed for different amplifier applications (booster, in-line and pre-amplifier) andconfigurations (co-propagating and bi-directional) at bit rates up to 10 Gbit/s. Thegain of the experimental PDFA (based on fluoride fibre) is independent of the polar-isation state of the signal light. When the experimental PDFA is used in a boosterapplication, the amplifier is saturated at high signal input powers. As saturation of

iv Towards more efficient praseodymium doped fibre amplifiers for the O-band

the PDFA does not result in bit pattern dependent fluctuations of the signal gain,PDFAs are well suited for as booster amplifiers.An optical recirculating loop was used to evaluate the transmission performance of asystem incorporating multiple PDFAs (operated as in-line amplifier) and fibre spans(of 2×12.5 km length) at bit rates of 622 Mbit/s and 10 Gbit/s. Increasing the num-ber of roundtrips (i.e. distance) results in degradation of the signal to noise ratio.This degradation is explained by the power self regulation process i.e. the averageoutput power of the PDFA remains constant while amplified spontaneous emission(ASE) noise power increases at the expense of signal power. A total distance ofcirca 2000 km (80 roundtrips) can be bridged at a bit rate of 622 Mbit/s. How-ever, pre-amplification of the signal at the receiver is necessary. At higher bit rates(e.g. 10 Gbit/s) error free transmission is obtained only for distances up to 25 km,due to the lack of optical pre-amplification at the receiver and the limited sensitivityof the 10 Gbit/s receiver (-15.5 dBm) compared to that of the 622 Mbit/s receiver(−32 dBm).Using the PDFA as a pre-amplifier, the receiver sensitivity is enhanced. The sen-sitivity of the receiver with fluoride fibre based PDFA pre-amplifier at bit rate of10 Gbit/s is approximately -30 dBm, which equals a 15 dB improvement comparedto the sensitivity of the receiver without pre-amplifier. The small signal gain is circa20 dB, while the noise figure, derived from these experiments, is 9 dB.

Modelling light amplification in praseodymium doped single-mode fibres

A spatially and spectrally resolved amplifier model, based on the four-level operationof praseodymium, is used to study amplifier operation using the optical properties ofthe praseodymium dopant and the host glasses in different configurations. The (steadystate) amplifier model describes the evolution of signal, ASE and pump power as afunction of distance within the praseodymium doped fibre. In addition, the noisefigure is calculated.The outcome of the model was validated by measurements of the gain and noise fig-ure of a PDFA assembled from commercially available components. The static gainand noise figure of this PDFA (based on fluoride host glasses) were determined usingmonochromatic continuous wave test signals, applying the interpolation-substractiontechnique on the optical output spectrum. In general, the gain as determined by theamplifier model is lower than the measured gain while the trends in the amplifiercharacteristics are well described by the model.When no pump power is applied, the wavelength dependent losses caused by signalground state absorption are slightly overestimated by the amplifier model. This re-sults in an underestimation of the gain by the model, especially at lower pump powers.The maximum measured gain is located at somewhat shorter wavelengths than themaximum gain calculated by the amplifier model. The model confirmed the smalldifferences observed in the measurements of the gain and noise figure for the amplifierin co-propagating, counter-propagating and bi-directional configurations.Taking the limited accuracy of the optical properties and the experimental errorsof the gain measurements into account, the results of the model have been found

Summary v

in trendwise agreement with the experimental data. The model is considered to besuitable for the design and development of PDFAs based on other glass compositions(such as praseodymium doped germanium gallium sulphide glasses) or geometricalconfigurations.The design of the amplifier for booster and pre-amplifier configurations, based on ger-manium gallium sulphide glasses, is optimised using the fibre amplifier model. Themain parameters involved in the optimisation of the praseodymium doped fibre itself,considered here, are numerical aperture, core radius and length. The optimum lengthof the praseodymium doped fibre, to obtain maximum gain for a given pump power,is inversely proportional to the dopant concentration. For a praseodymium dopedsulphide glass fibre with a core diameter of 4 µm, which can be obtained in pilot scalefibre drawing, calculated maximum gain is obtained for a numerical aperture of 0.182and a cut-off wavelength of 950 nm. For example, the calculated saturated signaloutput power of a booster amplifier is 30 dBm using 1700 mW pump power, whilethe calculated small signal gain obtained by a sulphide based preamplifier is 30 dBfor 165 mW pump power.The calculated maximum gain is obtained at a signal wavelength of 1342 nm, whichmatches the peak of the emission spectrum of praseodymium doped germanium gal-lium sulphide glasses. The output power of a saturated PDFA, based on sulphidefibre, is nearly independent of input power, i.e. the slope of the gain curve is approx-imately -1 dB/dBm. This phenomenon allows for stabilisation of the signal powerwithin a transmission link containing several in-line amplifiers.The performance of the PDFA based on germanium gallium sulphide host materialand fluoride host materials are compared using the amplifier model. In general, thecalculated quantum conversion efficiency (defined as the increase in the number ofsignal photons as a result of amplification divided by the number of launched pumpphotons) and gain efficiency of sulphide amplifiers are much higher than the efficiencyof fluoride amplifiers. For example, the calculated quantum conversion efficiency ofa booster amplifier (signal input power 0 dBm, signal output power 20 dBm) basedon sulphide host glasses is 0.5 mW/mW which is twice as large as that of a fluoridebased booster amplifier. The calculated gain efficiency of a pre-amplifier (signal inputpower -30 dBm, gain 20 dB) based on sulphide host glasses is 0.134 dB/mW higherthan that of a fluoride based amplifier. Due to the higher efficiency of the sulphideamplifier, less pump power is needed by this amplifier to obtain high gain. Due tothe longer emission lifetime of praseodymium in the sulphide glass host compared tofluoride host glasses (i.e. about 400 versus 130 µs), the efficiency of amplifiers basedon sulphide host glasses is much higher, leading to advantageous reduction of therequired pump power. The maximum gain wavelength of the sulphide amplifier is ap-proximately 1340 nm, and is shifted to longer wavelengths compared to the maximumgain wavelength of the fluoride amplifier, which is approximately 1310 nm. This shiftof the maximum gain to longer wavelengths is considered as a drawback for the useof sulphide host glass for the PDFA in telecommunication systems operating around1.31 µm.

vi Towards more efficient praseodymium doped fibre amplifiers for the O-band

Conclusions

Based on the observed performance of the experimental PDFA based on fluoride hostglass and the high, calculated efficiency of the PDFA based on sulphide glass, it is ex-pected that the PDFA based on germanium gallium sulphide glass will be a promisingcandidate as fibre amplifier for the O-band (1290–1340 nm). However, experimentaltechniques should be improved to allow production of single mode praseodymiumdoped fibre based on germanium gallium sulphide glasses with a core diameter of lessthan 4 µm and absorption and scattering losses of less than 0.1 dB/m.As powerful pump lasers (operating in the wavelength range 1010–1040 nm) have be-come available, the development of PDFA with high gain and high saturation outputpower is feasible. When the PDFA based on sulphide host glasses becomes available,the choice whether to apply a PDFA based on sulphide host glasses or based on flu-oride host glasses is strongly dependent on the intended application.Due to the high quantum conversion efficiency, the PDFA based on sulphide hostglasses offers a potentially better performance in booster applications (e.g. amplifi-cation of (analogue) CATV signals) than the PDFA based on fluoride host glasses.In contrast with semi-conductor amplifiers and Raman amplifiers, the PDFA is wellsuited for the amplification of amplitude modulated signals, because signal distortionby the saturated amplifier (e.g. pattern effect) is negligible.The signal output power of the saturated PDFA, based on a sulphide fibre, will benearly independent of signal input power, which is a favourable phenomenon whenused as an in-line amplifier. The ability of stabilisation of the signal power within atransmission link containing several in-line amplifiers is more pronounced for PDFAsbased on sulphide host glasses compared to PDFAs based on fluoride host glasses.Due to its high small signal gain and low noise figure, the PDFA can also be used asa pre-amplifier to enhance receiver sensitivity. In this application, the performanceof the PDFA based on either sulphide or fluoride host glasses will be similar and thedifference in gain efficiency is less decisive.

Contents

1 Introduction 1

1.1 Optical amplifiers in optical telecommunication systems . . . . . . . . 11.2 Optical amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Rare-earth doped fibre amplifiers . . . . . . . . . . . . . . . . . 41.2.2 Other types of optical amplifiers . . . . . . . . . . . . . . . . . 11

1.3 General application of optical amplifiers . . . . . . . . . . . . . . . . . 121.4 Scope and objective of this thesis . . . . . . . . . . . . . . . . . . . . . 14

1.4.1 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . 151.5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Praseodymium doped germanium gallium sulphide glasses 19

2.1 Preparation of the glass host . . . . . . . . . . . . . . . . . . . . . . . 202.1.1 The glass forming region . . . . . . . . . . . . . . . . . . . . . . 202.1.2 Preparation methods . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2 Optical properties of the host glass . . . . . . . . . . . . . . . . . . . . 232.2.1 IR transmittance spectra . . . . . . . . . . . . . . . . . . . . . 252.2.2 UV VIS NIR transmittance spectra . . . . . . . . . . . . . . . 282.2.3 Refractive index . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3 Optical properties of praseodymium in the host glass . . . . . . . . . . 362.3.1 Electronic structure . . . . . . . . . . . . . . . . . . . . . . . . 372.3.2 Absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . 382.3.3 Photoluminescence spectroscopy . . . . . . . . . . . . . . . . . 392.3.4 Radiative transitions . . . . . . . . . . . . . . . . . . . . . . . . 48

2.4 Interactions between host glass and dopant . . . . . . . . . . . . . . . 552.4.1 Structure and phonon energy . . . . . . . . . . . . . . . . . . . 562.4.2 Non-radiative transitions . . . . . . . . . . . . . . . . . . . . . 57

2.5 Thermal properties of the host glass . . . . . . . . . . . . . . . . . . . 602.5.1 Glass transition and crystallisation temperatures . . . . . . . . 612.5.2 Thermal expansion . . . . . . . . . . . . . . . . . . . . . . . . . 642.5.3 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.7 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692.8 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

vii

viii Towards more efficient praseodymium doped fibre amplifiers for the O-band

3 Fibre drawing of chalcogenide glasses 77

3.1 Structure of an optical fibre . . . . . . . . . . . . . . . . . . . . . . . . 783.2 Chalcogenide glass fibre drawing techniques . . . . . . . . . . . . . . . 79

3.2.1 Preform method . . . . . . . . . . . . . . . . . . . . . . . . . . 793.2.2 Double crucible method . . . . . . . . . . . . . . . . . . . . . . 823.2.3 Germanium gallium sulphide preforms . . . . . . . . . . . . . . 823.2.4 Etching of germanium gallium sulphide glasses . . . . . . . . . 84

3.3 Fibre drawing of germanium gallium sulphide glasses . . . . . . . . . . 883.3.1 Fibre drawing model . . . . . . . . . . . . . . . . . . . . . . . . 893.3.2 Fibre drawing operating conditions . . . . . . . . . . . . . . . . 1133.3.3 Experimental fibre drawing . . . . . . . . . . . . . . . . . . . . 115


4 Modelling light amplification in praseodymium doped single-

mode fibres 125

4.1 Praseodymium doped fibre amplifier model . . . . . . . . . . . . . . . 1264.1.1 Operation principle of the PDFA . . . . . . . . . . . . . . . . . 1284.1.2 Propagation equations . . . . . . . . . . . . . . . . . . . . . . . 1304.1.3 Light guiding in single-mode fibres . . . . . . . . . . . . . . . . 1324.1.4 Amplifier noise analysis . . . . . . . . . . . . . . . . . . . . . . 1334.1.5 Numerical solution of the model equations . . . . . . . . . . . . 137

4.2 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1384.2.1 Experimental determination of gain and noise . . . . . . . . . . 1384.2.2 Experimental set-up used for amplifier model validation . . . . 1414.2.3 Co-propagating pumping scheme . . . . . . . . . . . . . . . . . 1434.2.4 Counter-propagating pumping scheme . . . . . . . . . . . . . . 1464.2.5 Bi-directional pumping scheme . . . . . . . . . . . . . . . . . . 149

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1494.3.1 Amplifier model input data . . . . . . . . . . . . . . . . . . . . 1524.3.2 Amplifier model results . . . . . . . . . . . . . . . . . . . . . . 1534.3.3 Validity of the amplifier model . . . . . . . . . . . . . . . . . . 157


5 Performance and design of the PDFA for telecommunication

systems 163

5.1 PDFAs in communication systems . . . . . . . . . . . . . . . . . . . . 1645.1.1 Booster amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . 1665.1.2 In-line amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 1725.1.3 Pre-amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

5.2 Optical properties of the germanium gallium sulphide glass fibre . . . 1835.2.1 Attenuation at signal and pump wavelengths . . . . . . . . . . 183

Contents ix

5.2.2 Spontaneous emission . . . . . . . . . . . . . . . . . . . . . . . 1855.3 Design of an efficient PDFA . . . . . . . . . . . . . . . . . . . . . . . . 186

5.3.1 Design of the praseodymium doped fibre . . . . . . . . . . . . . 1895.3.2 Large signal amplifier . . . . . . . . . . . . . . . . . . . . . . . 1915.3.3 In-line amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 1975.3.4 Pre-amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1985.3.5 Performance of PDFA, based on different host glass types . . . 202


6 Conclusions and recommendations 213

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2146.1.1 Main results of this study . . . . . . . . . . . . . . . . . . . . . 2146.1.2 Prospects for a PDFA based on germanium gallium sulphide

glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2186.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

A Summary of differential operations in cylindrical coordinates 221

A.1 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

B Specifications of optical components 223

B.1 Praseodymium doped fluoride fibre modules . . . . . . . . . . . . . . . 223B.2 Dual output ytterbium fibre laser . . . . . . . . . . . . . . . . . . . . . 224

C Light guiding in single-mode fibres 225

C.1 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

D Noise in optical amplifiers 227

D.1 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

Scientific publications related to this thesis 235

List of abbreviations 237

Samenvatting 239

Dankwoord 247

Curriculum Vitae 249

x Towards more efficient praseodymium doped fibre amplifiers for the O-band

Chapter 1

Introduction

1.1 Optical amplifiers in optical telecommunication

systems

While the first optical systems deployed only a single wavelength channel for transmis-sion of the data signals, nowadays multiple wavelengths are simultaneously transmit-ted over a single fibre. The principle of wavelength division multiplexing (WDM), atechnique to combine the output of several transmitters (each operating at a differentwavelength channel) is shown in Figure 1.1. The signals are transferred throughoutthe network from transmitter to receiver, while routing of the signals (i.e. directinga specific signal towards one receiver out of a multitude receivers) is performed byelectronics incorporated in the optical part of the network [1].As a signal light pulse propagates through the transmission fibre, the duration of thepulse can change (broadening or narrowing) due to dispersion1. Furthermore, the sig-nal is attenuated by scattering and absorption. After a certain distance, the numberof photons within the signal becomes too small for detection and therefore amplifi-cation of the signal is necessary. Ideally, the amplifier must be capable of amplifyinghigh-speed WDM signals, providing uniform gain within a broad wavelength region,without distortion. An all-optical (so-called travelling-wave) amplifier can amplify allWDM channels within its bandwidth simultaneously.Historically, optical telecommunication systems operate at spectral regions (windows)where the attenuation spectrum of the used optical fibre exhibits low intrinsic losses(see Figure 1.2). The telecommunication regions around 1.31 µm and 1.55 µm areseparated by the presence of an absorption band around 1.4 µm caused by hydroxyl(OH−) impurities within the silica fibre (especially in earlier fibre types). In the1.55 µm wavelength region the absorption losses and Raleigh scattering losses areminimum (approx. 0.22 dB/km). In standard single mode fibres (s-SMF), the dis-persion is crossing the zero dispersion point around 1.31 µm. Near the dispersion

1Dispersion is caused by small differences in speed of the spectral components within a signal ofa finite duration ∆t and finite spectral width ∆λ [2].

1

2 Towards more efficient praseodymium doped fibre amplifiers for the O-band

λλ

λ

1

2

n

1 2 nλ + λ + ... + λ

λ 1 λ 2 λ n

Wavelength

Pow

er

...

...

WDM

Input fibre 1 ... n Output fibre

a) b)

Figure 1.1: Wavelength division multiplexing (WDM) is a technique for increasingthe transmission capacity C in the fibre to n × B bits/s where n is the numberof deployed wavelength channels and B the transmission rate in # bits/s. a) theprinciple of wavelength division multiplexing (schematically) and b) optical spectrumof the WDM-signal in the output fibre.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-25

-20

-15

-10

-5

0

5

10

15

20

25

Wavelength [µm]

Att

enuat

ion

[dB

/km

]

Dis

per

sion

[ps/

(nm·k

m)]

Figure 1.2: Example of the attenuation due to absorption losses and dispersion (ex-pressed as the broadening per unit spectral width per unit length of the fibre) in(silica based) standard single mode fibre (s-SMF).

Introduction 3

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65

Wavelength [µm]

SOA

DRA

O-band E-band S+-band S-band C-band L-band L+-band

2nd window 3rd window

Silica based EDFA

Telluride based EDFA

Fluoride based EDFA

Terbium co-doped TDFATDFA

Fluoride based PDFA

Chalcogenide based PDFA

NDFA

DDFA

Figure 1.3: An overview of the naming and allocation of wavelength bands in the2nd and 3rd telecommunication windows. The (fibre) amplifiers commonly applied atthese wavelengths are also indicated.

zero-point, a higher transmission capacity can be obtained [2]. The absorption lossesin the 1.31 µm wavelength region are approximately 0.3 dB/km.In the early 1980s, the application of distributed Raman amplifiers (DRA) and semi-conductor optical amplifiers (SOA) to overcome attenuation losses were investigated.In the mid 1980s rare earth doped fibre amplifiers were developed. Whereas DRA andSOA can be designed to operate at the desired wavelengths, rare earth doped fibreamplifiers are limited to the spectral regions coupled to the electron transitions whichoccur within the rare earth ions. Due to their potentially high efficiency, rare earthdoped amplifiers find a major field of application as a travelling-wave amplifier foroptical communication systems. Especially, the erbium doped fibre amplifier (EDFA)caused a breakthrough in the implementation of rare earth doped fibre amplifiers.The position of the 2nd and 3rd telecommunication windows and their partition in(wavelength) bands is depicted in Figure 1.3. The 1st window is located around 0.8 µm(not shown). The O-band (1290–1340 nm) is positioned in the 2nd window. The 3rd

window is divided in 5 equal width wavelength bands: S+-band (1450–1490 nm), S-band (1490–1530 nm), C-band (1530–1570 nm), L-band (1570–1610 nm) and L+-band(1610–1650 nm). The wavelength region between the 2nd and 3rd telecommunicationwindows is covered by the E-band. Currently, no rare earth doped fibre amplifiers areavailable for this wavelength region. Due to the increasing demand for data trans-mission capacity, it is expected that the entire wavelength region between 1290 and1650 nm will be used in near future.The operating wavelengths corresponding to the most important rare earth dopedamplifiers are also shown in Figure 1.3. The gain band of the EDFA (initially de-veloped in 1987) is located in the C-band [3]. Further developments of the EDFAresulted in the L-band amplifier (1580-1620 nm) [4]. Recently, the thulium dopedfibre amplifier (TDFA, 1450-1510 nm) operating in the S and S+-bands has become


0

1 12 2

3 3

3Ground state

Meta-stable state

Pump excited state

Three-level system Four-level system

Ener

gy[c

m−

1]

Figure 1.4: Energy level diagram indicating the principle of operation of rare earthdoped amplifiers: 1) Pump ground state absorption, 2) Signal emission, 3) Non-radiative decay.

available [5]. Praseodymium doped fibre amplifiers (PDFA), based on fluoride glassesare commercially available since 1995 [6], while alternative host glasses for the PDFAare currently being investigated. Also, neodymium doped fibre amplifiers (NDFA)and dysprosium doped fibre amplifiers (DDFA) are being developed for applicationin the O-band. In this study, the use of germanium gallium sulphide host glasses forthe PDFA is investigated in order to develop an efficient PDFA.

1.2 Optical amplifiers

1.2.1 Rare-earth doped fibre amplifiers

Rare earth ions that can be excited to a high energy state, which decays by emissionof radiation around the telecommunication wavelengths, can be used in optical ampli-fiers. These amplifiers are “optically pumped” by means of a laser to excite the rareearth dopant ions into the so-called pump excited state (see Figure 1.4). The lifetime(defined as the average time spent by ions in a specific excited state) of the pumpexcited state is short and the ions quickly decay to a lower energy manifold. Dueto its relatively long lifetime, this energy level is called the meta-stable state. Am-plification of the signal is obtained by, so-called, stimulated emission starting fromthe meta-stable state. In this process, illumination of the rare earth ion by incom-ing photons (e.g. signal), with an energy which equals the energy difference betweenthe meta-stable state and a lower energy level, results in de-excitation (decay) ofthe meta-stable state. The energy is released by emission of photons with exactlythe same wavelength as the incident photons [7, 8]. These emitted photons are inphase and radiated in a confined direction (coherent radiation [7, 8])2. Dependingon the type of rare earth ion and the radiative transition involved, the final level of

2A detailed description of the quantum mechanics related to the occurrence of spontaneous emis-sion can be found in e.g. Yariv [7] or Mandel et al. [8].

Introduction 5

Signal Amplified Signal

WSCPump

Rare EarthDoped Fibre

Figure 1.5: Schematic diagram of the rare earth doped fibre amplifier. Signal andpump light are combined by the WSC and fed into the rare earth doped fibre. (Notethat the secondary output of the WSC is not used.)

the stimulated emission transition is either an intermediate level or the ground state.By definition, the amplifier operation is designated as a four-level system, if the finallevel of the stimulated emission transition is an intermediate level, while the groundstate is the terminal state of a three-level system [9].A schematic representation of the rare earth doped fibre amplifier is shown in Figure1.5. The rare earth doped fibre is preceded by a wavelength selective coupler (WSC)which is used to combine the output of the pump laser with the input signal. Thesecondary output of the WSC can be used for monitoring the signal and pump power.The simplified energy level diagrams (i.e. only a limited number of energy levels andtransitions between them is shown) of praseodymium (Pr), neodymium (Nd), dys-prosium (Dy), erbium (Er), and thulium (Tm) are shown in Figure 1.6. The ionicenergy levels are labelled according to the Russell-Saunders notation for the angularmomentum properties of the ion (see section 2.3.1). In the host glass, the rare earthion is subjected to electric fields due to the surrounding atoms in the host lattice [10].The local electric fields around the rare earth ion, known as crystal fields, cause split-ting of the energy levels into multiplets (so-called Stark splitting). When the rareearth ions are incorporated in an amorphous material (e.g. glass host), the splittingis different for each site, i.e. at each position of the rare earth ions in the material.Stark splitting and site-to-site variations of the field result in the formation of energybands around the discrete energy levels (not shown).The main transitions (i.e. signal emission, ground state absorption (GSA), excitedstate absorption (ESA), amplified spontaneous emission (ASE) and non-radiative de-cay) between the energy levels are indicated in Figure 1.6. When an electron dropsto a lower energy level, the energy is either released by phonons (non-radiative decay,e.g. lattice vibrations) or in the form of photons (radiative decay). The efficiency ofthe amplifier is reduced by spontaneous transitions from the meta-stable state to alower energy level, as these transitions do not contribute to the amplification of thesignals by stimulated emission. The lifetime of the meta-stable state should be suffi-ciently long in order to limit the number of spontaneous transitions to lower energylevels.In the 3rd telecommunication window (around 1.55 µm), an efficient amplifier can beconstructed by doping silica fibre with erbium (Er) ions. The trivalent praseodymium(Pr), neodymium (Nd) and dysprosium (Dy) ions have radiative transitions withinthe 2nd telecommunication window (around 1.31 µm). Unfortunately, the radiative


(luminescence) properties of these ions cannot be fully utilised in a silica matrix (sil-ica) fibre. Due to non-radiative energy transfer from the meta-stable state to thenext lower energy level by lattice vibrations (phonons) of the glass host, the quantumefficiency of the radiative transitions is reduced. For praseodymium, the relaxationenergy3 (i.e. the energy difference between the levels 1G4 and next lower 3F4 level)is approx. 3000 cm−1 (see Figure 1.6a). The highest phonon energy in a silica glasshost is approx. 1100 cm−1. Hence, in a silicate glass only three of these phonons needto be emitted simultaneously, in order to bridge the energy gap [11]. Depopulationof the excited state by non-radiative energy transfer results in an efficiency loss. Toimprove the efficiency of these amplifiers, glass hosts with lower maximum phononenergy are required. As the number of phonons required to bridge this energy gapbecomes higher, the probability of simultaneous emission of phonons decreases, hencethe relaxation rate by non-radiative decay is lower.Fluoride and chalcogenide glasses are suitable low phonon energy host materials forefficient amplification due to their (maximum) phonon energy of 500 and 330 cm−1,respectively. Silicate glasses belong to the class of oxide glasses. The chalcogenideelements sulphur (S), selenium (Se) and tellurium (Te) can adopt the role of oxygenas the main anion in the glass structure. Stable chalcogenide glasses are obtainedby vitrification starting from a glass melt. Fluoride glasses are based on the glassforming ability of heavy metal fluorides [12].Currently, commercially available PDFAs are based on fluoride host glasses. It isexpected that PDFAs, based on chalcogenide glasses, will have a better efficiency dueto the low phonon energy of these host glasses. In this thesis, the main focus will beon the development of a praseodymium doped fibre amplifier based on germaniumgallium sulphide host glasses. The preparation and properties of the germanium gal-lium sulphide glasses used in this study, will be described in chapter 2. Due to thelow phonon energy of this host glass and the resulting long lifetime of the meta-stablestate, the development of an efficient praseodymium doped fibre amplifier seems fea-sible.

Praseodymium Doped Fibre Amplifier

The amplification of telecommunication signals by the Praseodymium Doped FibreAmplifier (PDFA) around 1.3 µm is based on the process of stimulated emission be-tween the 1G4 and 3H5 energy levels of the Pr3+ ions. The transitions between theenergy levels involved in the amplification process are shown in the simplified energydiagram, Figure 1.6a. The lower energy level of the stimulated emission transition inpraseodymium is the intermediate level 3H5. By definition, praseodymium effectivelyrepresents a four-level system [16], although merely three levels are involved (3H4,3H5 and 1G4).The electrons in the Pr3+ ions are pumped around 1.03 µm from the ground state(3H4) into the pump excited state (1G4). The 1G4 state is also the meta-stable state.

3Photon energy and atomic energy levels relative to a zero energy reference are expressed in termsof electron volts (eV) or wavenumbers (cm−1) [2]. 1

λ= E

hccan be used to convert the units of energy

E from electron volt (eV) into wavenumber (cm−1).

Introduction 7

To a large extent the efficiency of Pr-doped fibre amplifiers is related to the longemission lifetime of the meta-stable state (approx. 110 µs in fluoride and 350 µs inchalcogenide glasses [17]). This permits the large population inversion (almost allions are in a meta-stable excited state, instead of the ground state) needed to achievehigh gain, in the case pumping is sufficiently strong.The radiative transition from the 1G4 to the 3H5 level, around 1.31 µm, can beinduced by other photons with equal energy, e.g. telecommunication signals. Theemitted photons will have exactly the same frequency and phase as the incident sig-nal photons. Furthermore, the photons are radiated in a confined direction [7, 8].Thus, the process of stimulated emission provides amplification of the telecommuni-cation signal. After emission, the Pr3+ ion returns from the 3H5 state to the 3H4

ground state by fast non-radiative decay.Processes which reduce the population of the 1G4 level (other than stimulated emis-sion) reduce the efficiency of the amplifier. The 1G4 - 3H5 transition will also takeplace spontaneously and randomly (not induced by signal photons). The uncorrelated,spontaneous emitted photons are further amplified along the amplifier, resulting inamplified spontaneous emission (ASE) noise. Pump and signal Excited State Absorp-tion (ESA, absorption of a photon by an ion which is already in the excited state) canalso cause depopulation of the 1G4 meta-stable state. Furthermore, the 1G4 level isdepopulated by non-radiative energy transfer to lower energy levels. The energy gapbetween 1G4 level and the next-lower 3F4 is approximately 3000 cm−1. The efficiencyloss due to multi-phonon relaxation can be reduced by the use of a low phonon energyglass host (see chapter 2 for the measured phonon energy of the germanium galliumsulphide host glass).Due to the length of the fibre amplifier, photon densities and densities of occupied

states will vary in the longitudinal direction of the fibre. A spatially and spectrallyresolved amplifier model, to evaluate and optimise the performance of praseodymiumdoped fibre amplifiers, will be presented in chapter 4.In the next paragraphs, the properties of alternative fibre amplifiers for the 2nd

telecommunication window, based on neodymium and dysprosium are discussed,followed by a description of erbium and thulium doped fibre amplifiers for the 3rd

telecommunication window. Some properties of these rare-earth doped amplifiers aresummarised in Table 1.1.

Neodymium Doped Fibre Amplifier

Like praseodymium, the Neodymium Doped Fibre Amplifier (NDFA) is based on four-level operation. The neodymium ions are excited into the 4F5/2 state by pumping at0.81 µm (see Figure 1.6b). Radiation around 1.32 µm is obtained from the 4F3/2 -4I13/2 transition.The major disadvantages of the neodymium system are the signal excited state ab-sorption (ESA, from the 4F3/2 to the 4G7/2 level, not shown) and additional amplifiedspontaneous emission (ASE) at 1.05 µm. The first process limits the operating wave-length to wavelengths longer than 1.31 µm [18], while the latter reduces the amplifierefficiency due to the 1.05 µm 4F3/2 - 4I11/2 radiative transition [19]. In terms of


a)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000Pr

Pum

pG

SA

Sig

nal

Em

issi

on

Sig

nal

GSA

Sig

nal

ESA

Ener

gy[c

m−

1]

3H4

3H5

3H6

3F2

3F3

3F4

1G4

1D2

b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000Nd

Pum

pG

SA

Sig

nal

Em

issi

on

1.05

µm

ASE

Ener

gy[c

m−

1]

4F9/24F7/24F5/24F3/2

4I15/2

4I13/2

4I11/2

4I9/2

c)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000Dy

Pum

pG

SA

(0.8

1µm

)

Pum

pG

SA

(0.9

1µm

)

Pum

pG

SA

(1.2

5µm

)

Sig

nal

Em

issi

on

Ener

gy[c

m−

1] 6F5/2

6H5/2

6F7/2

6H7/2,6F9/2

6H9/2,6F11/2

6H11/2

6H13/2

6H15/2

Introduction 9

d)

0

5000

10000

15000

20000

Er

Pum

pG

SA

(0.8

2µm

)

Pum

pG

SA

(0.9

8µm

)

1.48

µm

(Pum

p)

GSA

Sig

nal

Em

issi

on(1

.55

µm

)

Ener

gy[c

m−

1]

4F7/2

4F9/2

4S3/2

4I9/24I11/2

4I13/2

4I15/2

e)

0

5000

10000

15000

20000

Tm

Pum

pG

SA

(1.0

5µm

)

Pum

pE

SA

(1.0

5µm

)

Sig

nal

Em

issi

on(1

.47

µm

)

Ener

gy[c

m−

1]

1G4

3F23F3

3F4

3H4

3H5

3H6

Legend:

0

Abso

rpti

on

Em

issi

on

Non

-rad

iati

ve

Dec

ay

Ener

gyLev

el

Ground state

Excited state

Figure 1.6: The simplified energy level diagrams of a) Praseodymium (Pr, [13]),b) Neodymium (Nd, [14]), c) Dysprosium (Dy, [15]), d) Erbium (Er, [9, 10]) ande) Thulium (Tm, [5]).


Table 1.1: Some characteristics of rare earth doped fibre amplifiers.

PDFA NDFA DDFA EDFA TDFA

Telecom. window second second second third third3/4 level operation four four three three fourSignal GSA negligible negligible possible possible negligibleLow phonon host necessary necessary necessary unnecessary necessarymaterial requiredlifetime of the 300 [17] 450 [17] 60 [17] 10800 [17] 1000 [5]meta-stable level[µs]Stimulated emis- 10.5 8 38 5.7 n.a.sion cross section× 10−21 [cm2] [17]

the signal ESA cross section, fluoride glasses are preferable over silica glasses [20].Chalcogenide glasses are also suitable host materials for the NDFA [18].

Dysprosium Doped Fibre Amplifier

The Dysprosium Doped Fibre Amplifier (DDFA) is a three-level system. The am-plifier is pumped at 0.81, 0.91 or 1.24 µm into the 6F5/2,

6F7/2 and 6H9/2 - 6F11/2

levels, respectively. Compared to praseodymium, dysprosium has large absorptionand emission cross sections4. This allows for a shorter fibre length at the same dopantconcentration. The transition between the 6H9/2 - 6F11/2 levels (which overlap eachother) and the ground state is situated around 1.3 µm (see Figure 1.6c). The smallenergy difference between the 6H9/2 - 6F11/2 levels and the lower 6H11/2 level reducesthe amplifier efficiency due to non-radiative energy transfer [21]. Low phonon energyhost materials like chalcogenide glasses are required to reduce the non-radiative en-ergy transfer [22]. The efficiency is further hampered by the short lifetime (approx.35 µs) of the meta-stable level [22]. This lifetime can be increased by the addition ofCsBr to the host glass [23].

Erbium Doped Fibre Amplifier

In the 3rd telecommunication window (1.55 µm), an efficient amplifier can be con-structed by doping silica fibre with erbium ions [4]. Fluoride glasses are used toimprove the width and flatness of the amplifier gain profile [24]. In telluride glassesthe gain band is shifted towards longer wavelengths.

4The (closely) related absorption and emission cross sections are defined as the emission or absorp-tion of radiation per dopant ion. The absorption cross section is given by the absorption coefficientα and the dopant concentration Ndopant: σabs = α

Ndopant.

Introduction 11

The amplification within the Er-doped fibre is based on transitions between threeenergy levels (three-level system). Radiation at 1.55 µm is obtained from the 4I13/2 -4I15/2 transition. A high efficiency of the amplifier is obtained due to the long lifetimeof the 4I13/2 state (order of ms). Erbium is pumped at either 0.82 µm, 0.98 µm or1.48 µm (see Figure 1.6d). In the case of pumping at 1.48 µm, the erbium ions are di-rectly pumped into the upper sublevels of the meta-stable state (4I13/2 ). Commercialerbium doped fibre amplifiers are mostly pumped at 0.98 µm or 1.48 µm.

Thulium Doped Fibre Amplifier

Figure 1.6e shows the energy level diagram of thulium. Amplification around 1.47 µmis obtained from the 3H4 - 3F4 transition (four-level operation). The long lifetime ofthe lower level 3F4 compared to the short lifetime of the upper level 3H4 has a detri-mental effect on the population inversion [25]. Fluoride and chalcogenide glass hostsare preferred for the TDFA [25, 26]. Upconversion pumping schemes (i.e. pumpingusing an intermediate energy level) are employed in order to reduce the populationof the 3F4 level while increasing the population in the meta-stable 3H4 level. TDFAswith upconversion pumping behave like three-level amplifiers, where the 3F4 level actsas virtual ground state.

1.2.2 Other types of optical amplifiers

Semiconductor optical amplifier

Like the rare earth doped fibre amplifier, signal light is amplified by the semiconductoroptical amplifier (SOA) through stimulated emission. The basic structure of a SOAchip consists of an active layer sandwiched between two cladding layers on top of asubstrate and covered by a contact layer [2]. The optical power is confined into theactive layer by the cladding layers. Within the semiconducting active layer, the signallight is amplified by stimulated emission. The energy needed for the amplificationprocess is provided by an injection current (DC), which is transferred to the activelayer of the SOA by the substrate and contact layers. An anti-reflection coating isapplied at both ends of the active region, in order to prevent undesirable reflectionscausing laser oscillations [27].In a semiconductor material, the energy levels of the charge carriers (electrons andholes) are located in the valence band and the conduction band [1]. These bands areseparated by an energy difference, the so-called band gap. Within the band gap, noenergy levels exist. The operating wavelength of the amplifier is determined by theenergy gap between the conduction and valence bands.The active region of the SOA is located at the junction of a p-type (having an excessconcentration of holes) and a n-type (excess concentration of electrons) semiconductormaterial. At the pn-junction, a region with net negative charge is formed in the p-type semiconductor and a region with net positive charge is obtained in the n-typesemiconductor due to diffusion of electrons and holes. When a sufficiently high voltage(bias) is applied to the pn-junction, the increased minority carrier concentrations (i.e.electrons in the p-type region and holes in the n-type region) result in a population


inversion [1]. Stimulated emission, originating from recombination between electronsand holes at the pn-junction, results in amplification of the light propagating throughthe active region [1]. The emitted photons will have exactly the same frequency andphase as the incident signal photons and these photons are radiated in a confineddirection [7, 8].Proper design of the structure of the active layer is required in order to achieveamplification characteristics that are independent of the state of polarisation of theincident beam.

Raman fibre amplifier

The principle of Raman amplification is the stimulated emission process associatedwith Raman scattering in a fibre. Whereas rare earth doped fibre amplifiers requiredopants in the fibre in order to provide gain, Raman gain is obtained in the transmis-sion fibre itself. The pump and signal light (at a longer wavelength than the pumpwavelength) are combined and fed into a fibre. In the stimulated Raman scatteringprocess, absorption of a pump photon by the host material is followed by emissionof a new (Stokes) photon at the signal frequency, whilst the residual energy (of theabsorbed pump photon) is absorbed as phonons (vibrational energy) by molecules inthe host material. As there is a wide range of vibrational states above the groundstate, gain is obtained in a broad wavelength region [28].The Raman gain strongly depends on the pump power and the frequency offset be-tween pump and signal. The operating wavelength of the amplifier can be adjustedby tuning the pump wavelength. In Raman amplifiers utilising silica fibre, the high-est gain is obtained when the difference between the pump and the signal frequency(Stokes shift) is approximately 13 THz. The gain bandwidth (i.e. the wavelengthrange where the gain of the amplifier is at least half the maximum obtainable gain) ofa Raman amplifier, pumped at a single wavelength, is about 48 nm. Multi-wavelengthpumping could be used to broaden and flatten the Raman gain profile. The gain pro-file of a multi-wavelength pumped Raman amplifier is a superposition of the gainprofiles obtained by pumping at the respective pumping wavelengths. Proper selec-tion of the pump power at the pumping wavelengths is necessary to obtain a flat gainprofile. An advantage of Raman amplification is that the same fibre used for signaltransmission can also be used for signal amplification (distributed amplification asopposed to the lumped amplification provided by other types of amplifiers). In thecase of distributed Raman amplification (DRA), the signal losses are compensatedthroughout the fibre. This results in a better signal to noise ratio (SNR) comparedto lumped amplification. [10].

1.3 General application of optical amplifiers

In telecommunication systems, which are limited by attenuation, the optical ampli-fier application ranges from power booster at the transmitter via in-line amplifier inlong-haul transmission links, to pre-amplifier at the receiver end. Amplification of thesignal is required to overcome intrinsic fibre absorption and scattering losses, losses

Introduction 13

Table 1.2: Some requirements for optical amplifiers in different applications.

Function booster in-line pre-amp

High gain necessary essential essentialHigh saturation output power essential essential unnecessaryLow noise characteristics unnecessary necessary essentialPolarisation independence unnecessary necessary essentialLow insertion loss unnecessary necessary essential

of additional optical components and coupling losses due to network branching. Inaddition to the gain provided by the optical amplifier, some spontaneous emissiongenerated by the optical amplifier is also added to the signal. The noise originatingfrom the amplified spontaneous emission will decrease the signal to noise ratio (SNR).At the opto-electronic receiver, the degradation of the SNR results in an increasedprobability of erroneous interpretation of the received data.The main requirements for the use of amplifiers in booster, in-line and pre-amplifierapplications are listed in Table 1.2 [27].At the transmitter, a booster amplifier is used to improve the signal power of the(amplitude, phase or frequency) modulated data signals. The amplifier is operatingin the so-called saturation regime (i.e. the input power of the amplifier is relativelyhigh and a high signal output power is required). The amplifier must provide highsaturated output power which is desirable for some applications (e.g. for distributionof common antenna television (CATV) signals to a group of subscribers). The sat-uration output power is defined as the level at which the amplifier gain is decreasedby a factor of two with respect to the small signal gain (i.e. gain at low signal inputpower). At high signal input powers, the gain of the amplifier decreases. This re-duction of gain is caused by depletion of the excited state due to stimulated emissionand a limited replenishing rate. Due to the relatively large signal input and outputpower, the noise characteristics of the booster amplifier are less important.The in-line amplifiers provide amplification of the signals along the transmission link.In a long-haul communication system, a large number of amplifiers is cascaded. Insuch a system, the performance is affected by accumulation of amplified spontaneousemission (ASE) noise. As the level of ASE grows, the amplifiers along the trans-mission line tend to saturate and the signal gain is reduced. The net result of thereduced signal level and increased ASE level is a considerable degradation of the sig-nal to noise ratio (SNR) [29]. As the state of polarisation of the signal may changeupon transmission through a fibre, this application requires polarisation independentamplifiers with a high saturation output power.At the receiver, an optical pre-amplifier can be used to improve the signal prior to de-tection and electrical amplification. The pre-amplifier operates in the so-called smallsignal gain regime. Due to the low input power, low loss between the fibre and theamplifier (insertion loss) is required. Furthermore, a relatively high gain and low noise


contribution by the pre-amplifier are important.A general overview of the characteristics of PDFA, SOA and DRA amplifiers oper-ating around 1.3 µm are presented in Table 1.3. In this table, typical figures for thesmall signal gain5 and noise figure (pre-amplifier) as well as the saturated outputpower6 (booster) of the different types of amplifiers are summarised.The application of the praseodymium doped fibre amplifier as a booster, in-line andpre-amplifier will be discussed in chapter 5. In fibre amplifiers, the length of the fibreand the propagation direction of the pump light are important parameters to influ-ence gain and noise properties (see chapter 4). The SOA and DRA can be designedto operate at the desired wavelength by tuning the bandgap and pump wavelength,respectively. However, not all amplifier characteristics can be influenced by the de-sign of the amplifier. The possible pump and operating wavelengths of the PDFA(and other rare earth doped amplifiers) are mainly determined by the applied hostmaterial.Due to the cylindrical geometry of the fibre, both PDFA and DRA are polarisationinsensitive. In a SOA, low polarisation dependence of the amplifier characteristics isachieved by proper design of the structure of the active layer.The energy for stimulated emission in a PDFA is provided by a powerful (up to 1 W)pump laser. The (distributed) Raman amplifier requires even higher optical pumppowers. The SOA is driven by an (electric) injection current.The performance of all mentioned amplifier types is hampered by amplified sponta-neous emission (ASE) noise. The best noise performance is obtained for PDFA andDRA (noise figure of 3–4 dB), whereas the noise figure of SOA is approx. 3 dB higher.

1.4 Scope and objective of this thesis

The development of optical telecommunication systems for signal wavelengths around1.55 µm was greatly enhanced by the development of the erbium doped fibre ampli-fier. In order to fully exploit the transparent windows of the installed fibre, andparticularly the 1.31 µm wavelength region in the near future, a powerful amplifiertechnique for these wavelengths is needed. Although the praseodymium doped fibreamplifier is commercially available, the efficiency of these (fluoride based) amplifiersis low. Therefore, high pump powers are needed to achieve reasonable gain. Theobjective and motivation of this thesis is the development of a praseodymium dopedfibre amplifier with improved efficiency. As an efficient PDFA can be constructedonly using low phonon energy glass hosts (e.g. chalcogenide glasses), this study willfocus on the development of chalcogenide glasses and determination of the physical

5Gain and attenuation are often expressed on the logarithmic scale of decibels (dB). G[dB] =10 log(G[−]) is used to convert the value from a linear scale to decibel. Optical power relative to a

power of 1 mW is often expressed in terms of dBm. The formula P [dBm] = 10 log(P [mW ]1mW

) can beused to convert the power P from mW into dBm.

6This power equals the maximum output power, while the 3 dB saturation output power is definedas the output power level at which the amplifier gain is decreased by a factor of 2 with respect tothe gain of the unsaturated amplifier e.g. at low signal input power.

Introduction 15

Table 1.3: Some properties of the praseodymium doped fibre amplifier (PDFA), semi-conductor optical amplifier (SOA), and distributed Raman amplifier DRA at an op-erating wavelength around 1.3 µm (after [30]).

PDFA SOA DRA

Peak gain wavelength 1300-1350 nm 1280-1330 nm 1310 nmOptical bandwidth 20–40 nm 60 nm 20–45 nm3 dB saturation power 10–18 dBm 13–18 dBm 1

2Ppump

Saturated output power 13–20 dBm 16–20 dBm 34Ppump

Small signal gain > 40 dB > 33 dB > 40 dBNoise figure 3.5–4 dB 6.5–9 dBm 3–4 dBPump wavelength 1015–1035 nm – 1240 nmPump power 20–30 dBm – > 30 dBmPolarisation sensitivity none < 0.5 dB noneRadiative lifetime 110-400 µs 200 ps –

properties of these (praseodymium doped) chalcogenide host glasses (see chapter 2).In general, the preparation and processing of these glasses is complex. As a part ofthis work, the technology needed for melting germanium gallium sulfide glasses andfibre drawing (from a fibre preform) is investigated (see chapter 3).Furthermore, the objective of this study is to establish knowledge and understandingof the performance of praseodymium doped fibre amplifiers in telecommunication sys-tems. This system performance is evaluated in using a transmitter, an experimentalpraseodymium doped fibre amplifier, based on commercially available praseodymiumdoped fluoride fibre modules and a receiver. Due to the modular setup of the ex-perimental PDFA, the amplifier characteristics in different configurations (e.g. co-propagating, counter-propagating and bi-directional pumping schemes) can be as-sessed. Different applications (e.g. booster, in-line or pre-amplifier) put differentdemands on the design (e.g. fibre length, core radius, etc.) and configuration of thepraseodymium doped fibre amplifier. The requirements for rare earth doped fibres,used in fibre amplifiers (e.g. dispersion, absorption and scattering losses of the fibre),are not equal to those used for long-haul transmission. A mathematical amplifiermodel is used to study the amplifier characteristics of the praseodymium doped fibreusing the optical properties of both fluoride and chalcogenide glasses. The model isvalidated for praseodymium doped fluoride fibre. Furthermore, the model is used tooptimise the design of the praseodymium doped fibre amplifier based on the germa-nium gallium sulphide host glass.

1.4.1 Outline of this thesis

In the next chapter, the preparation of germanium gallium sulphide host glasses andtheir, for this study relevant, thermal, rheological and optical properties are described.


This information is used to select suitable core and cladding glass compositions. Inchapter 3 an overview of fibre drawing processes for chalcogenide glasses is given,followed by a description and results of the applied fibre fabrication processes forgermanium gallium sulfide glasses. The working area for fibre drawing of germaniumgallium sulphide glasses using fibre preforms is established using a mathematical fibredrawing model. In chapter 4, a detailed description of a spatially and spectrally re-solved praseodymium doped fibre amplifier model is presented. The model outcome isvalidated using the results of measurements on the experimental praseodymium dopedfluoride fibre amplifier. In chapter 5 the performance of the PDFA in telecommunica-tion systems is discussed. The experimental PDFA, based on a praseodymium dopedfluoride fibre, was used to determine the properties of the PDFA in booster, in-lineor pre-amplifier applications. Furthermore, the optical properties of a praseodymiumdoped germanium gallium sulfide fibre, prepared for this study, are described. Usingthe amplifier model of chapter 4, the optimum design (e.g. fibre length, core radius,etc.) of an efficient PDFA, based on germanium gallium sulphide host glass, is dis-cussed. At the end of chapter 5, a comparison between the praseodymium dopedamplifier based on chalcogenide and fluoride fibre is given. In the final chapter, thiswork is concluded, and some prospects for telecommunication systems incorporatingPDFAs will be given.

1.5 Bibliography

[1] R. Ramaswami and K. Siravajan, Optical networks. A practical Perspective. SanFrancisco: Morgan Kaufmann publishers, 2nd ed., 2002. ISBN 1-55860-655-6.

[2] C.-L. Chen, Optoelectronics & fiber optics. Chicago, USA: Irwin, 1996. ISBN0-256-14182-7.

[3] R. Mears, L. Reekie, I. Jauncey, and D. Payne, “Low-noise erbium-doped fibreamplifier operating at 1.54 µm,” Electron. Lett., vol. 23, no. 19, pp. 1026–1028,1987.

[4] E. Desurvire, Erbium-doped fiber amplifiers. Principles and applications. NewYork, NY.: John Wiley & Sons, Inc., 1994. ISBN 0-471-58977-2.

[5] F. Roy, D. Bayart, A. le Sauze, and P. Baniel, “Noise and gain band managementof thulium-doped fiber amplifier with dual-wavelength pumping schemes,” IEEEPhotonics Technol. Lett., vol. 13, pp. 788–790, August 2001.

[6] T. Whitley, “A review of recent system demonstrations incorporating 1.3-µmpraseodymium-doped fluoride fiber amplifiers,” J. Lightwave Technol., vol. 13,pp. 744–760, May 1995.

[7] A. Yariv, Optical electronics. London: Saunders College, 4th ed., 1991. ISBN0-03-047444-2.

Introduction 17

[8] L. Mandel and E. Wolf, Optical coherence and quantum optics. Cambridge:Cambridge University Press, 1995. ISBN 0-521-41711-2.

[9] S. Sudo, Optical fiber amplifiers: materials, devices, and applications. Norwood,MA: Artech House, Inc., 1997. ISBN 0-89006-809-7.

[10] A. Bjarklev, Optical Fiber Amplifiers, Design and system applications. Norwood:Artech House, 1993. ISBN 0-89006-659-0.

[11] K. Wei, D. Machewirth, J. Wenzel, E. Snitzer, and G. Sigel Jr., “Pr3+-doped Ge-Ga-S glasses for 1.3 µm optical fiber amplifiers,” J. Non-Cryst. Solids, vol. 182,pp. 257–261, 1995.

[12] D. Aggarwal and G. Lu, Fluoride glass fiber optics. San Diego, CA: AcademicPress, 1991. ISBN 0-12-044505-0.

[13] D. Simons, A. Faber, and H. d. Waal, “GeSx glasses for Pr3+-doped amplifiersat 1.3 µm,” J. Non-Cryst. Solids, vol. 185, pp. 283–288, 1995.

[14] I. Mitchell, V. Bogdanov, and P. Farell, “Energy transfer in praseodymium andneodymium co-doped fluorozirconate glass,” Opt. Communications, vol. 155,pp. 275–280, October 1998.

[15] D. Machewirth, K. Wei, V. Krasteva, R. Datta, E. Snitzer, and G. Sigel Jr.,“Optical characterisation of Pr3+- and Dy3+- doped chalcogenide glasses,” J.Non-Cryst. Solids, vol. 213&214, pp. 295–303, 1997.

[16] S. Fleming, “Crosstalk in 1.3 µm praseodymium fluoride fiber amplifiers,” J.Lightwave Technol., vol. 14, pp. 66–71, January 1996.

[17] D. Simons, Germanium Gallium Sulfide Glasses for Pr-Doped Fiber Amplifiersat 1.3 µm. PhD thesis, Technische Universiteit Eindhoven, 1995. ISBN 90-386-0496-3.

[18] J.-L. Adam, J.-L. Doualan, L. Griscom, S. Girard, and R. Moncorge, “Excited-state absorption at 1.3 µm in Nd3+-doped fluoride and sulfide glasses,” J. Non-Cryst. Solids, vol. 256&257, pp. 276–281, 1999.

[19] A. Jha, M. Naftaly, E. Taylor, B. Samson, D. Marchese, and D. Payne, “1310-1320 nm emission in Nd3+-ion doped fluoroaluminate glasses,” in Conference onInfrared Glass Optical Fibers and Their Applications, vol. 3416, pp. 115–123,SPIE, July 1998.

[20] T. Sugawa, Y. Miyajima, and T. Komukai, “10 dB gain and high saturationpower in a Nd3+-doped fluorozirconate fibre,” Electron. Lett., vol. 26, pp. 2042–2044, November 1990.

[21] D. Hewak, B. Samson, J. Medeiros Neto, R. Lamming, and D. Payne, “Emis-sion at 1.3 µm from dysprosium-doped Ga-La-S glass,” Electron. Lett., vol. 30,pp. 968–970, June 1994.


[22] K. Wei, D. Machewirth, J. Wenzel, E. Snitzer, and G. Sigel Jr., “Spectroscopyof Dy3+ in Ge-Ga-S glass and its suitability for 1.3-µm optical amplifiers appli-cations,” Opt. Lett., vol. 19, pp. 904–907, June 1994.

[23] Y. Shin, J. Heo, and H. Kim, “Modification of the local phonon modes andelectron-phonon coupling strengths in Dy3+-doped sulfide glasses for efficient 1.3µm amplification,” Chem. Phys. Lett., vol. 317, pp. 637–641, February 2000.

[24] H. Ono, M. Yamada, T. Kanamori, S. Sudo, and Y. Ohishi, “1.58 µm bandfluoride-based Er3+-doped fibre amplifier for WDM transmission systems,” Elec-tron. Lett., vol. 33, pp. 1471–1472, August 1997.

[25] S. Aozaso, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, andM. Shimizu, “Tm-doped fiber amplifiers for 1470-nm-band WDM signals,” IEEEPhotonics Technol. Lett., vol. 12, pp. 1331–1333, October 2000.

[26] K. Kandono, T. Yazawa, M. Shojiya, and Y. Kawamoto, “Judd-Ofelt analysisand luminescence property of Tm3+ in Ga2S3-GeS2-La2S3 glasses,” J. Non-Cryst.Solids, vol. 274, pp. 75–80, 2000.

[27] S. Shimada and H. Ishido, Optical amplifiers and their applications. Chichester:John Wiley & Sons, Inc., 1994. ISBN 0-471-94005-4 transl. by F.R.D. Apps.

[28] M. Nissov, Long-haul optical transmission using distributed Raman amplification.PhD thesis, Technical University of Denmark, December 1997.

[29] G. Agrawal, Fiber-optic communication systems. Microwave and Optical Engi-neering, New York: John Wiley, 2nd ed., 1997. ISBN 0-471-17540-4.

[30] J. Jennen, Noise and saturation effects in high-speed transmission systems withsemiconductor optical amplifiers. PhD thesis, Eindhoven University of Technol-ogy, 2000. ISBN 90-386-1760-7.

Chapter 2

Praseodymium doped

germanium gallium sulphide

glasses

In this chapter, the melting process and relevant properties determined for praseody-mium doped germanium gallium sulphide glasses are described. The germanium gal-lium sulphide glasses are studied as alternative host materials for the praseodymiumdoped fibre amplifier (PDFA). The PDFA is used for amplification of telecommu-nication signals around 1.31 µm and is optically “pumped” with laser light around1.03 µm.In the first section, an overview of the glass forming region of the germanium galliumsulphide system and the preparation techniques of the glasses is given. Purificationof the glass or its raw materials is needed to obtain highly transparent host glasses,especially around the amplifiers’ pump and signal wavelengths.In the following section, the optical properties of the germanium gallium sulphidehost glass and the applied measuring techniques are summarised. The germaniumgallium sulphide glasses are transparent in a broad wavelength range. The transmit-tance properties of the glasses in the ultra violet (UV), visible (VIS) and infrared(IR) wavelength range are presented in this section. Absorption phenomena causedby impurities are observed in the IR spectra. The source and amount of the impu-rities incorporated in the host glass and their influence on the optical properties arediscussed.The light guiding properties of a glass fibre depend on both the core diameter and therefractive index difference between the core and the cladding. In an optical fibre, therefractive index of the cladding glass is usually less than one percent lower than therefractive index of the core. Therefore, precise measurement of the refractive index ofthe glasses is necessary to select suitable core and cladding glasses. In section 2.2, thedetermination of the refractive index (as a function of wavelength) of the germaniumgallium sulphide glasses by ellipsometry and the measurement of the Brewster angle

19


is discussed, also.In section 2.3, the optical properties of the praseodymium dopant in germaniumgallium sulphide host glasses are described with respect to their use in the fibre am-plifier. Trivalent praseodymium ions are optically active in the IR wavelength range(e.g. around 1.03 and 1.31 µm), via electronic transitions between its 4f levels. Ab-sorption and photoluminescence spectroscopy are used to measure the absorption andemission (as a function of wavelength) and the emission lifetimes. Then, the radia-tive properties (e.g the radiative lifetime, absorption and emission cross sections) ofthe praseodymium in the germanium gallium sulphide host glass are quantitativelycharacterised, using the Judd-Ofelt theory.Besides absorption or emission of photons, the energy state of the praseodymium ioncan change by non-radiative (e.g. multi-phonon) energy transfer to the host glass.This interaction between the praseodymium dopant and the host glass, which reducesthe efficiency of the praseodymium doped fibre amplifier, is discussed in section 2.4.In section 2.5, the thermal properties of the germanium gallium sulphide glasses arereviewed. These properties of the host glass (e.g. the glass transition and crys-tallisation temperatures, thermal expansion and rheological properties) are of majorimportance for the fibre drawing process.In the last section of this chapter, the main conclusions concerning the optical, me-chanical, structural and thermal properties of the praseodymium doped germaniumgallium sulphide glasses, relevant for the preparation and application of glass fibresof these materials, are given.

2.1 Preparation of the glass host

In this section, an overview of the compositions of germanium gallium sulphide com-positions with glass forming ability is given. Here, the preparation techniques, whichhave been used to melt the germanium gallium sulfide glasses from their raw materials,are described. Also the purification of the starting materials is discussed briefly.

2.1.1 The glass forming region

The glass forming region (i.e. the chemical composition of the materials that canform glasses upon cooling of the melt) of the germanium gallium sulphide system isshown in the ternary diagram 2.1, which summarises the results of several investiga-tors [1–6]. The binary germanium sulphide glasses (Ge-S) were studied thoroughlyby Kawamoto et al. [1, 2], while Loireau-Lozac’h et al. [3] investigated stoichiomet-ric1GeS2 – Ga2S3 compositions. The stoichiometric tie-line composition for the Ge-Ga-S system is defined as the line joining the stoichiometric compounds GeS2 andGa2S3. Any composition with germanium (Ge) content greater than those on the

1Stoichiometry refers to the amounts of substances that satisfy the balanced chemical reactionequation (e.g. Ge+2S → GeS2) for a particular chemical reaction [7]. The composition of theproduct, formed in this chemical reaction (e.g. GeS2), is called stoichiometric.

Praseodymium doped germanium gallium sulphide glasses 21

100

80

60

40

20

0 100

80

60

40

20

0

S

Ga Ge100806040200

GaS1.5

GeS2

glass formingnon-glasforming

Stochimetric tie-lineSimons

This work

Figure 2.1: Ternary diagram for germanium (Ge), gallium (Ga) and sulphur (S)indicating the glass forming compositions. The fractions of Ge, Ga and S are expressedin mol%.

tie-line (i.e. non-stoichiometric composition) is referred to as Ge-rich (or equivalentlysulphur deficient) composition and that with more sulphur (S) content is referred toas S-rich composition (or germanium deficient). The properties of non-stoichiometric,sulphur rich and sulphur deficient compositions were systematically studied by Abeet al. [4] and Saffarini [5].Binary germanium sulphide glasses are formed by air quenching between 66–90 at.% S[6]. Ternary glasses are obtained containing up to 15 at.% Ga and 55-85 at.% S, seeFigure 2.1. However, the range of composition of glasses which can be drawn intofibre is limited. This is mainly caused by crystallisation and decomposition sensitivityof some glass compositions.The solubility of praseodymium in germanium sulphide glasses is enhanced by a smallamount of gallium in the glass host [8]. Simons investigated glasses with general com-position (GeSx)100−y(Ga2S3)y where x=2–4 and y=0–20. The glasses were meltedfrom germanium, gallium metals and sulphur as starting materials. In this work,glasses in the region x=2.25–2.6 and y=2–5 were investigated.


2.1.2 Preparation methods

Purification

Using the elements as a starting material, allows the production of stoichiometric,sulphur rich and sulphur deficient glasses. Another way to prepare, in particular stoi-chiometric, chalcogenide glasses is to start from the (technical grade) metal-sulphides.As impurities affect the transmittance of the glass material at certain wavelengths,high purity starting materials are needed to obtain a highly transparent host glass.Furthermore, impurities (especially hydroxyl) can cause a decrease in the fluorescencelifetime of the excited states of praseodymium, due to an increase of the non-radiativetransition rates [9]. Several chalcogenide raw material purification techniques havebeen developed. Vacuum distillation is proposed to separate both poorly volatileimpurities (e.g. suspended particles, which become a residu) and volatile impurities(like water, carbon oxides, sulphur oxides and hydrocarbons) from the sulphur, due todifference in vapour pressure between sulphur and the impurities [4, 10]. In addition,heating the sulphide for several hours in the presence of magnesium (submerged insulphur melt) can be used to reduce the oxide impurities [11]. Removal of OH andSH impurities using a reactive gas atmosphere (e.g. S2Cl2 vapour) was reported byShibata et al. [12].

Melting

In this study, the starting materials were commercially available germanium (Ge,≥ 99.9999% pure, semiconductor grade ingots) supplied by Highways2, gallium (Ga,≥ 99.999% pure, ingots) by Johnson Matthey3, and sulphur (S, ≥ 99.999% pureflakes) by Cerac4. Praseodymium (as a sulphide) is added as ≥ 99.99% pure Pr2S3,supplied by Cerac. The quoted purity levels are based on the total metallic contentonly (spectrographic analysis, performed by the supplier). In this figure, carbon, oxy-gen, nitrogen and hydrogen and surface deposits are not taken into account .In this study, the sulphur was purified by sublimation in vacuum at 120 C in or-der to remove H2O, H2S, SO2, and SO3 [13] and some less volatile impurities. Inthis process, the sulphur is heated, under vacuum, inside a small vessel. The sulphurevaporates, and subsequently sublimates on a cold surface, mounted within the vessel.The sublimated sulphur was used to prepare the germanium gallium sulphide glasses.All materials were stored and handled in a glovebox (MBraun MB-150) under argonatmosphere (≤ 1 ppm H2O and O2). Inside this glove box, the germanium ingotswere crushed and ground in a mortar. Sufficiently small particles of gallium were pre-pared by melting the gallium at 35 C, and subsequent separation of small amountsof gallium (droplets) from the melt using a small spoon. These small droplets werecooled at room temperature in order to solidify.Fused silica ampoules were used in the melting experiments. The ampoules have antypical length of 200 mm and an inner diameter of 8 and 10 mm. In order to withstand

2Highways International, PO box 153, 3740 AD Baarn, NL3Johnson Matthey Plc. 2–4 Cockspur Street, London SWIY 5BQ, UK4Cerac Inc., PO box 1178, Milwaukee, WI 53201, USA


the internal pressure of several MPa’s [13] (caused by the high vapour pressure of thechalcogenide glass batch upon heating) at elevated temperatures the wall thickness is3.5 and 4.0 mm, respectively.The ampoules were first etched with HNO3 acid, rinsed with distilled water and ace-tone, before being vacuum treated at 1000 C for 8 hours. The purpose of this vacuumtreatment was dehydration of the ampoule.In the experiments, batches of approximately 20 g mixed raw materials were pre-pared. The ampoules, filled with the raw materials mixture, were vacuum-sealed(at p ≤ 10−4 mmHg) using an oxygen-natural gas torch. After being mounted ona support, the ampoules were placed horizontally in an electrical chamber furnace.The temperature was gradually heated to melting temperature and the glasses weremelted overnight at 1000 C. At the beginning of the melting process, the raw mate-rials inside the ampoule tend to segregate due to the different melting temperaturesand the large difference in density of the materials. This segregation was minimisedby placing the ampoules in a horizontal position. The melt was homogenised by nat-ural convection of the melt. If necessary, the support axis could be rotated in orderto mix the materials inside. At the end of the melting time, the ampoules were gentlyput into a vertical position in order to prepare glass rods directly by solidification ofthe glass melt. In this position the material gathers in the ampoule’s bottom end.During this stage, confinement of gas bubbles into the melt phase could occur5. Theampoules were withdrawn from the furnace, quenched in air (typically 90 – 120 s) andannealed. Due to the higher thermal expansion coefficient of the germanium galliumsulphide glasses compared to that of silica, the glass shrinks more than the ampoulewall during quenching and cooling. Therefore, after breaking the ampoule, the (de-tached) rods can easily be removed from the ampoule. To determine the physicalproperties of the germanium gallium sulphide glass, pieces of at least 10 mm lengthare needed, while rods of at least 50 mm long are required for fibre drawing. Piecesof glass containing defects (e.g. bubbles, crystals or cracks) are rejected for furtherprocessing.

2.2 Optical properties of the host glass

In this section, various optical techniques are described, that are used to determinethe properties (transmittance, reflectance and refractive index) of the germanium gal-lium sulphide host glasses. These glasses are highly transparent in the 0.5 – 8.0 µmregion. A typical transmittance spectrum is shown in Figure 2.2.The optical properties of the host glass are dependent of the wavelength λ. In thischapter, the wavelength dependence in the notation of the optical functions is omittedfor the purpose of convenience.

5Gas composition measurements using mass spectrometry indicated that the bubble containsargon and a species with a mass/charge of 76 (probably CS2). The ratio Ar:CS2 is approximately1:3. Other species are below detection limits. The argon must be a remainder of the atmospherein the glove-box. The CS2 is probably a result of the reaction between carbon impurities from theraw materials and sulphur. The measurement confirms that bubble formation is probably caused byenclosure of gas in the melt during the procedure of turning the furnace.


0

0.2

0.4

0.6

0.8

1.0

0 2000 4000 6000 8000 10000 12000

Tra

nsm

ittan

ce [

-]

Wavelength [nm]

Figure 2.2: Total transmittance spectra (i.e. including the losses due to reflection(at normal incidence) at both glass interfaces) of praseodymium doped germaniumgallium sulphide glass (Ge27.7Ga1.1S71.1) from the UV to IR range. The absorptionpeaks are discussed in section 2.2.1 and 2.2.2.

The glasses are characterised by their wavelength dependent complex index of refrac-tion

N = n − jk (2.1)

where the real part of the index of refraction N (i.e. N(λ)) is called the refractiveindex n (i.e. n(λ)) and the imaginary part k (i.e. k(λ)) is the extinction coefficient.The refractive index n is an inverse measure of the phase velocity v in the materialrelated to the speed of light c in vacuum

n =c

v(2.2)

In an absorbing material, the internal transmittance τ is related to the absorptioncoefficient α and optical path length d (e.g. the thickness of the sample), accordingto Lambert-Beer’s law

τ = e−αd (2.3)

The internal transmittance τ is determined from the measured total transmittance ofincident radiation Ttr, after correcting for reflection losses. The extinction coefficientk is related to the absorption coefficient α by

k =λ

4πα (2.4)

The presence of impurities incorporated in the host glass is indicated by absorptionbands in the infrared (IR) transmittance spectra. In section 2.2.1, the concentrations


of impurities present in the glass are estimated from the absorption spectra. Impuri-ties can affect the radiative properties of praseodymium (see section 2.4).In section 2.2.2, the transmittance of the host glass in the ultraviolet (UV) to nearinfrared (NIR) is discussed.The wavelength dependent refractive index in the UV to NIR range is determinedfrom ellipsometry and from measurements of the Brewster angle. The determinationof the refractive index of the host glasses is discussed in section 2.2.3.

2.2.1 IR transmittance spectra

The absorption spectra in the infrared (2.5 – 12.5 µm) range were measured using aPerkin-Elmer model 883 spectrophotometer. The glasses, used in the optical analy-sis, were cut and both sides were polished to optical quality. The cylindrical shapedsamples have an optical path length of 12 mm and a diameter of 10 mm.The total transmittance spectra of the prepared germanium gallium sulphide glassesin the IR range are depicted in Figure 2.3. The IR absorption edge, which is de-fined as the wavelength where the internal transmittance is 0.5 times the averagetransmittance around 2500 nm (4000 cm−1), is approximately 8 µm (1250 cm−1).Theoretically, the infrared transmittance of the germanium gallium sulphide glassesis limited to wavelength values smaller than 13.2 µm due to the Ge-S intrinsic 2-phonon absorption process [14]. In practice, the absorption edge is determined byGe-O and Ga-O absorptions due to the oxygen impurities in the glass.Absorption of radiation in the IR, is related to molecular vibrational modes (e.g.bending and streching) in the material [21]. In IR spectroscopy, the wavelength isoften expressed in terms of wavenumber, which is a measure of energy of the vibra-tions 6. Throughout this chapter, the wavelength dependent optical properties of thematerial are either expressed using wavenumbers (to emphasise the energy involvedin the optical transitions) or using units of wavelength (when the wavelength of anoptical transition is of major importance).The designation of the main absorption bands in the germanium gallium sulphideglasses is listed in Table 2.1 and depicted in Figure 2.3. The impurity level is deter-mined from the absorption peaks. The concentration Cppm of a species (expressedin ppm weight) can be determined from its absorption coefficient α (in cm−1) andthe molar extinction coefficient ǫM (expressed in l mole−1 cm−1), both at the peakwavelength of the absorption. The concentration Cppm [8] is given by

Cppm =α

ǫM ln 10

106M

ρ(2.5)

where M is the molar mass (in g mole−1) and ρ is density of the glass (in kg m−3).In this equation, the factor 106 is used to convert all volume units into cm3, while the

6In IR spectroscopy, the wavelength is often expressed in terms of wavenumber, which is a measureof energy. 1

λ= E

hccan be used to convert the units of energy E from electron volt (eV) into

wavenumber (cm−1) [22].


Table 2.1: Absorption peak wavelengths and molar extinction coefficients, at the ab-sorption peak wavelength, of impurities causing these absorption bands in germaniumgallium sulphide glasses and fibres.

Assignment Wavenumber Wavelength Molar Ext. Coef. ǫM

[cm−1] [µm] [l mole−1 cm−1]

Ge–OH 3545, 3450 2.82 [8], 2.90 [15] 149 [16], 14.5 [15]Ga–OH 3330 3.00 [8] -S–H 3270 3.06 [8] -S–H 2525 3.96 [8] -Ge(Ga)–OH ∼ 2500 ∼ 4 [8] -S–H 2500 4.00 [16] 80 [16]S–H 2450 4.08 [15] 65 [15]Ge–H 2325 4.30 [8] -CO2 2310 4.33 [8, 17] 36 [18]C–S (CS2) 2150 4.65 [17] -C–S (COS) 2030 4.92 [8, 19] 2038 [18]C–S (CS2) 1510 6.61 [17, 19] 713 [18]Ge–O 1335 7.49 [8] -Ga–O 1115 8.97 [8] -Si–O 1085, 1050, 9.2, 9.5, -

1000, 960 10.0, 10.4 [20]Ge–O 770 12.99 [8] -Ge–S 760 13.2 [8] -

0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000 2500 3000 3500 4000

20 10 5 2.5

Tra

nsm

ittan

ce [

-]

Wavenumber [cm-1]

Wavelength [µm]

Ge-

-OH

Ga-

-OH

S--H

S--H

Ge(

Ga)

--O

HG

e--H

CO

2

C--

S (C

S 2)

C--

S (C

OS)

C--

S (C

S 2)

Ge-

-O

Ga-

-OSi

--O

Ge-

-OG

e--S

Figure 2.3: Infrared total transmittance spectrum of germanium gallium sulphideglass.


factor ln 10 accounts for a conversion of the base of the logarithm (the molar extinc-tion coefficient ǫM is defined on basis of log(Ttr0

/Ttr), while the absorption coefficientα is defined on basis of ln(Ttr0

/Ttr)).In Table 2.1, assignment of the absorption bands and the molar extinction coefficients(at the peak wavelengths) caused by several impurities are listed. It is assumed thatthe extinction coefficients of the impurities do not change significantly between differ-ent chalcogenide glass compositions [16]. The OH and SH impurities are chemicallybonded to the glass components. The listed extinction coefficients for CO2, COSand CS2 were derived by Devyatykh et al. [18] for As2S3 glasses. These species aredissolved in the glass.The molar extinction coefficients for OH and SH at 2.9 µm and 4.0 µm in GeS2

were published by Kale et al. [15]. The S–H absorption (bending vibration) and theGe(Ga)–OH...S absorption (stretching vibration) [8] are both located around 4.0 µm.Kale et al. [15] have derived a linear relationship between the concentration and theabsorbance of OH and between the concentration and absorbance SH near 2.90 µm(3450 cm−1) and 4.08 µm (2450 cm−1), respectively.The OH and SH content of the glasses, prepared in this study, were estimated usingthe extinction coefficients derived by Kale et al. [15]. The OH content varied between2.5 and 4.5 ppm, while the SH content varied between 16 and 85 ppm. The hydroxyl(OH) concentration of our glasses is relatively low compared to the lowest value of60 ppm reported by Liu et al. [23] for purified GeS2.The main impurities carbon, oxygen and hydrogen mainly enter the glass via the rawmaterials used, the vitreous silica ampoule and the processing steps. The oxide impu-rities are either originating from the oxides on the surface of the germanium, galliumand sulphur starting materials or caused by the reaction between the melt and thesilica ampoule [4]. Hydrogen diffusion from the ampoule into the melt is anothersource for impurities [17], which can account for approximately 10 ppm hydrogen inour glasses [8].Simons [8] investigated the amount of carbon, oxygen and hydrogen impurities in-troduced by different starting materials into the glass. This resulted in the selectionof germanium and gallium ingots and sulphur pieces as starting materials. Furtherpurification of the sulphur by vacuum sublimation resulted in lower OH and SH im-purity levels, however carbon absorption peaks became stronger.Hydrocarbon impurities can react with hydroxyl and oxide impurities in the glassmelt [24]. This reaction can lead to the formation of carbon oxy sulfide (COS) andcarbon dioxide (CO2). These species remain (partly) dissolved in the glass.The dissolved impurities H2S, CS2, CO2 and COS can cause problems in processingof the glasses due to their tendency to outgas during thermal treatment [24]. Fur-thermore, bubble formation in glass matrix and surface defects (e.g. on the interfacesbetween core and cladding material during fibre drawing) reduce the transmittanceof the glass.The negative impact of chemically bound impurities (e.g. OH) on the radiative prop-erties of the praseodymium will be discussed in section 2.3.


0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000 2500 3000

20000 10000 5000 4000T

rans

mitt

ance

[-]

Wavelength [nm]

Wavenumber [cm-1]

Figure 2.4: UV, VIS and NIR transmittance spectra of a 700 ppm praseodymiumdoped (GeS2.5)98(Ga2S3)2 glass. (The absorption bands, around 1500 and 2000 nm,caused by praseodymium are discussed in section 2.3.)

2.2.2 UV VIS NIR transmittance spectra

The transmittance spectra were measured using a Perkin-Elmer model Lambda-9spectrophotometer in the UV, VIS and NIR range (0.25 – 2.5 µm). The transmit-tance spectrum of a praseodymium doped germanium gallium sulphide glass, preparedin this study, is shown in Figure 2.4. The (weak) absorption bands originate from theground state absorption transitions of praseodymium. The ground state absorption(GSA) of the praseodymium dopant will be discussed in section 2.3.2. No groundstate absorption is observed around the signal wavelength (1310 nm). The visible ab-sorption edge is defined as the wavelength where the transmittance has dropped 50 %compared to the transmittance at 800 nm. The absorption edge of the germaniumgallium sulphide host glasses is approximately 510 nm. Germanium gallium sulphideglasses are bright yellow coloured. The location of the absorption edge is related tothe glass composition. Sometimes, dark amber or even red glasses were obtained.This is related to the incorporation of impurities in the glass matrix. These glassestend to crystallise, since the impurities act as nuclei for crystallisation processes. Thedark amber or red colour is possibly caused by scattering of light by the small crystalsinside the glass.In the vicinity of the optical absorption edge (approximately 0.55 µm), the absorptioncoefficient increases exponentially with increasing photon energy [25] (or decresingwavelength, see Figure 2.5). This energy region is know as the Urbach tail or edge.In this wavelength range, the glasses behave like an amorphous semiconductor [25].At energies larger than the Urbach edge, the optical transitions are assigned to inter-band transitions between extended electronic states of the valence and conduction


10-2

10-1

10 0

10 1

14000 15000 16000 17000 18000 19000 20000 21000

Abs

orpt

ion

coef

fici

ent [

cm-1

]

Wavenumber [cm-1]

1D2

1D2

Weak Absorption Tail

Urbach Tail

(GeS2.25)98(Ga2S3)2(GeS2.5)98(Ga2S3)2

Figure 2.5: Urbach tail and weak absorption tail in germanium gallium sulphideglasses. The arrows indicate the praseodymium 3H4–

1D2 absorption.

bands. The so-called weak absorption tail is located at the lower energy range, nextto the Urbach tail. The change over between the weak absorption tail and the Urbachedge is situated around 18000 cm−1 (approximately 550 nm). In this spectral range,the slope of the photon energy versus absorption coefficient is smaller. The lossesin this spectral range originate from absorption by impurities and defects which arecharacteristic of the host glass and its preparation [25]. Due to the overlap of someof the electronic transitions of the rare earth dopant and absorption by the host glassin this wavelength region, interactions between optical absorption and emission pro-cesses of the dopant and the host glasses are possible [26]. The luminescent propertiesof the praseodymium ions in the germanium gallium sulphide glass are discussed insection 2.3. In that section, also the absorption bands in the UV Vis NIR spectracaused by the praseodymium dopant will be discussed in more detail.

2.2.3 Refractive index

Determination of the refractive index by ellipsometry

Ellipsometry is an optical technique to determine the properties of a surface [27]using polarised light. The state of polarisation (SOP)7 of light is changed when it isreflected at a surface. If linearly polarised light of a known orientation is reflected at

7The state of polarisation (SOP) describes the evolution of the electric field vector (described bythe solution of Maxwell’s wave equations for electro-magnetic fields) as a function of time at a givenlocation. The SOP is denoted linear, circular or elliptical depending on the trajectory traced by the

tip of the electric field E, which is related to the ratio of the maximum amplitudes|Ey0|

|Ex0|and the

phase difference φy −φx of the waves. The x and y components of the electric field are perpendicularto the direction of propagation of the light. A detailed description is given by Chen [22].


Plane of Incidence

E

E

φ φ

φ

E

E

linearly polarised light

elliptically polarised light

p

s Es

Ep

N1

N2

1 1

2

a) b)

Figure 2.6: a) Reflection and refraction of light at the interface of two materials withcomplex index of refraction N1 and N2. b) Reflection of linearly polarised light ona surface, indicating the p-, s-directions and direction of propagation prior and afterreflection. The reflected light is elliptically polarised.

oblique incidence from a surface then the reflected light is elliptically polarised.In ellipsometry, light with a known SOP is reflected on the surface of a sample. Theeffect of the reflection on the SOP of the reflected beam depends on the SOP of theincident light, the angle of incidence and the reflection properties of the surface. Theangle of incidence φ1 is defined as the angle between the incident light beam andthe normal to the surface (see Figure 2.6a). The plane of incidence is defined asthat plane which contains the incident and reflected light beams and the directionnormal to the sample surface. The SOP of the incident and reflected light beams isexpressed using the orthogonal basis vectors p and s. The p-direction is taken to beperpendicular to the direction of propagation and contained in the plane of incidence.The s-direction is taken to be perpendicular to the direction of propagation andparallel to the sample surface (i.e. perpendicular to the plane of incidence). The p-,s-directions and direction of propagation define a right-handed Cartesian coordinatesystem (see Figure 2.6b). This coordinate system is used to define the orthogonalcomponents of the electric field of the light beams Ep and Es in the parallel (p) andperpendicular (s) directions, respectively.The phase differences of the p- and s-components of the electric field before reflectionand after reflection are δ1 and δ2, respectively. Upon reflection, a phase shift mayoccur, which is not necessarily the same for both directions [27]. The phase difference∆ between the incident light and the reflected light is defined by

∆ = δ1 − δ2 (2.6)

In addition to the phase shift, the reflection is not necessarily the same for bothdirections [27]. The tangent of Ψ is defined as the ratio of magnitude of the Fresnellreflection coefficients rp and rs in the p and s directions

tan Ψ =

|Erp|

|Eip|

|Ers|

|Eis|

=|rp||rs| (2.7)


Table 2.2: The refractive indices of gallium sulphide glasses prepared in this studydetermined by ellipsometry at λ=588 nm.

Composition [at.%] Refractive index n [-]

Ge29.7Ga1.2S69.1 2.126Ge29.7Ga1.2S69.1 2.144Ge28.8Ga1.2S70.0 2.144Ge27.7Ga1.1S71.1 2.160Ge27.0Ga1.1S71.9 2.149Ge29.2Ga1.8S69.0 2.144Ge28.5Ga3.0S68.5 2.154

where Eip and Ei

s are the orthogonal components of the electric field incident on thesurface, while Er

p and Ers are the components of the electric field after reflection on

the surface. The wavelength dependent refractive index n and extinction coefficientk, which are related to the dielectric constant ǫ, are calculated from the measuredquantities ∆ and Ψ [27]. The real part and imaginary part of the dielectric constantǫ = ǫ1 − jǫ2 are determined from the measured values by

ǫ1 = n20 sin2 φ1

[

1 +tan2 φ1(cos

22Ψ − sin2 ∆sin2 2Ψ)

(1 + sin 2Ψ cos∆)2

]

(2.8)

ǫ2 =n0 sin2 φ1 tan2 φ1 sin 4Ψ sin ∆

(1 + sin 2Ψ cos∆)2(2.9)

where n0 is the refractive index of air [27]. The real part and imaginary part of thedielectric constant are functions of the refractive index n and extinction coefficient k

ǫ1 = n2 − k2 (2.10)

ǫ2 = 2nk (2.11)

The spectra of the refractive index n and extinction coefficient k are calculated fromthe measured Ψ and ∆ data, for different wavelengths, using equations 2.8 – 2.11.Ellipsometric Ψ and ∆ data were acquired at an angle of incidence φ1 of 75 over thespectral range of 245 - 1000 nm with a resolution of 1.6 nm using a Woollam M-2000Fellipsometer.The measured Ψ and ∆ and calculated n and k spectra of a glass with compositionGe29.7Ga1.2S69.1 are depicted in Figure 2.7. Note that both refractive index n andthe extinction coefficient k should decrease for higher wavelengths. However, smallextinction coefficients k (i.e. less than 10−3) could not be determined accurately byellipsometry [27].The refractive index spectra for glasses with different compositions are shown in Fig-ure 2.8. The refractive index at a wavelength of 588 nm is listed in Table 2.2. For


a)

0

10

20

30

40

0 200 400 600 800 10000

10

20

30

40

Elli

psom

etri

c Ψ

[o ]

Elli

psom

etri

c ∆

[o ]

Wavelength [nm]

Ψ∆

b)

2.0

2.1

2.2

2.3

2.4

2.5

0 200 400 600 800 10000

0.2 10-4

0.4 10-4

0.6 10-4

0.8 10-4

1.0 10-4

Ref

ract

ive

inde

x n

[-]

Ext

inct

ion

coef

fici

ent k

[-]

Wavelength [nm]

nk

Figure 2.7: a) Ellipsometric Ψ and ∆ and b) calculated n and k of a glass withcomposition Ge29.7Ga1.2S69.1.


2.0

2.1

2.2

2.3

2.4

400 500 600 700 800 900 1000

Ref

ract

ive

inde

x [-

]

Wavelength [nm]

1

4

Composition at.% 1=Ge29.7Ga1.2S69.12=Ge29.7Ga1.2S69.13=Ge28.8Ga1.2S70.04=Ge27.7Ga1.1S71.15=Ge27.0Ga1.1S71.96=Ge29.2Ga1.8S69.07=Ge28.5Ga3.0S68.5

Figure 2.8: Refractive index n of germanium gallium sulphide glasses determined byellipsometry. Series order at 500 nm is 1 (lowest n), 6, 2, 3, 5, 7 and 4 (highest n).

Table 2.3: The refractive indices of germanium sulphide and germanium galliumsulphide glasses taken from literature.

Composition [at.%] Refractive index n [-] Wavelength λ [nm]

GeS2 2.3 ± 0.2 633 [28]GeS2 2.144 632.8 [29]GeS2 2.011 633 [30]GeS2 2.073 1060 [10]Ge25.8Ga9.0S65.2 1.997 633 [30]Ge20S40 2.094 632.8 [29]Ge40S60 2.616 632.8 [29]GeS3 2.113 589.3 [31]Ge29Ga1S70 2.158 587.6 [4]Ge27.5Ga2.5S70 2.168 ± 0.001 587.6 [4]Ge25Ga5S70 2.174 ± 0.001 587.6 [4]Ge22.5Ga7.5S70 2.183 ± 0.001 587.6 [4]Ge31.7Ga6.3S62 2.310 ± 0.001 587.6 [4]Ge28.6Ga5.7S65.7 2.178 ± 0.001 587.6 [4]Ge23.3Ga4.7S72 2.172 ± 0.001 587.6 [4]Ge21.7Ga4.3S74 2.163 ± 0.001 587.6 [4]Ge18.3Ga3.7S78 2.130 ± 0.001 587.6 [4]


wavelengths > 500 nm, the difference between the refractive index values of the differ-ent glasses is less than 1%. However, a remarkable difference of 2% for two samples ofthe same nominal composition (Ge29.7Ga1.2S69.1) is observed in these measurements.Probably, the difference in the refractive index is explained by a difference in theactual composition of the samples.Refractive index data, taken from literature, for some selected germanium gallium sul-phide glass compositions are listed in Table 2.3. The refractive index of the glasses,prepared in this study, is slightly lower than the refractive index of the glasses re-ported by Abe et al. [4]. However, the germanium gallium sulphide glasses preparedby Abe et al. [4] have a higher gallium content compared to the gallium content ofthe glasses, prepared in this study. Generally, the refractive index data (determinedby ellipsometry) are in good agreement with the data listed in literature.In a glass fibre, a small difference (typically less than 1%) in the refractive index ofthe core and cladding material for a wavelength near the signal wavelength is neededin order to confine the light within the waveguide. As can be seen from Figure 2.8,only a relatively small change in composition is needed to obtain a small change inthe refractive index.For example, the refractive index difference (near 1000 nm) of approximately 0.35%is observed for Ge27.7Ga1.1S71.1 and Ge27.0Ga1.1S71.9 glasses. Based on the observeddifference in the refractive index, these glasses could be used to construct an opticalfibre with a core-cladding structure.The compositional dependence of the refractive index is dependent on the sulphurand gallium content. Glasses containing less sulphur than the stoichiometric sulphurcontent, show a high refractive index. According to Abe et al. [4], the refractive indexincreases as the gallium content increases (lowering the at.% fraction of germaniumwhile keeping the at.% fraction of sulphur in the glass constant), due to the largerpolarisability of gallium compared to germanium. Based on the bond types [4, 32],the sulphur content dependence of the refractive index is divided into three regions:cation excess (S < 66.7 at.%) with contribution of Ge-Ge bonds, anion excess regionwith major contributions of GeS4/2 and GaS4/2 tetrahedra connected by S-S bondsand an anion excess region with dominant S-S bonds and S8 (S > 75 at.%) rings.In the first and last region, the refractive index decreases with sulphur content. Theglasses, used in this study, are situated in the middle region where the refractive indexremains almost constant with increasing at.% fraction of sulphur in the glass.The refractive indices of the germanium gallium sulphide glasses under investigationare less than the refractive indices of other chalcogenide systems (e.g. gallium lan-thanum sulphide [33]). In general, a lower refractive index value of the glass willresult in lower overall background losses and reduced end-to-end coupling losses (i.e.reflection losses).

Determination of the refractive index from the Brewster angle

The reflection of light on a surface, given by the Fresnell reflection coefficients rp andrs, is different for the p and s directions of the reflected beam, except at normal inci-dence (φ1=0) and grazing incidence (φ1=90). The difference in reflectance between


Table 2.4: The refractive indices based on the measurement of the principal angle atλ=1310 nm.

Composition (at.%) Refractive index [-]

Ge29.7Ga1.2S69.1 2.067Ge29.7Ga1.2S69.1 2.062Ge28.8Ga1.2S70.0 2.080Ge27.7Ga1.1S71.1 2.070Ge27.0Ga1.1S71.9 2.070Ge29.2Ga1.8S69.0 2.073Ge28.5Ga3.0S68.5 2.065

the p and s directions varies with angle of incidence. At the Brewster (or principal)angle, the value of rp goes through a minimum. At this Brewster angle φB the angleof the reflected beam φ1 and the transmitted beam φ2 (as defined in Figure 2.6a) areat right angle [27], i.e.

cos φ2 = sin φ1 = sin φB (2.12)

Furthermore, the phase shift of the electric field before and after reflection δ1 passesthrough 90, at the principal angle [27]. The Brewster angle is a wavelength dependentfunction of the refractive index. At the Brewster angle

tanφB =n1

n0(2.13)

where n1 and n0 are the refractive indices of the material and air, respectively.The Brewster angle at 1310 nm was determined using the setup shown in Figure 2.9.The orientation of linearly polarised light, provided by a 1310 nm laser diode (LD),was adjusted using a polarisation controller. A beam of light, polarised in the p-direction, was formed using a lens at the output of the fibre (lens ferrule). Thesample was mounted on a precision rotation stage. An additional detector mountedto a 2x2 coupler8 was used to determine the position of the rotation stage at normalincidence. The power reflected by the sample, as measured by the detector mountedto the 2x2 coupler, attains its maximum at normal incidence. The power of thereflectance in the parallel (p) direction was recorded at different angles of incidence.The principal angle was deduced from the minimum in the power curve obtained fromthe reflected power at different angles. The refractive indices based on the measure-ment of the principal angle at 1310 nm are listed in Table 2.4. The inaccuracy of thedetermination of the Brewster angle is at least 0.1, which results in an uncertaintyin the refractive index ∆n of 0.009 % (for n ≈ 2).The absolute values of the refractive indices at 1310 nm, derived from the Brewsterangle, are in good agreement with the refractive indices determined by ellipsometry

8This coupler is used to distribute the optical power at one of its input fibres equally among twooutput fibres [34].


LD 1310 nm

Power meter Power meter

Lensferrule2x2 Coupler

φ

Rotation Stage with Sample

Polarisation Controller

1

Figure 2.9: Setup for determination of Brewster angle. Linearly polarised light isprovided by a 1310 nm laser diode (LD). The SOP of the incident beam is adjustedto the p-direction using a polarisation controller. The angle of incidence is determinedby the rotation stage. A power meter is used to measure the intensity of the reflectedlight.

around 1000 nm. Due to the low gallium content of the germanium gallium sulphideglasses, it is expected that the measured refractive indices are nearly equal to therefractive index of GeS3. The refractive indices at 1310 nm of GeS2 and GeS4 glassesare 2.12 and 2.05, respectively [29].

2.3 Optical properties of praseodymium in the host

glass

Trivalent praseodymium ions are optically active in the IR range, via electronic tran-sitions between its 4f levels. A detailed description of the electronic structure of rareearth ions and the quantum mechanics related to the transitions between the energylevels is beyond the scope of this thesis and can be found in e.g. [35]. In section 2.3.1,the electronic structure of the praseodymium ion and the electronic transitions be-tween its energy levels are briefly described, to facilitate the description of the opticalproperties of the praseodymium dopant in the germanium gallium sulphide glasses.Absorption spectroscopy (see section 2.3.2) and photoluminescence spectroscopy (seesection 2.3.3) are used to determine absorption and emission wavelengths, band shapesand emission lifetimes.A quantitative description of the intensity of the optical transitions (e.g. absorptionor emission) by the electrons within the praseodymium ions is needed to predict theperformance of a PDFA and to improve its design using a spectrally resolved ampli-fier model (e.g. see chapter 4). The Judd–Ofelt [36, 37] theory is a phenomenological


approach, used to calculate the host dependent intensity parameters Ωt (t=2, 4, 6) forthe electronic transitions of the praseodymium dopant. The application of the Judd–Ofelt theory to determine the radiative properties of praseodymium is discussed insection 2.3.4. The host dependent intensity parameters Ωt (t=2, 4, 6) are used todetermine the oscillator strengths9 of the radiative transitions of the electrons of thepraseodymium dopant in the germanium gallium sulphide host glass, which in turnare used to obtain radiative properties like cross sections and lifetimes. These crosssections and lifetimes are required for the calculation of population densities of theexcited states and eventually the modelling of light amplification within the PDFA.

2.3.1 Electronic structure

The electronic structure of the trivalent praseodymium ion (Pr3+) is [Xe]4f 2. The 4felectrons, which can only occupy discrete energy states, are electronically shielded bythe outer 5s2 and 5p2 shells10. The optical transitions of interest are associated withthe transitions of 4f electrons between those energy states11. The wavelengths of theoptical transitions are relative insensitive to the host matrix due to the shielding [35].A simplified energy level diagram for praseodymium is presented in Figure 1.6a. Theenergy levels in this figure are labelled according to the Russell-Saunders 2S+1LJ

notation [35]. In this notation, based on the Russell-Saunders coupling scheme, thequantum numbers for each electron state are combined to obtain the total spin (S)and the total orbital angular momentum (L, where L=0,1,2,3,4,5, ... are S, P, D, F,G, H, ...) of the ion. The total angular momentum J is given by the coupling of Sand L (J=S+L). J may take values (L+S), (L+S)-1, ..., (L-S). For example, for theenergy state 3H4, the total orbital angular momentum L equals H, the total spin Sequals 1 and the total angular momentum J equals 4. These quantum numbers arefound by application of Hund’s rules [35]. The quantum mechanics related to theelectronic spectra and magnetic properties of praseodymium are beyond the scope ofthis thesis.The splitting of the energy levels of electron states for praseodymium is illustrated inFigure 2.10 (in which only the lower energy levels 3H, 3F and 1G are shown). Themain energy levels 3H, 3F, 1G, 1D 1I, 3P and 3S are caused by electron–electron (i.e.spin-spin) interactions, while the J sublevels are caused by spin-orbit coupling [38].Each 2S+1LJ state is split into 2J+1 states having the same energy (this effect isknown as degeneracy) and the split level is called a Stark level [35].The 3H4 level is the ground state level of the trivalent praseodymium ion. In thefollowing sections, the Russell-Saunders notation will be used to describe transitions

9The oscillator strength is a quantum mechanically-derived transition probability for a transitionbetween to energy levels.

10A detailed description of the electronic structure of rare earth ions and the quantum mechanicsrelated to the transitions between the energy levels can be found in e.g. [35].

11In principle, electric dipole transitions (i.e. interactions of electromagnetic radiation with anatom) between the 4f states, having the same parity, are forbidden. In practice, radiative transitionsare possible by the admixing of the 4f states with states of opposite parity belonging to the 5dconfiguration [38].


3H4

3H5

3H6

3F2

3F3

3F4

1G4

4f2

3H

3F

1G

centalfield

Spin-spincoupling

Spin-orbitcoupling

Structure

Ene

rgy

Figure 2.10: The energy level diagram of the trivalent praseodymium ion, indicatingthe splitting of the 4f 2 level into 2S+1L energy levels with J sublevels (only splittingof the 3H, 3F and 1G levels is indicated).

between the energy levels of praseodymium.

2.3.2 Absorption spectroscopy

The absorption bands in the wavelength range 250–2500 nm (i.e. UV to the NIR, seeFigure 2.4) of a praseodymium doped germanium gallium sulphide glass are partlycaused by ground state absorption of the praseodymium dopant. The absorptioncoefficient α of each band, caused by absorption of the praseodymium dopant, isdetermined from the internal transmittance τ using Lambert-Beer’s law (equation2.3). The absorption cross sections σi of absorption band i is defined by

σai=

αi

NPr3+

(2.14)

where αi is the absorption coefficient derived from the spectroscopic data and NPr

is the number of praseodymium ions per unit volume. In Figure 2.11, the absorptioncross sections of praseodymium for various compositions of the host glass, measuredin this study, are depicted. In this figure, the absorption cross sections for the groundstate absorption (GSA) are labelled according to the energy level of the indicatedexcited states (see Figure 1.6a) related to the wavelength of absorption.The pump GSA (3H4 →1G4) around 1030 nm and the signal GSA (3H4 →3F4)in the 1.3 µm region are of major importance for the amplifier application of the


0

0.5 10-20

1.0 10-20

1.5 10-20

2.0 10-20

2.5 10-20

3.0 10-20

3.5 10-20

4.0 10-20

500 1000 1500 2000 2500

Abs

orpt

ion

cros

s se

ctio

n [c

m2 ]

Wavelength [nm]

1D2

1G4

3F4

3F33F2

3H6

Composition at.%Ge29.7Ga1.2S69.1Ge24.3Ga1.0S74.7Ge27.7Ga1.1S71.1

Figure 2.11: Absorption cross sections for transitions from the ground state (3H4) ofpraseodymium doped germanium gallium sulphide glasses.

praseodymium doped host glass. Fortunately, the signal GSA around 1.3 µm is neg-ligible.The 3H4 →1D2 absorption is close to the absorption edge of the germanium galliumsulphide host glass. The energy involved in the 3P0,

3P1 and 3P2 GSA transitions isapproximately 20000 cm−1 (not shown in Figure 1.6a). Hence, the 3P0,

3P1 and 3P2

GSA (around 500 nm) could not be observed, as these transitions are located belowthe absorption edge of the germanium gallium sulphide glass. The 3F4 – 3F3 and 3F2

– 3H6 GSAs show strong overlap.In Table 2.5, the energy levels determined by absorption spectroscopy are listed. Theoptimum pump wavelength, which corresponds to the peak absorption wavelength ofthe 3H4 →1G4 transition, is 1038 nm. Due to non-radiative energy transfer from the1G4 excited state to the next lower energy level 3F4 by lattice vibrations (phonons)of the glass host, the quantum efficiency of the radiative transitions is reduced. Theenergy difference between the 1G4 and 3F4 state of praseodymium in the germaniumgallium sulphide glasses is approximately 2945 cm−1.

2.3.3 Photoluminescence spectroscopy

In photoluminescence spectroscopy, a sample is continuously irradiated by a lightsource (e.g. laser), while the spontaneous emission power originating from radiativedecay from an excited state to the lower energy levels is measured as a function ofwavelength [7]. In the photoluminescence lifetime measurements, the decay of thephotoluminescence intensity (at a single wavelength) is recorded after the light sourceis temporarily switched off.


Table 2.5: Energy, wavelength and cross sections of praseodymium ground state ab-sorption in germanium gallium sulphide glass with composition Ge29.2Ga1.8S69.0

Level Energy Wavelength Cross section[cm−1] [nm] [cm2]

1D2 16340 611 5.8 10−21

1G4 9635 1038 1.5 10−21

3F4 6690 1495 1.5 10−20

3F3 6270 1595 2.6 10−20

3F2 4925 2030 2.4 10−20

3H6 4250 2353 4.2 10−21

Experimental procedure

Photoluminescence spectroscopy is performed on cylindrical shaped glass samples,with a diameter of 10 mm, which were also used for absorption and reflection spec-troscopy. The surfaces of these samples were polished to optical quality.The samples were irradiated (“pumped”) with a monochromatic beam originatingfrom either a Coherent Innova 90 Argon ion laser or a Coherent 980 Titanium–Sapphire laser (which was pumped by the Argon ion laser). The photoluminescenceoriginating from the praseodymium doped glass samples was focused on the entranceslit of a CVI DK 480 (double pass) monochromator. A filter was placed betweenthe sample and the monochromator in order to filter higher order radiation of theAr laser beam or to filter out the pump wavelength of the Ti:Sa laser. Furthermore,it prevented the entrance of reflected light originating from the incident beam intothe monochromator. The photoluminescence spectra were obtained by sweeping themonochromator wavelength with 1 nm steps. The measuring time at each wavelengthwas approximately 2 s.The intensity of the light was detected by a North Coast EO-8175 germanium photodetector. The detector was cooled with liquid nitrogen. Lock-in detection techniques(provided by a Stanford SR 510 Lock-in-amplifier and a Stanford SR 540 chopper)were used to improve the signal-to-noise ratio. The beam of the laser source wasmodulated by a Stanford SR 540 chopper. The rise time (i.e. the time at which thelaser beam is not completely switched on or off) of the chopped beam was reduced byputting the chopper in the focal point of two lenses (i.e. at the chopper, the diameterof the laser beam is minimised using lenses). The chopper frequency was used as areference for the Stanford SR 510 Lock-in-amplifier. The chopper frequency was 12.5– 30 Hz. The chopper frequency was used to trigger the Stanford SR 510 Lock-in-amplifier.In the photoluminescence lifetime measurements, the photoluminescence decay curveswere recorded for a single wavelength and averaged using a Philips PM3350A digitis-ing oscilloscope. The system response time (for switching the laser light off) was lessthan 30 µs.


0

5000

10000

15000

20000E

nerg

y [c

m-1

]

3H4

3H5

3H6

3F2

3F3

3F4

1G4

1D2

3P0

3P1

3P2

Ar

ion

lase

r 51

5 nm

Ar

ion

lase

r 48

8 nm

Ti:S

a la

ser

1005

nm

Figure 2.12: The energy level diagram of Praseodymium indicating Ar-ion andtitanium–sapphire laser pump absorption and observed radiative transitions.

Results and discussion

The titanium–sapphire laser operating at 1005 nm was used to excite praseo-dymiumions into the 1G4 level (see Figure 2.12). The optimum pumping wavelength, deter-mined by absorption spectroscopy, is 1038 nm. Measurements by Simons [8] showedthat the optimum pump wavelength, determined by absorption spectroscopy, matchesthe pumping wavelength which provides the maximum output power for the 1G4 –3H5 photoluminescence (i.e. found by excitation spectroscopy). The spectral shapeof the 1G4 – 3H5 photoluminescence is shown in Figure 2.13. The full-width at half-maximum (FWHM) of the 1G4 – 3H5 transition is approximately 80 nm.The Ar-ion laser operating at either 488 or 514.5 nm was used to excite the 3Px

levels (see Figure 2.12). The photoluminescence spectra at both pump wavelengthsare shown in Figure 2.14. The average pump power was approximately 14 mW forboth wavelengths. The wavelengths of the transitions within this wavelength regionwere estimated from the energy levels obtained by transmittance spectroscopy (seeTable 2.5). Those locations are indicated by the dotted lines in Figure 2.14. The exactposition of the 3Px levels of praseodymium doped germanium gallium sulphide glassescould not be determined using transmittance spectroscopy, due to the absorption edgelocated around 550 nm. However, the energy of the 3Px levels (see Figure 2.12) canbe derived from the photoluminescence spectra (e.g. Figure 2.14), using energy of thelower energy levels as determined by transmittance spectroscopy (see section 2.3.2).Using the Ar-ion laser, operating at either 488 or 514.5 nm, the samples were ex-cited near or even below the Urbach edge. In this wavelength range, energy transferbetween the rare-earth dopant and point defects in the host glass can occur. These(charged) defects are formed when the normal coordination cannot be satisfied, dueto constraints in local structure (so-called dangling bonds [39]) or are induced by


1.20 1.25 1.30 1.35 1.40 1.45 1.50

Inte

nsity

[a.

u.]

Wavelength [µm]

1 G4-

3 H5

Figure 2.13: The 1G4 – 3H5 photoluminescence spectrum of a 391 ppm praseodymiumdoped Ge29.2Ga1.8S69.0 glass pumped at 1005 nm.

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Inte

nsity

[a.

u.]

Wavelength [µm]

3 P 0-1 G

41 D

2-3 F 3

1 D2-

3 F 4

1 G4-

3 H5

488 nm515 nm

Figure 2.14: The photoluminescence spectra of a 378 ppm praseodymium dopedGe28.8Ga1.2S70.0 glass pumped at 488 and 514.5 nm.


E

E

Valence band

Conduction band

Energy transfer

Lattice relaxation

Recominationwith electron

hν

Hole capture

Host glass Pr dopant

c

v

F32

F33

F34

H36

H35

H34

G14

D12

P32

P31

P30

Defectstate

Figure 2.15: A schematic overview of energy transfer processes between host glassand the rare earth ions, as proposed by Turnbull et al. [26].

impurities [26].The mechanism of energy transfer between defects and dopant was described by Turn-bull et al. [26] and is schematically outlined in Figure 2.15. Optical excitation of thematerial near the Urbach edge, with light of energy hν, promotes an electron of thehost glass from the valence band into the conduction band. The energy of the valenceband and conduction band is Ev and Ec, respectively. When the resultant hole (i.e.electron vacancy) is captured by a nearby negatively charged defect-related site inthe glass, the charge of this defect is neutralised. (The capture is indicated by thearrow labelled “Hole capture” in Figure 2.15.) The energy state of the hole trappedat the defect is then lowered by bonding to adjacent atoms. This structural relaxationmoves the defect state deeper into the bandgap. Subsequently, an electron from theconduction band recombines with the hole trapped at the defect site (indicated by thearrow labelled “Recombination with electron” in Figure 2.15), transferring its energynon-radiatively to a nearby praseodymium ion. After recombination, the defect sitereturns back to its original energy state by rearrangement of the lattice around thedefect. The energy difference between the energy of the light of energy hν and theamount of energy transferred to the praseodymium ion is related to the energy usedfor structural relaxation around the defect state.The excited defects in the glass host transfer their energy more readily to the lower


excited states of the praseodymium dopant than to the praseodymium ions’ higherenergy states [40].Energy transfer from the praseodymium dopant to a host defect is also possible andcan occur when the absorption energy of the defects in the host matches the emis-sion energy of the electron transitions of the praseodymium ion. Unfortunately, thisprocess is expected to be much more efficient than defect to dopant transfer due tothe relatively long lifetime of excited states of praseodymium [41]. However, onlyfew praseodymium ions are in these high energy excited states (3P0,

3P1 and 3P2

and 1D2), as these energy levels are populated by either direct excitation into theseenergy levels (by pumping at short wavelengths) or by excited state absorption.The energy of the Ar-ion laser operating at either 488 or 514.5 nm was close to the en-ergy of 3Px levels (see Figure 2.12). Hence, it is expected that the photoluminescencespectra will reveal radiative transitions originating from 3Px, 1D2 and 1G4 levels. The1G4–

3H5 transition is rather strong. Weak photoluminescence peaks originating fromthe 1D2 are observed, but the 1D2 – 1G4 transition (around 1.5 µm) is not revealed(see Figure 2.14). Apparently, the defect centres effectively absorb the light from the1D2 level and the Ar-laser and sensitise the fluorescent emissions of the lower energystates.Simons [8] reported the 1D2 – 1G4 emission in his GeS2 and (GeS2)80(Ga2S3)20 glasses.The composition of these glasses is stoichiometric. However, the glass samples usedin this study contain excess sulphur. The local structure is influenced by the sulphurexcess and this may affect the number of defect centres in the host glass.The measured photoluminescence spectra of a Ge29.2Ga1.8S69.0 glass (doped with 391ppm praseodymium) in the NIR en VIS regions are depicted in Figure 2.16. The pumpwavelength is 514.5 nm. With the Ar-laser as excitation source, the emissions from the3Px, 1D2 and 1G4 levels are detected simultaneously. The energy difference betweenthe 1D2 and 1G4 levels is comparable to the energy difference between the 1G4 and3H5 levels. The shape of the photoluminescence spectrum around 1340 nm pumpedat 514.5 nm equals the spectrum pumped at 1005 nm (see Figure 2.13 and 2.16a,respectively). Similar results are observed, when the pump wavelength is 488 nminstead of 514.5 nm. As no overlap from the 1D2 – 1G4 and 1G4 – 3H5 emission isobserved, the radiation originates solely from the 1G4 – 3H5 transition in both cases.The photoluminescence originating from the 3P0 – 1G4 transition is located between900 and 1000 nm, but this weak photoluminescence band is overlapped by other tran-sitions.Usually, the shape of the 1D2 – 1G4 and 3P0 – 1G4 photoluminescence bands (deter-mined by excitation around 500 nm) will be used to determine the signal excited stateabsorption (ESA) cross section (1G4 – 1D2 transition) and pump ESA cross section(1G4 – 3P0 transition) using McCumber theory [42]. This will be discussed in thenext section.The energy levels of several excited states were determined from the photolumines-cence spectra (Figure 2.13 and 2.16). These levels are listed in Table 2.6, relative tothe energy of the ground state (3H4).The spacing between the energy levels is affected by the bond type. In chalcogenideglasses, the nature of the bond between praseodymium and sulphur is predominantly


a)

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Inte

nsity

[a.

u.]

Wavelength [µm]

3 P 0-1 G

41 D

2-3 F 3

1 D2-

3 F 4

1 G4-

3 H5

b)

0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.71

Inte

nsity

[a.

u.]

Wavelength [µm]

3 P 0-3 H

51 D

2-3 H

4

3 P 0-3 H

6

1 D2-

3 H5

Figure 2.16: The photoluminescence spectra of a 391 ppm praseodymium dopedGe29.2Ga1.8S69.0 glass pumped at 514.5 nm.


Table 2.6: Energy levels determined by photoluminescence spectroscopy on praseo-dymium doped sulphide glasses.

Level Energy [cm−1]3P1 201973P0 190341D2 166911G4 94213F4 70793F3 65313H6 38913H5 19453H4 0

0

1

-4

-3

-2

-1

0.009 0.0095 0.01 0.0105 0.011 0.0115 0.012

time [s]

Inte

nsity

[a.

u.]

τe

0

1

-4

-3

-2

-1

0.009 0.0095 0.01 0.0105 0.011 0.0115 0.012

time [s]

Inte

nsity

[a.

u.]

τe

ln(

I I0)

[-]

ln(

I I0)

[-]

Figure 2.17: Decay of the 1G4 – 3H5 photoluminescence intensity recorded at 1340 nm.The pump wavelength is 1005 nm.


350

400

450

500

550

200 300 400 500 600 700

Em

issi

on li

fetim

e τ e

[µs

]

Pr dopant concentration [ppm]

x=2.25 y=2

x=2.25 y=3x=2.5 y=2

x=2.6 y=2 x=2.375 y=2

x=3 y=2

Figure 2.18: The emission lifetime τe of the 1G4 – 3H5 transition in(GeSx)100−y(Ga2S3)y glasses. The dotted line presents the average emission lifetimeof (GeS2)97(Ga2S3)3 with various doping levels.

covalent. The strength of the covalent bond results in compression of the energy levels(due to the stronger local electric field around the praseodymium ion), compared tothe energy levels of a praseodymium ion in ionic bonded glass types (e.g. in a fluorideglass host) [8].The emission lifetime τe of the 1G4 – 3H5 transition was determined using theTitanium–Sapphire laser operating at 1005 nm. After blocking the pump laser lightby the chopper, the photoluminescence intensity is decreasing exponentially. Theemission lifetime is defined as the time in which the intensity I of the photolumi-nescence has dropped to 1/e (approximately 0.368) of its initial value I0. A typicalphotoluminescence decay curve is shown in Figure 2.17. The discrete noise levelsoriginate from the digitizing (sampling) oscilloscope.The measured emission lifetimes at 1340 nm of several praseodymium doped germa-nium gallium sulphide glasses and doping levels are depicted in Figure 2.18. Theparameters x and y are used to denote the composition of the glasses, which is rep-resented by the general formula (GeSx)100−y(Ga2S3)y. The emission lifetime of thesulphur rich (x=3) glasses at room temperature is approximately 400 µs. The emissionlifetime increases as the sulphur excess is reduced. The measured emission lifetimeof the 1G4 – 3H5 transition in germanium gallium sulphide glasses is up to 1.5 timeslonger than those of the praseodymium doped GeSx glasses produced by Simons [8].Furthermore, the lifetime in the germanium gallium sulphide glasses is more than fourtimes longer than in ZBLAN12 fluoride glass (110 µs).The concentration of praseodymium dopant in the germanium gallium sulphide glasses,

12Fluorozirconate glass containing ZrF4-BaF2-LaF3-AlF3-NaF


Table 2.7: Emission lifetime of several glasses and doping levels recorded at wave-lengths 1340 and 1373 nm. The pump wavelengths are 514.5 and 1005 nm.

Composition [at.%] and τλ=1340 [µs] τλ=1374 [µs] τλ=1340 [µs]Pr3+ conc. [ppm Wt] (λp = 514.5 nm) (λp = 514.5 nm) (λp = 1005 nm)

Ge29.7Ga1.2S69.1 398 356 351 545Ge29.7Ga1.2S69.1 393 368 311 508Ge28.8Ga1.2S70.0 378 322 293 414Ge27.7Ga1.1S71.1 383 380 339 470Ge27.0Ga1.1S71.9 371 339 338 438Ge29.2Ga1.8S69.0 391 365 339 476Ge28.5Ga3.0S68.5 439 322 371 453

prepared in this study, is well below 900 ppm Wt. When the praseodymium concen-tration exceeds 1×1019 cm−3 [8] (approximately 900 ppm), the emission lifetime isshortened by concentration quenching13. Furthermore, the photoluminescence decayis influenced by hydroxyl impurities in the host glass [8]. A measure for the concen-tration of hydroxyl is the absorption coefficient at 3350 cm−1. Hydroxyl-quenchingresults in non-exponential decay curves. The degree of non-exponential decay in-creases with increasing hydroxyl concentration. The hydroxyl concentrations in theselected glasses are below 50 ppm and hence no hydroxyl quenching is observed.The emission lifetimes at 1340 and 1374 nm were recorded using the argon laser at514.5 nm. Using this pump wavelength, the 1G4 level is populated either by de-cay from higher energy levels or by energy transfer by the host glass. The emissionlifetimes of several glasses and doping levels are listed in Table 2.7. As a reference,the emission lifetimes obtained by pumping at 1005 nm are also presented in Ta-ble 2.7. The observed lifetime of the 1G4 – 3H5 transition (pumped at 514.5 nm) isshorter than the lifetime observed by pumping the 1G4 level directly. When pumpingat 515 nm, the measured photoluminescence lifetimes at 1340 nm and 1374 nm arecomparable. This also indicates that the broad 1G4 – 3H5 photoluminescence peakaround 1340 nm is not overlapped by the 1D2 – 1G4 transition, although the energydifference is similar for both transitions.

2.3.4 Radiative transitions

A quantitative description of the optical transitions (e.g. absorption or emission)within the praseodymium ions is needed to estimate the population densities of theexcited states and the transition rates between the energy states. Eventually, the

13Concentration quenching is caused by non-radiative energy transfer between two praseodymiumions. In this process, the energy of an excited praseodymium ion is partly transferred to a nearbypraseodymium ion. After the energy transfer, both ions are in an intermediate state, which subse-quently decay non-radiatively to the ground state [8].


data describing the optical transitions are used to calculate excited state absorptionand emission cross sections, which are used by spectrally resolved amplifier models(e.g. see chapter 4), to evaluate the performance of the amplifier.Besides absorption or emission of photons, the energy state of the dopant can changeby non-radiative (e.g. multi-phonon) transitions. Non-radiative transitions are dis-cussed in section 2.4.2.The radiative (absorption and emission) transition rates between all the energy levelsof the dopant ion are quantitatively characterised using Judd-Ofelt theory [36, 37].In this phenomenological approach, the radiative transition rates in the rare earthdoped host glass, are described by the characteristic intensity parameters Ω2, Ω4, andΩ6. Usually, these so-called Judd-Ofelt parameters are not directly determined fromabsorption and emission transitions, but related to the oscillator strengths f of thesetransitions. The oscillator strength f of a transition is calculated from spectroscopicdata (e.g. ground state absorption).The oscillator strength f(aJ, bJ ′)abs of a transition between levels aJ (e.g. 3H5) andbJ ′ (e.g. 1G4), due to absorption, is given by

f(aJ, bJ ′)abs = 4πǫ0

(mc

πe2

)

∫

σa(ν)dν (2.15)

where ǫ0 is the permittivity of vacuum, m is the electron mass, c is the velocity oflight in vacuum, e is the elementary charge, and σa the absorption cross section forthe appropriate absorption transition (see section 2.3.2). The integral is taken overthe entire absorption line shape. Similarly, the oscillator strength f(aJ, bJ ′)abs canbe expressed as a function of the absorption coefficient α using equation 2.14

f(aJ, bJ ′)abs = 4πǫ0

(

mc2

πe2NPr

)∫

α(λ)

λ2dλ (2.16)

where NPr is the number of praseodymium ions per unit volume and α is the measuredabsorption coefficient.According to Judd-Ofelt theory [36, 37], the oscillator strength f(aJ, bJ ′)ed of anelectric-dipole transition (i.e. absorption or emission of electromagnetic radiation byan atom or an ion)) between levels aJ and bJ ′ is given by

f(aJ, bJ ′)ed =

(

8π2mcχ

3h(2J + 1)n2λ

)

∑

i=2,4,6

Ωi〈aJ‖U (i)‖bJ ′〉2 (2.17)

where h is Planck’s constant, λ is the average wavelength of the transition, aJ andbJ ′ are the total angular momentum of the initial state and terminal state, respec-tively, (2J + 1) is the degeneracy of level aJ , n is the refractive index at λ and theelements 〈‖U (i)‖〉 are the doubly reduced unit tensor operators U (i) calculated in theintermediate-coupling approximation. These elements are assumed to be independentof the host glass. The values of U (i) for praseodymium in a LaF3 host were deter-mined by Weber [43]. The factor χ is a local field correction factor for the electricfield around the rare earth ion in a medium of isotropic refractive index and is given


by

χ =n(n2 + 2)2

9(2.18)

The Judd-Ofelt parameters Ωt (t=2, 4, 6) are obtained by multi-linear regressionanalysis on M independent experimental transition oscillator strengths f(aJ, bJ ′)abs

and the squared doubly reduced tensor operators for the corresponding transitions.For every observed ground state transition j (j = 1 · · ·M), the linear expression(based on equation 2.17)

Ω2Vj2 + Ω4V

j4 + Ω6V

j6 = Bjf(aJ, bJ ′)j

abs (2.19)

is obtained, where V ji is a short notation for the squared doubly reduced matrix

elementV j

i = 〈aJ‖U (i)‖bJ ′〉2 (2.20)

for the jth transition and

Bj =3h(2J + 1)n2λ

8π2mcχ(2.21)

and f(aJ, bJ ′)jabs are the oscillator strengths for the jth ground state absorption tran-

sition (j = 1...M), determined from absorption spectroscopy (see equation 2.16).The Judd-Ofelt parameters, derived from the absorption cross section data, can beused to calculate the oscillator strength between any pair of energy states using equa-tion 2.17. These calculated oscillator strengths are used to calculate the radiativeproperties, due to emission or absorption, of the dopant.The transition rate A(aJ, bJ ′) of an electric-dipole transition between level aJ andbJ ′ [35] is

A(aJ, bJ ′) =1

4πǫ0

(

64π4e2χ

3h(2J + 1)λ3

)

∑

i=2,4,6

Ωi〈aJ‖U (i)‖Bj′〉2 (2.22)

The transition rate is proportional to f/λ2 [42]. The radiative lifetime τr of an excitedstate is inversely proportional to the sum of the all possible radiative transition ratesA(aJ, bJ ′) from level aJ to all its lower lying levels states J ′ by

τr =1

∑

J‘ A(aJ, bJ ′)(2.23)

If an excited state is only depopulated by radiative transitions, the measured emissionlifetime τe would be equal to its radiative lifetime τr. However, in addition to de-population of the excited state by radiative transitions, also non-radiative transitionsoccur (see section 2.4.2).The branching ratio βr, which is the probability of a radiative transition from excitedlevel aJ to level bJ ′, is given by

βr =A(aJ, bJ ′)

∑

J‘ A(aJ, bJ ′)= τrA(aJ, bJ ′) (2.24)


The oscillator strength f(aJ, bJ ′)emit for emission of radiation due to a transitionbetween levels aJ and bJ ′ is

f(aJ, bJ ′)emit = 4πǫ0

(mc

πe2

)

∫

σe(ν)dν (2.25)

where σe is the emission cross section. The shape of the emission cross section fora particular transition, is directly related to its photoluminescence spectrum. Theabsolute value of the emission cross section is obtained from the oscillator strengthby substitution of equations 2.17, 2.22 and 2.25 into 2.24

∫

σe(λ)

λ4dλ =

βr

τr

1

8πcn2(2.26)

where the branching ratio βr and the radiative lifetime τr are determined using theJudd-Ofelt parameters Ωt (t=2, 4, 6). Equation 2.26 is used to calculate the (inte-grated) stimulated emission cross section σsem of praseodymium, i.e. the cross sectionrelated to the 1G4 – 3H5 transition.To obtain reliable Judd-Ofelt parameters, a sufficient number of transitions must beincluded in the analysis (i.e. at least 5 measured oscillator strengths are required [44]).Alternatively, the Judd-Ofelt parameters Ωt (t=2, 4, 6) are derived using closed formexpressions derived by Quimby et al. [44]. The method, presented by Quimby etal. [44], can be extended to incorporate measured branching ratios βr obtained byphotoluminescence spectroscopy.The McCumber theory is applied to calculate the signal excited state absorption(ESA) cross sections σs−esa and pump ESA cross sections σp−esa of praseodymium,i.e. the cross sections related to the 1G4 – 1D2 and 1G4 – 3P0 transitions, respec-tively. The McCumber theory [42] relates the absorption and emission cross sectionsbetween two energy levels, under the assumption that the time required to establish athermal equilibrium distribution of the population within these energy levels is shortcompared to the lifetime of that level. The measurement of the spectral shape of theemission cross section is sufficient to determine the shape of spectrum of the absorp-tion cross section (and vice versa). The absorption cross section is derived from theemission cross section by [42]

σa(λ) = σe(λ)e( hc

λ−E0)

kBT (2.27)

where E0 is the temperature-dependent excitation energy, which is the net free energyrequired to excite a rare earth ion from a particular energy level into an excited stateof higher energy at temperature T [35]. At the crossover frequency νc (νc = E0/h),the emission equals absorption. Although the shape of the absorption and emissioncross sections are slightly different, the integrated absorption and emission cross sec-tions are equal.The McCumber method is often used to determine the excited state absorption crosssections. Generally, for praseodymium, the shape of the 1D2 – 1G4 and 3P0 – 1G4

photoluminescence bands will be used to determine the signal excited state absorp-tion (ESA) and pump ESA cross sections, however in the selected germanium gallium


sulphide glasses, the 1D2 – 1G4 emission could not be observed and the photolumi-nescence originating from the 3P0 – 1G4 transition is overlapped by other transitions.Hence, no ESA cross sections could be determined for praseodymium doped germa-nium gallium sulphide glasses.


The results of the absorption spectroscopy and photoluminescence spectroscopy mea-surements were combined to perform a Judd-Ofelt (J-O) analysis. The J-O param-eters were obtained through a least-squares fitting algorithm and using the matrixelements U (i) for praseodymium by Weber [43]. The J-O parameters, derived fromthe absorption cross section data, were used to calculate the oscillator strength. Theexperimentally measured (using equation 2.16) and calculated oscillator strengths arepresented in Table 2.8.The Judd-Ofelt parameters obtained for praseodymium doped germanium galliumsulphide glasses are summarised in Table 2.9. In contrast to its theoretical defini-tion14, in some cases a negative Judd-Ofelt parameter Ω2 is obtained from the fits.The negative value for Ω2 and the high degree of uncertainty in several of the pa-rameters is a common occurrence when the J-O theory is applied to praseodymiumions [44]. If the parameter Ω2 is negative, it is a common procedure to set Ω2 to zeroand recalculate Ω4 and Ω6 for this case (see Table 2.9). The margins of error in Ω2,Ω4 and Ω6, due to the linear regression procedure, are also listed in Table 2.9 andthese values are caused by the linear regression only.The processing of the experimental data and the least squares fitting algorithm areimportant factors determining the outcome of the J-O analysis. The accuracy of themeasured oscillator strength is affected by the deconvolutions necessary to separatethe 3H4 to (3F4,

3F3) and 3H4 to (3F2,3H6) ground state absorptions. Ω2 is strongly

related to the 3H4 – 3F2 transition. Furthermore, the ground state absorption tothe 1G4 and 1D2 levels are weak compared with the other transitions. The leastsquares fitting algorithm takes the absolute differences between the experimental andcalculated values of the oscillator strength into account. In the fitting procedure,small errors on a large oscillator strength will contribute as much as a relatively largediscrepancy on a small oscillator strength. Hence, the J-O parameters can dependstrongly on the relative magnitude of the data included in the fit. Quimby et al. [45]and Goldner et al. [46] proposed a weighted linear regression method, by minimisingthe sum of the relative differences. However, application of the weighted least-squaresestimation provides similar results as presented in Table 2.9, including negative valuesof Ω2. If the parameter Ω2 is negative, it is a common procedure to set Ω2 to zeroand recalculate Ω4 and Ω6 for this case.The assumption in the J-O theory that the energy difference between the 5d and 4flevels is much greater than the splitting of the 4f levels into the various [L,S,J] statesis not satisfied for praseodymium [47]. This is another source for imperfections when

14The parameters Ω2, Ω4 and Ω6 contain implicitly radial integrals, perturbation denominatorsand odd-symmetry terms of the crystalline field. As such, they should be intrinsically positive [38].


Table 2.8: The measured (using equation 2.16) and calculated oscillator (from J-Oanalysis) strengths of praseodymium doped germanium gallium sulphide glass.

Transition Measured Calculatedoscillator strength oscillator strength

3H4–3H6 67 10−8 79 10−8

3H4–3F2 562 10−8 563 10−8

3H4–3F3 953 10−8 951 10−8

3H4–3F4 444 10−8 440 10−8

3H4–1G4 119 10−8 100 10−8

3H4–1D2 509 10−8 475 10−8

applying the J-O theory to praseodymium. Therefore, the 3H4–3P2 ground state ab-

sorption is usually omitted.The parameter Ω2 is correlated with the degree of covalency of the bonds [48]. Dueto the high degree of covalency of the bonds between praseodymium and sulfide ingermanium gallium sulfide glasses, relatively high values for Ω2 are observed [8, 48]for this host material. The low values for Ω2, observed in this study may be causedby the non-stoichiometric host glass composition.The wavelength dependency of cross sections for stimulated emission were determinedfrom the 1G4 –3H5 photoluminescence spectra, exciting the glass using 1005 nm light(see Figure 2.13). Based on the calculated J-O parameters, the integrated stimulatedemission cross sections are listed in Table 2.10.The cross sections for pump ESA σp−esa could not be determined due to the overlapof the 3P0 – 1G4 and other transitions. The shape of the signal ESA cross sectionσs−esa could not be determined, because the 1D2 – 1G4 emission is not observed in thephotoluminescence spectra. However, the magnitudes of the pump ESA and signalESA cross sections are derived from the J-O analysis. The integrated excited stateabsorption cross sections based on the J-O parameters are listed in Table 2.10. Thesignal ESA cross sections are nearly three times smaller than the stimulated emissioncross section σsem.The absorption (and emission) cross sections are proportional to the transition ratesbetween the energy levels of praseodymium. These transition rates are strongly de-pendent on the local electric field around the praseodymium ion in the host glass.The refractive index is a measure of the strength of the local electric field. Due to therelatively high refractive index (n ≈ 2) of the sulphide host glasses, the cross sectionsare large compared to those of e.g. fluoride glasses (n ≈ 1.5) [8].The luminescence quantum efficiency is defined as the ratio between the (measured)emission lifetime τe and the radiative lifetime τr

ηpl =τe

τr(2.28)


Table 2.9: The Judd-Ofelt parameters of praseodymium doped germanium galliumsulphide glasses determined in this study.

Composition [at.%], Ω2 Ω4 Ω6

Pr conc. [ppm Wt] [×10−20 cm2] [×10−20 cm2] [×10−20 cm2]

Ge29.7Ga1.2S69.1 398 -2.3 ± 9.5 5.2 ± 11 4.2 ± 4.70 2.6 ± 3.5 5.1 ± 2.3

Ge29.7Ga1.2S69.1 393 0.4 ± 1.9 6.2 ± 2.2 6.2 ± 0.9Ge28.8Ga1.2S70.0 378 0.2 ± 1.0 4.2 ± 1.2 4.2 ± 0.5Ge27.7Ga1.1S71.1 383 -0.5 ± 1.8 4.8 ± 2.2 4.2 ± 9.1

0 4.2 ± 0.7 4.4 ± 0.5Ge27.0Ga1.1S71.9 371 -0.8 ± 1.2 6.8 ± 1.4 5.2 ± 0.6

0 5.9 ± 0.5 5.5 ± 0.3Ge29.2Ga1.8S69.0 391 -0.1 ± 0.9 5.2 ± 0.9 4.2 ± 0.4

0 5.0 ± 0.3 4.2 ± 0.2Ge28.5Ga3.0S68.5 439 0.5 ± 1.4 6.3 ± 1.7 6.1 ± 0.7

Table 2.10: The integrated stimulated emission σsem (1G4–3H5) , signal ESA σs−esa

(1G4–1D2) and pump ESA σp−esa (3P0–

1G4)cross sections from the Judd-Ofelt pa-rameters for praseodymium doped germanium gallium sulphide glasses.

Composition [at.%], σsem [cm−2] σs−esa [cm−2] σp−esa [cm−2]Pr conc. [ppm Wt]

Ge29.7Ga1.2S69.1 398 1.4 10−8 3.4 10−9 1.9 10−9

Ge29.7Ga1.2S69.1 393 1.9 10−8 6.4 10−9 4.7 10−9

Ge28.8Ga1.2S70.0 378 1.3 10−8 4.1 10−9 3.1 10−9

Ge27.7Ga1.1S71.1 383 1.3 10−8 3.7 10−9 3.2 10−9

Ge27.0Ga1.1S71.9 371 1.7 10−8 4.8 10−9 4.4 10−9

Ge29.2Ga1.8S69.0 391 1.3 10−8 3.8 10−9 3.8 10−9

Ge28.5Ga3.0S68.5 439 1.9 10−8 6.5 10−9 4.7 10−9


Table 2.11: Measured emission lifetimes τe and calculated radiative lifetimes τr,branching ratios βr and luminescence quantum efficiency ηpl of the 1G4 – 3H5 tran-sition from the Judd-Ofelt parameters for praseodymium doped germanium galliumsulphide glasses.

Composition [at.%], τe(λ = 1340) τr βr ηpl

Pr3+ conc. [ppm Wt] [µs] [µs] [-] [-]

Ge29.7Ga1.2S69.1 398 356 1610 0.68 0.22Ge29.7Ga1.2S69.1 393 368 1030 0.63 0.36Ge28.8Ga1.2S70.0 378 322 1540 0.63 0.21Ge27.7Ga1.1S71.1 383 380 1510 0.64 0.25Ge27.0Ga1.1S71.9 371 339 1180 0.64 0.29Ge29.2Ga1.8S69.0 391 365 1570 0.64 0.23Ge28.5Ga3.0S68.5 439 322 1090 0.64 0.30

The radiative lifetime τr and branching ratio βr for the 1G4 – 3H5 transition are de-rived from the J-O parameters. The emission lifetime, radiative lifetime and branchingratio and luminescence quantum efficiency are summarised in Table 2.11. The radia-tive lifetime and the quantum efficiency of the 1G4 level are strongly determined byΩ6. The emission lifetime is comparable to results published by Simons [8], whilethe radiative lifetime is longer than observed by Simons. The emission lifetime andradiative lifetime are 360 µs and 500 – 680 µs [8], respectively. Hence, the lumines-cence quantum efficiency for the praseodymium doped germanium gallium sulphideglasses is lower than reported by Simons. The branching ratio is slightly higher. Thesignificance of the longer radiative lifetime is explained in the next section. In thepraseodymium doped germanium gallium sulphide glasses, the signal GSA and signalESA around 1310 nm (signal wavelength) are negligible. The pump power efficiency(i.e. the gain divided by absorbed pump power) of a fibre amplifier (for small inputsignals) is proportional to the product of the cross section for stimulated emissionσsem and the emission lifetime τe [49]. For the selected germanium gallium sulfideglasses σsemτe is 160–260 10−16 cm2s, slightly lower than the efficiency for glasseswith higher gallium content reported by Simons [8]. The typical σeτe product influoride glasses (ZBLAN) is 35–40 10−16 cm2s [8, 48]. Hence, it is expected that thepump power efficiency for an amplifier based on germanium gallium sulphide glassesis higher than that of an amplifier based on fluoride glasses.

2.4 Interactions between host glass and dopant

Depopulation of the 1G4 state by non-radiative energy transfer (lattice vibrations(phonons) of the glass host) is an important source for efficiency losses in praseody-mium doped fibre amplifiers. The number of phonons needed to bridge the energygap non-radiatively decreases as the energy of the involved phonons is higher. The


rate of the relaxation process is governed by the highest energy phonons in the glasshost, while the phonon energy is determined by host glass composition and structure.Glasses, in which the energy of the most energetically phonons is low, are so-calledlow phonon energy glasses. In these glasses, the multi-phonon relaxation rate is low,due to the lower probability of simultaneous emission of a large number of phonons,and hence a high luminescence quantum efficiency is obtained.In the next section, the structure and phonon energy level of germanium galliumsulphide glass is discussed. In section 2.4.2, the depopulation of the exited statesthrough non-radiative transitions (i.e. energy transfer due to phonons) is described.

2.4.1 Structure and phonon energy

The structure of germanium sulphide glasses has been studied by several authors(see e.g. [32, 50] and references therein). Germanium sulphide glasses consist of athree-dimensional, short term, chemically ordered network of four-coordinated ger-manium atoms and two-coordinated sulphur atoms. The amorphous network is builtby four-coordinated germanium and two-coordinated sulphur, which form [GeS4]

4−

tetrahedral units which are linked by edges and corners. In sulphur rich glasses alsoS-S bonds co-exist. The tetrahedral germanium sites are linked by one or two sulphuratoms. Sulphur S8 rings are incorporated in the structure when the sulphur contentexceeds 75 at.%.In germanium gallium sulphide glasses containing less than 5 at.% gallium, the basicstructural units in the glass network are germanium tetrahedra. Inanova [51] sug-gested the formation of three-coordinated gallium sites [51]. According to March-ese et al. [52], gallium is incorporated in the glass matrix as [GaS4]

5− tetrahe-dra. In praseodymium doped glasses, the electro-neutrality is kept by the positivelycharged praseodymium dopant, which is located near these negatively charged gal-lium sites [8, 52]. Hence gallium facilitates the solubility of praseodymium ions.Vibrational spectroscopy (Raman and IR) can be used to characterise the structureof the glass. Here, Raman scattering spectroscopy is used to determine the phononenergy. A (GeS3)98(Ga2S3)2 glass sample was irradiated with a focused Kr-ion laser.The intensity of the (polarised) incident beam was 50 mW at 647 nm. The anglebetween the incident and scattered beams is 45. The Raman peaks were detected inthe HH (horizontal-horizontal, i.e. the state of polarisation (SOP) of the incident andscattered light beams are parallel) and VH polarisations (vertical-horizontal, i.e. theSOP of the incident and scattered light beam are perpendicular). The positions of thepeaks are the same in both polarisations, while the intensities are different. The depo-larisation ratio HV/HH provides information about the symmetry characteristics ofthe vibrations. However, the state of polarisation of the Raman scattering is affectedby slight spatial variations of the effective refractive index e.g. due to inhomogeneityof the glass. The temperature dependency of the Raman intensity was eliminatedfrom the experimental Raman spectra using the reduction scheme by Shucker andGammon [50].The reduced HH and VH Raman spectra of a (GeS3)98(Ga2S3)2 glass are shown inFigure 2.20. The assignment of the observed bands to the vibrational modes is well


a) b) c) d)

Figure 2.19: Vibration modes of GeS4 and GaS4 tetrahedra [54]. a) A1 symmetricalstretching mode b) E1 symmetrical bending c) F2 asymmetrical stretching d) F2

asymmetrical bending.

documented [8, 32, 50, 51, 53]. The vibration modes are depicted in Figure 2.19. Thepeak at 344 cm−1 is assigned to the A1 modes of [GeS4]

4− and [GaS4]5− tetrahedra.

The shoulder at 370 cm−1 represents the F2 mode of the germanium and galliumtetrahedra. In the Raman spectrum, S-S bonds are observed around 475 cm−1 (A1

stretching mode). The small peaks at 152 cm−1 and 219 cm−1 indicate the presenceof sulphur S8 rings in the glass. These vibrations are associated to the E2 (bending)and A1 (symmetric) modes respectively. The vibrations of S3Ge-S-GeS3 and S3Ga-S-GaS3 are located at approximately 435 cm−1, while S3Ge-GeS3 and S3Ga-GaS3

vibrations are located at 265 cm−1 The effective phonon energy of the germaniumgallium sulphide glass (i.e. the cut-off energy determined from Figure 2.20) is limitedto approximately 490 cm−1, due to the presence of S-S bonds in this sulphur richglass. No Raman bands beyond 500 cm−1 were observed in sulphur rich germaniumgallium sulfide glasses [8].Impurities may affect the phonon energy in the vicinity of the praseodymium dopant(i.e. the phonon energy of Ge-O is approximately 780 cm−1 [8]). Both Simons [8] andMarchese et al. [30] suggest that hydroxyl in the vicinity of gallium tetrahedra mayprovide an attractive site for praseodymium ions. According to Simons, incorporationof hydroxide is associated with the replacement of sulphur from the tetrahedron byoxygen attached to OH. In this case, praseodymium is attracted by the negative chargeof the hydroxyl ion. Marchese et al. propose a compensation of the negative chargeof the gallium tetrahedron by the overall positive charge of a [−H...O-Pr3+-O...H−]structural unit.

2.4.2 Non-radiative transitions

In general, the radiative lifetime τr calculated by equation 2.23 exceeds the measuredemission lifetime τe, due to non-radiative relaxation. The non-radiative lifetime τnr isderived from the measured emission lifetime τe and the calculated radiative lifetimeτr

1

τnr=

1

τe− 1

τr(2.29)


0

500

1000

1500

2000

2500

0 50 100 150 200 250 300 350 400 450 500

Inte

nsity

[a.

u.]

Raman shift [cm-1]

HH

VH

Figure 2.20: Raman spectra of a (GeS3)98(Ga2S3)2 glass in HH (horizontal-horizontal)and VH (vertical-horizontal) polarisations.

The non-radiative rate Wnr, to the next lower energy level, is given by

1

τnr= Wnr (2.30)

Low non-radiative relaxation rates are advantageous because the transitions becomepredominantly radiative (less quenched) resulting in a higher photoluminescence effi-ciency.In the non-radiative relaxation process, the energy of the excited rare earth ion islowered by generation of phonons (lattice vibrations). When the energy differencebetween the excited state and the next lower level ∆E (expressed in cm−1) is largerthan the phonon energy, a discreet number of phonons of an energy hω is emitted. Ac-cording to the multi-phonon relaxation theory by Riseberg and Moos for non-radiativedecay [55]), the non-radiative relaxation rate Wnr at low temperature is given by

Wnr(0) = Bnre(−Anr∆E) (2.31)

where Anr and Bnr are phenomenological constants. Anr is determined by the effec-tive phonon energy and the rare earth ion-phonon coupling strength. At low dopantconcentrations, the non-radiative transition is mainly due to interaction of the excitedrare earth ion and the lattice vibrations of the host. Hence, the relaxation rate is onlyrelated to the glass composition and not on the rare earth ion involved or a particulartransition. The temperature dependence of the non-radiative relaxation rate [55], tothe next lowest energy level of the rare earth ions, is given by

Wnr(T ) = Wnr(0)

[

1

e

“

hωkBT

”

− 1

+ 1

]pp

(2.32)


Table 2.12: Phonon energy hω, multi-phonon relaxation parameters Anr and Bnr forvarious glass hosts [56, 57].

host glass hω Bnr Anr

[cm−1] [s−1] 10−3 [cm]

silicate 1100 1.4 1012 4.7fluorozirconate 500 1.6 1010 5.2Ge25Ga10S65 375 7.9 106 3.2Ga-La sulfide 350 1.0 106 2.9

where kB is the Boltzmann constant and the number of phonons (with vibrationenergy ω) required to bridge the energy gap is given by

pp =∆E

hω(2.33)

The parameters describing the multi-phonon relaxation rates of rare earths in severalhost glasses and low dopant concentrations are listed in Table 2.12 [56, 57]. Theserelaxation rates were derived from the measured emission lifetimes and radiative life-times (calculated by J-O analysis) for multiple rare earth ions as a function of theenergy gap to the next lower level.The non-radiative lifetime of the transition between the 1G4 and 3F4 level for praseo-dymium doped germanium gallium sulfide glasses is estimated using the data byShin [57] for a Ge25Ga10S65 host glass (see Table 2.12). Note that non-radiative de-cay to intermediate energy levels lower than the 3F4 level is negligible due to theincreased energy difference. The energy difference between the 1G4 and 3F4 states isapproximately 2945 cm−1 (see section 2.3.2). Based on the maximum phonon energyof the germanium gallium sulphide glass host of 490 cm−1, the number of phonons tobridge this energy gap equals 6. The multi-phonon relaxation rate Wnr is estimatedusing equations 2.31 and 2.32 and the values for Anr and Bnr as listed in 2.12. Themulti-phonon relaxation rate Wnr of the 1G4 level to the 3F4 level is approximately1150 s−1 (at room temperature), which corresponds to a non-radiative lifetime of870 µs. A non-radiative lifetime of 450–575 µs is obtained, for the glasses preparedin this study, from direct calculation using equation 2.29 on the data as presented inTable 2.11. Using these non-radiative lifetimes τnr (as listed in in Table 2.11) and thedata for Anr and Bnr for effective phonon energy of Ge25Ga10S65 (see Table 2.12), theestimated phonon energy of the germanium gallium sulphide glasses, prepared in thisstudy, is 410 – 416 cm−1. These values are lower than the maximum phonon energy(490 cm−1) determined by Raman spectroscopy directly. This result indicates thatthe multi-phonon relaxation rate is probably not predominantly determined by themaximum phonon energy of the host glass, but on a lower, effective phonon energy.The luminescence quantum efficiency is affected by the multi-phonon relaxation rate(see equation 2.28), which is directly related to the rate of multi-phonon decay in thehost glass. Due to the strong dependency on the effective phonon energy (hω), large


differences are observed for the non-radiative relaxation rates between rare earth en-ergy levels in different host glasses [47].Impurities incorporated in the glass host (see section 2.2.1) facilitate non-radia-tivetransitions. The emission lifetime of the 1G4 state decreases with increasing hydroxyand oxygen content [8]. In the case of oxygen impurities, which are incorporatedin the structure, the luminescence quenching is caused by multi-phonon relaxation.Quenching by hydroxyl (OH−) ions is especially significant, due to their strong broadabsorption bands and overtones in mid infrared region [58]. The main absorptionpeak of hydroxyl is located around 2.8 µm (3545 cm−1). The overtone of the stretch-ing vibration mode is situated around 1.4 µm (7090 cm−1), which overlaps with the1.3 µm 1G4–

3H5 transition. The energy of the excited praseodymium ions is con-verted non-radiatively into vibrations of the hydroxyl ions.In germanium gallium sulfide glasses praseodymium ions tend to locate in the neigh-bourhood of the gallium and hydroxyl sites [8, 30]. In these gallium containing glasses,hydroxyl quenching is dominated by the Ga-OH absorption around 3350 cm−1 [8].The luminescence quenching is governed by the coupling (interaction distance) be-tween the praseodymium ion and hydroxyl ions. An empirical relationship betweenthe measured emission lifetime and the emission lifetime τe,0 in the absence of hy-droxyl quenching [58] is given by

1

τe=

1

τe,0+ 8πC

3/4Pr C

1/4OHNPrNOH (2.34)

The transfer constants CPr and COH are host dependent. The luminescence quench-ing is proportional to both the number of hydroxyl (NOH) and praseodymium (NPr)ions per unit of volume. The luminescence quenching becomes less pronounced as theconcentration of hydroxyl is smaller than the concentration of praseodymium.While the wavelength dependent intensity of the photoluminescence spectrum is notaffected by hydroxyl quenching, the quenching results in non-exponential photolu-minescence decay curves (i.e. multiple decay processes with different time constantsare involved in the photoluminescence decay). The effect of hydroxyl quenching onthe lifetime is observed by the presence of a fast decay component (τ ≈ 40 µs [30])in the photoluminescence decay curves in hydroxyl containing glasses. No hydroxylquenching was observed in the photoluminescence decay of the samples used in thisstudy.

2.5 Thermal properties of the host glass

The “thermal properties”, in particular the glass transition Tg, crystallisation Tx andso-called melting temperatures Tm, thermal expansion coefficient αl and viscosity µ,are important in view of the selection of suitable glasses for fibre drawing. The ther-mal properties of the core and cladding materials should be compatible in order toprocess the material and manufacture fibres without defects. The difference betweenthe glass transition temperature Tg and the higher crystallisation temperature Tx (no


crystallisation occurs below this temperature within normal time spans) is a measurefor the glass stability. The working temperature in the fibre drawing process is re-stricted to the region between Tg (lower boundary temperature) and Tx (maximumtemperature). In this temperature range, the material can be deformed without theoccurrence of crystallisation. If the difference between Tg and Tx is small, the tem-perature at which the viscosity of the material is low enough to produce a fibre, isclose to the crystallisation temperature and the material will tend to crystallise duringdrawing.In the next section, the determination of glass transition and crystallisation tempera-tures of the germanium gallium sulphide glasses using differential scanning calorimetry(DSC) is described. The thermal expansion of the glasses is described in section 2.5.2,while the rheological behaviour (i.e. viscosity-temperature relationship) is given insection 2.5.3.

2.5.1 Glass transition and crystallisation temperatures

In Table 2.13, the glass transition temperatures and crystallisation temperatures forvarious germanium gallium sulphide glasses, given in literature, are summarised. Theglass transition temperatures and crystallisation temperatures are usually determinedby differential scanning calorimetry (DSC). In DSC, a sample and a reference mate-rial are simultaneously heated according to a pre-defined temperature programme.The temperature of both sample and reference is controlled in order to keep the sametemperature. While being heated, the difference in energy inputs to the sample andreference are measured. The energy input to the sample changes remarkably whenthe heat capacity of the sample changes [59] e.g. when a phase or other structuraltransition occurs, or at the glass transition temperature or crystallisation tempera-ture15.According to Abe et al. [4] and Saffarini [5], the highest glass transition temper-ature is observed for germanium gallium sulfide glasses glasses with stoichiometriccomposition16. In ternary glasses, excess sulphur reduces the glass transition tem-perature. For binary GeSx glasses, the glass transition temperature also decreaseswith increasing sulphur content [2]. In the Ge-S binary system, the glasses becomemore stable when increasing the sulphur content, while the stability decreases for Gacontaining glasses [4]. The changes in the glass transition temperature observed byLoireau et al. [3] in germanium gallium sulphide glasses as a function of Ga2S3 con-tent are much smaller than the differences observed by Abe [4]. The crystallisationbehaviour of ternary glasses is dependent on the Ga2S3 contents of the glass [3]. InDSC measurements, crystallisation is characterised by the release of crystallisationenergy (exothermic reaction). Below 15 mole% Ga2S3 (in stoichiometric germaniumgallium sulphide glasses) only a single crystallisation peak (around 520 C) is found.The crystalline phase contains α-GeS2 and crystalline Ga2S3. At higher Ga2S3 con-

15The definition of characteristic temperatures and the methods for determination of these tem-peratures from the DSC measurements are explained in e.g. Brown et al. [59].

16The definitions of stoichiometric and non-stoichiometric glass compositions are given in section2.1.1.


tent, a new crystalline phase is formed between 450 and 480 C. The composition ofthis phase could not be determined by Loireau et al. [3]. Around 520 C, this phasedecomposes into a mixture of crystalline α-GeS2 and Ga2S3. According to Simons [8]in ternary glasses containing excess sulphur ((GeS3)100−y(Ga2S3)y) this phenomenonstarts at y = 10 mole%.In this study, some thermal properties of the germanium gallium sulphide glasses wereevaluated with combined differential scanning calorimetry / thermogravimetry (DSC/ TG). The mass loss due to decomposition of the glass samples (small particles) atelevated temperatures was studied using a Netzsch STA 409C. The space inside thefurnace section was flushed with argon at a flow rate of 50 ml/min. The weights ofboth sample and alumina powder reference were approximately 100 mg. The sampleand reference were heated simultaneously in alumina crucibles at a rate of 5 K/minfrom ambient temperature to 900 C, while the difference in energy inputs (heat flow)to the sample and reference is measured. Note that the measured characteristic tem-peratures will shift to higher temperatures when higher heating rates are applied.The thermogravimetry curve is shown in Figure 2.21. Although the sample containedexcess sulphur over the stoichiometric value, no mass loss (associated with volatilisa-tion of sulphur [1]) is observed between 160 and 300 C. In the region above 600 Cmass loss is observed. The mass loss is probably caused by the release of sulphur.The arrows in the figure indicate the mass loss due to sulphur evaporation, associ-ated with the formation of the stoichiometric compositions a) (GeS2)98(Ga2S3)2 andb) (GeS1)98(Ga2S3)2 and gaseous sulphur species. Simultaneous to the mass loss, abroad exothermal effect between 600 and 750 C is observed in the DSC signal (seeFigure 2.21). The exothermal effect indicates a slow crystallisation process, whichprobably can be associated to the crystallisation of a mixture of GeS2 and Ga2S3.The endothermic peak, at temperatures above 750 C may be caused by melting ofthe residual sample material.Near the glass transition temperature Tg, the temperature dependency of the specificheat of a glass changes slightly and this can normally be detected by DSC. The Net-zsch STA 409C was not sensitive enough to detect the glass transition temperature. ATA Instuments STD 2960 was used for simultaneous DSC / TG analysis at a heatingrate of 5 K/min from ambient temperature to 600 C. The samples (small particles)of approximately 20 mg were heated in alumina crucibles. As a reference, an emptyalumina crucible was used. The furnace section was flushed with argon at a flow rateof 100 ml/min. The DSC curves for different germanium gallium sulphide glasses,prepared in this study, are shown in Figure 2.22. The measured glass transition tem-peratures Tg and crystallisation temperatures Tx (at the onset of the crystallisationpeak) are summarised in Table 2.14. In all cases the crystallisation of the glasses iscombined with simultaneous mass loss (decomposition). The measured crystallisa-tion temperatures Tx are higher than the values obtained by Simons [8]. The lowercrystallisation temperature of Simons’ glasses (see Table 2.13) may be explained bythe higher sulphur content of the glasses, compared to the glasses listed in Table 2.14.The sulphur content of the glasses, prepared in this study, is more close to the stoi-chiometric composition. Probably, decomposition of the sulphur rich glasses resultsin local defects, which act as nuclei for the crystallisation process.


Table 2.13: Glass transition temperatures Tg and onset crystallisation temperaturesTx as determined by DSC.

Nominal composition Tg [C] Tx [C] Tx-Tg [C] Reference

Ge25Ga5S70 450 [60]Ge25Ga10S65 400 780 380 [61]Ge29.1Ga5S65.9 436 567 131 [62]Ge32.5Ga5S62.5 377 481 104 [62]Ge10Ga4S86 228 [5]Ge12Ga4S84 267 [5]Ge14Ga4S82 305 [5]Ge16Ga4S80 318 [5]Ge18Ga4S78 330 [5]Ge20Ga4S76 346 [5]Ge22Ga4S74 361 [5]Ge24Ga4S72 380 [5]Ge26Ga4S70 401 [5]Ge28Ga4S68 418 [5]Ge30Ga4S66 437 [5]Ge32Ga4S64 424 [5]Ge10Ga12S78 308 [5]Ge12Ga12S76 328 [5]Ge14Ga12S74 342 [5]Ge16Ga12S72 359 [5]Ge18Ga12S70 389 [5]Ge20Ga12S68 396 [5]Ge22Ga12S66 415 [5]Ge24Ga12S64 433 [5]Ge26Ga12S62 416 [5]Ge28Ga12S60 400 [5]Ge23.5Ga11.8S64.7 400 480, 520 80 [3, 63]Ge23.5Ga11.8S64.7 490, 525 [8]Ge24.4Ga1.0S74.6 515 [8]Ge23.5Ga2.5S74.1 260 515 255 [8]Ge22.0Ga4.9S73.2 440, 515 [8]Ge19.0Ga9.5S71.5 440, 515 [8]Ge25.8Ga9.1S65.2 459 619 160 [30]Ge–Ga–S 292 422, 510 130 [64]


50

60

70

80

90

100

0 100 200 300 400 500 600 700 800 900-3

-2

-1

0

1

2

Mas

s lo

ss [

%]

Hea

t flo

w [

W/g

]

Temperature [oC]

a

b

Exo

Figure 2.21: Simultaneous differential scanning calorimetry (dotted line) and thermo-gravimetry (continuous line) for a (GeS2.37)98(Ga2S3)2 sample (fine particles). Theheating rate is 5 K/min. The arrows in the figure indicate the mass loss associatedwith the formation of the stoichiometric compositions a) (GeS2)98(Ga2S3)2 and b)(GeS1)98(Ga2S3)2.

A marked difference is observed between two samples of the same nominal compo-sition (Ge29.7Ga1.2S69.1). As these samples also showed different optical properties(e.g. refractive index), the real compositions of these samples may be dissimilar.The glass stability depends on the molecular structure of the glass. In the S-richregion, S-S bonds and S8 rings are formed, while S-S bonds connect GeS4/2 andGaS4/2 [4]. In germanium gallium sulphide glasses, gallium competes with germa-nium to form tetrahedra [8]. Due to the loss of excess sulphur (decomposition) atelevated temperatures the composition of the remaining material will resemble thestoichiometric composition. Probably, decomposition of the sulphur rich glasses re-sults in local defects, which act as nuclei for the crystallisation process. Hence, thismaterial may be prone to crystallisation.The fibre drawing process is hampered by both crystallisation and decomposition ofthe glass, which reduces the strength of the fibre (causing breakage of the fibre). Fur-thermore, the optical properties of the glass fibre are deteriorated (e.g. attenuationlosses increase due to scattering).

2.5.2 Thermal expansion

At the glass transition temperature Tg a small change in the thermal expansion coef-ficient is observed, which can be detected using dilatometry. Samples with an initiallength of about 25 mm and a diameter of 8 mm were heated at a rate of 5 K/minin the measuring chamber of a Bahr 801v dilatometer. The measuring chamber was


-0.20

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

0.20

0.25

0.30

150 200 250 300 350 400 450 500 550 600

Hea

t flo

w [

W/g

]

Temperature [oC]

Tg Tx

Exo

Composition at.% Ge29.7Ga1.2S69.1Ge29.7Ga1.2S69.1Ge28.8Ga1.2S70.0Ge27.7Ga1.1S71.1Ge27.0Ga1.1S71.9Ge29.2Ga1.8S69.0Ge28.5Ga3.0S68.5

Figure 2.22: Differential scanning calorimetry for various (GeSx)100−y(Ga2S3)y sam-ples. The heating rate is 5 K/min.

Table 2.14: Onset glass transition temperatures Tg and crystallisation temperaturesTx as determined by DSC.

Nominal composition Tg [C] Tx [C] Tx-Tg [C]

Ge29.7Ga1.2S69.1 351.8 560 208.2Ge29.7Ga1.2S69.1 390.2 572.4 182.2Ge28.8Ga1.2S70.0 374.4 530.1 155.7Ge27.7Ga1.1S71.1 329.5 508.4 178.9Ge27.0Ga1.1S71.9 314.2 542.8 228.6Ge29.2Ga1.8S69.0 367.7 540.4 172.7Ge28.5Ga3.0S68.5 373.4 547.2 173.8


0

0.2

0.4

0.6

0.8

1.0

50 100 150 200 250 300 350 400 450

Rel

. Len

gth

chan

ge [

%]

Temperature [oC]

Tg

Composition at.% Ge24.4Ga1.0S74.6Ge27.8Ga1.1S71.1Ge29.7Ga1.2S69.1

Figure 2.23: Dilatometry on (GeSx)98(Ga2S3)2 glass samples.

Table 2.15: Glass transition temperature Tg and Thermal expansion coefficient αl

between 150 – 250 C from dilatometric measurement of (GeSx)98(Ga2S3)2 glasses.

Nominal composition Tg [C] αl [K−1]

Ge29.7Ga1.2S69.1 384 18 10−6

Ge27.8Ga1.1S71.1 325 21 10−6

Ge24.4Ga1.0S74.6 285 22 10−6

flushed with argon. The results are depicted in Figure 2.23 and summarised in Ta-ble 2.15. As the sulphur content of the glasses increases, the glass transition tempera-ture decreases, which is in agreement with the data obtained by differential scanningcalorimetry. The difference in the glass transition temperature obtained by dilatome-try and by DSC, may be explained by the slower internal heating of the large samplesused in the dilatometer.The linear thermal expansion coefficient was determined in the 150 – 250 C region.The expansion coefficient increases as the sulphur contents increases.

2.5.3 Viscosity

The viscosity temperature relationship, in the viscosity range relevant for fibre draw-ing, was measured by parallel plate rheometry using a Perkin-Elmer TMA-7. Thistechnique is suitable to determine the glass viscosity between 106 and 1010 Pa s [65].For the Ge24.4Ga1.0S74.6 glass the experimentally determined viscosity is shown inFigure 2.24. The line in Figure 2.24 presents the so-called Vogel-Fulcher-Tammannn


106

107

108

109

1010

1011

1012

1013

250 300 350 400 450 500

Vis

cosi

ty [

Pa.s

]

Temperature [oC]

Viscosit

Figure 2.24: The viscosity-temperature relation for Ge24.4Ga1.0S74.6 glass melt. Thesymbols (+) represent the measured data, the dashed line is an extrapolation of theexperimental data using equation 2.35.

viscosity relation [66] determined for this glass, which is given by

logµ

Pa s= −39.6 +

81.8 × 103

T + 13.0 × 102(2.35)

with the viscosity µ in Pa s and the temperature T in C. The glass transition tem-perature Tg is estimated from this relationship as the temperature at a viscosity µ ofapproximately 1012.4 Pa s.The estimated glass transition temperature Tg is 275 C, which is in close agreementwith the value 285 C obtained by dilatometric measurement. At the softening pointthe glass has a viscosity of approximately 108.6 Pa s. The onset fibre drawing tem-perature Tf is defined as the minimum temperature required for fibre drawing, i.e.at sufficiently low viscosity for fibre drawing. The onset fibre drawing temperatureTf (at µ = 107 Pa s) is 465 C. The viscosity of binary GeSx melts was investi-gated by Malek [67]. Increasing the sulphur content, in excess of the stoichiometriccomposition, results in a decreased viscosity.

2.6 Conclusions

Praseodymium doped germanium gallium sulphide glasses can be prepared by meltinghigh purity germanium, gallium and sulphur in silica ampoules at 1000 C. Purifica-tion of the raw materials, especially sulphur, is needed to obtain highly transparenthost glasses. The OH and SH impurity levels in the glasses, prepared in this study,are 2.5 – 4.5 ppm and 16 – 85 ppm, respectively. These impurity levels are sufficiently


low to obtain germanium gallium sulphide glasses, which are highly transparent inthe 0.5–8.0 µm wavelength range.The refractive index of the glasses, which is slightly dependent of the composition,was determined in the wavelength range 0.4–1.0 µm. The refractive index, determinedby ellipsometry, and measurements of the Brewster angle, are in good agreement withthe refractive indices for germanium gallium sulphide glasses reported in literature.The refractive index, near the praseodymium doped fibre amplifiers’ pump and signalwavelengths, is approximately 2.07.It is concluded that the difference in the refractive index of core and cladding glass,needed to construct an optical fibre, can be achieved by a small difference in thesulphur content of core and cladding glasses.The radiative (absorption and emission) properties of the praseodymium in the germa-nium gallium sulphide host glass were quantitatively characterised using Judd-Ofelttheory. The Judd-Ofelt parameters, for the electron transitions due to absorptionand emission of radiation by the praseodymium ions, were used to establish the sig-nal emission cross section and both pump and signal ground state absorption crosssections. These cross sections are needed to predict the performance of a PDFA andto improve its design using a spectrally resolved amplifier model (e.g. see chapter 4).The signal excited state absorption (ESA) and pump ESA cross sections could not bedetermined for the selected germanium gallium sulphide glasses, because respectivelythe 1D2 – 1G4 emission could not be observed and the photoluminescence originat-ing from the 3P0 – 1G4 transition is overlapped by other transitions. This lack ofdata for both cross sections will have a minor effect on the optimum design of thepraseodymium doped fibre amplifier as determined by the amplifier model.Besides absorption or emission of photons, the energy state of the praseodymium ioncan change by non-radiative (e.g. multi-phonon) energy transfer to the host glass.The energy difference between the 1G4 and 3F4 state of praseodymium in the germa-nium gallium sulphide glasses is approximately 2945 cm−1, while the effective phononenergy of the host glass is limited to 490 cm−1. The (measured) emission lifetime ofthe 1G4 – 3H5 transition is approximately 400 µs. The estimated multi-phonon relax-ation rate of the 1G4 level is approximately 1150 s−1 (at room temperature), whichcorresponds to a non-radiative lifetime of 870 µs. The luminescence quantum effi-ciency (circa 30%) of the germanium gallium sulphide glasses, prepared in this studyis lower than the efficiency of the glasses reported by Simons [8] (53–72%) but higherthan the efficiency of fluoride (ZBLAN) glasses (4%, [8]).The difference between the glass transition temperature Tg and the crystallisationtemperature Tx is a measure for the glass stability in the forming process (e.g. fi-bre drawing). The glass transition temperature of the germanium gallium sulphideglasses, prepared for this study, is approximately 360 C, and the crystallisation tem-perature is approximately 185 C higher than the glass transition temperature. Fromthe viscosity - temperature relation, it is concluded that the viscosity of the glass issufficiently low to draw fibres well below the crystallisation temperature (see chap-ter 3).


2.7 Nomenclature

VectorsEp electric field strength parallel direction V m−1

Es electric field strength perpendicular direction V m−1

ScalarsA transition rate of electric dipole transition HzAnr multi-phonon relaxation parameter mBnr multi-phonon relaxation parameter HzBj short notation for the factor defined by equation 2.21 m2

c speed of light in vacuum =2.99792 108 m s−1

C concentration mole l−1

Cppm concentration ppmCPr host dependent transfer constant s−1m6

COH host dependent transfer constant s−1m6

d optical path length me elementary charge = 1.602 10−19 CE energy eVE0 temperature-dependent excitation energy JEv energy of valence band eVEc energy of conduction band eVf oscillator strength -fabs oscillator strength of absorption transition -fed oscillator strength of electric dipole transition -femit oscillator strength of emission transition -h Plank’s constant =6.62559 10−34 JsI intensity -I0 initial intensity -aJ total angular momentum of the initial statebJ ′ total angular momentum of the terminal statek extinction coefficient -kB Boltzmann’s constant =1.38066 10−23 J K−1

M molar mass g mole−1

m electron mass = 9.10953 10−31 kgN complex index of refraction -NOH hydroxyl concentration 1 m−3

NPr3+ praseodymium dopant concentration 1 m−3

n index of refraction -n0 index of refraction of air -n1 index of refraction of glass -p pressure Papp number of phonons -rp perpendicular Fresnell reflection coefficient -rs parallel Fresnell reflection coefficient -


Ttr total transmittance -Ttr0

intensity of incident light -T temperature KTg glass transition temperature KTd decomposition temperature KTm melting temperature KTx crystallisation temperature Kv phase velocity of light in a material m s−1

V ji short notation for the probability defined by -

equation 2.20Wnr non-radiative transition rate Hz

α absorption coefficient m−1

αl linear thermal expansion coefficient K−1

βr branching ratio -∆ phase difference between incident and reflected light

∆E Energy difference between two energy levels Jδ1 phase difference between p and s components

of the electric field of the incident light

δ2 phase difference between p and s componentsof the electric field of the reflected light

ǫM molar extinction coefficient l mole−1cm−1

ǫ dielectric constant -ǫ0 permittivity of vacuum =8.85419 10−12 Fm−1

ǫ1 real part of the dielectric constant -ǫ2 imaginary part of the dielectric constant -ηpl luminescence quantum efficiency -µ viscosity Pa sλ wavelength mλp pump wavelength mν frequency Hzνc crossover frequency Hzρ density kg m−3

σa absorption cross section m2

σe emission cross section m2

σp−esa pump excited state absorption cross section m2

σs−esa signal excited state absorption cross section m2

σsem signal emission cross section m2

τ internal transmittance -τe emission lifetime sτr radiative lifetime sτnr non-radiative lifetime sφ1 angle of incidence

φ2 angle of refraction

φB Brewster (principal) angle


χ local field correction factor for the electric field -Ψ angle which tangent is the ratio of the absolute values -

of the parallel and perpendicular total reflectioncoefficients

ω vibration frequency HzΩt characteristic (Judd-Ofelt) intensity parameters m2

2.8 Bibliography

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[23] X. Liu, B. Kale, V. Tikhomirov, and A. Jha, “Reduction of OH−-related photo-luminescence quenching in Pr3+-doped GeS2-based glasses by means of purifica-tion,” J. Non-Cryst. Solids, vol. 256&257, pp. 294–298, 1999.

[24] J. Kobelke, J. Kirchhof, K. Schuster, and A. Schwuchow, “Effects of carbon,hydrocarbon and hydroxide impurities on praseodymium doped arsenic sulfidebased glasses,” J. Non-Cryst. Solids, vol. 284, pp. 123–127, 2001.

[25] D. Wood and J. Tauc, “Weak absorption tails in amorphous semiconductors,”Phys. Rev. B, vol. 5, no. 8, pp. 3144–3151, 1972.


[26] D. Turnbull and S. Bishop, “Rare earth dopants as probes of localized states inchalcogenide glasses,” J. Non-Cryst. Solids, vol. 223, pp. 105–113, 1998.

[27] H. Tompkins and W. McGahan, Spectroscopic ellipsometry and reflectometry :a user’s guide. New York: John Wiley & Sons, Inc., 1999. ISBN 0-471-18172-2.

[28] O. Martins, J. Xu, and R. Almeida, “Sol-gel processing of germanium sulfidebased films,” J. Non-Cryst. Solids, vol. 256&257, pp. 25–30, 1999.

[29] R. Todorov, T. Iliev, and K. Petkov, “Light-induced changes in the optical prop-erties of thin films of Ge-containing chalcogenide glasses,” in Proceedings of theXIIIth international symposium on non-oxide glasses and new optical materials,(Pardubice, Czech Republic), pp. 382–385, September 2002.

[30] D. Marchese and A. Jha, “The structural aspects of the solubility of Pr3+ ionsin GeS2-based glasses,” J. Non-Cryst. Solids, vol. 213&214, pp. 381–387, 1997.

[31] S. Shibata, Y. Terunuma, and T. Manabe, “Sulfide glass fibers for infrared trans-mission,” Mat. Res. Bull., vol. 16, pp. 703–714, 1981.

[32] H. Takebe, H. Maeda, and K. Morinaga, “Compositional variation in the struc-ture of Ge-S glasses,” J. Non-Cryst. Solids, vol. 291, pp. 14–24, 2001.

[33] A. Seddon, D. Furniss, and D. Sims, “Gallium-lanthanum-sulphide glasses: ex-trusion of fibreoptic preforms and relevant physical properties,” in Infrared opti-cal fibers and their applications, vol. 3849, (Boston, Massachusetts), pp. 38–49,SPIE, September 1999.



[36] B. Judd, “Optical absorption intensities of rare-earth ions.,” Phys. Rev., vol. 127,pp. 750–761, August 1962.

[37] G. Ofelt, “Intensities of crystal field spectra of rare-earth ions.,” J. Chem. Phys.,vol. 37, pp. 511–520, August 1962.

[38] B. Bowlby and D. B., “Applications of the Judd-Ofelt theory to thepraseodymium ion in laser solids,” J. Luminescence, vol. 100, pp. 131–139, 2002.

[39] R. Street and N. Mott, “States in the gap in glassy semiconductors,” Phys. Rev.Lett., vol. 35, pp. 1293–1296, November 1975.

[40] S. Gu, D. Turnbull, and S. Bishop, “Broad-band excitation of Pr3+ luminescenceby localized gap state absorption in Pr:As12Ge33Se55 glass,” IEEE Photon. Tech-nol. Lett., vol. 8, no. 2, pp. 260–262, 1996.


[41] R. Quimby and B. Aiken, “Anomalous temperature quenching of fluorescence inPr3+ doped sulfide glass,” J. Appl. Phys., vol. 82, pp. 3992–3996, October 1997.

[42] D. McCumber, “Einstein relations connecting broadband emission and absorp-tion spectra,” Phys. Rev. A, vol. 136, pp. 954–957, November 1964.

[43] M. Weber, “Spontaneous emission probabilities and quantum efficiencies for ex-cited states of Pr3+ in LaF3,” J. Chem. Phys., vol. 48, pp. 4774–4780, May1968.

[44] R. Quimby and W. Miniscalco, “Modified Judd-Ofelt technique and applicationto optical transitions in Pr3+-doped glass,” J. Appl. Phys., vol. 75, pp. 613–615,January 1994.

[45] R. Quimby, K. Gahagan, B. Aiken, and M. Newhouse, “Self-calibrating quantumefficiency measurement technique and application to Pr3+ doped sulfide glass,”Opt. Lett., vol. 20, no. 19, pp. 2021–2023, 1995.

[46] P. Goldner and F. Auzel, “Application of standard and modified Judd-Ofelttheories to a praseodymium-doped fluorozirconate glass,” J. Appl. Phys., vol. 79,pp. 7972–7977, May 1996.

[47] D. Aggarwal and G. Lu, Fluoride glass fiber optics. San Diego, CA: AcademicPress, 1991. ISBN 0-12-044505-0.

[48] K. Wei, D. Machewirth, J. Wenzel, E. Snitzer, and G. Sigel Jr., “Pr3+-doped Ge-Ga-S glasses for 1.3 µm optical fiber amplifiers,” J. Non-Cryst. Solids, vol. 182,pp. 257–261, 1995.

[49] M. Digonnet, “Closed-form expressions for the gain in three- and four-level laserfibers,” IEEE J. Quant. Electron., vol. 26, pp. 1788–1796, October 1990.

[50] G. Lucovsky, F. Galeener, R. Keezer, R. Geils, and H. Six, “Structural interpre-tation of the infrared and Raman spectra of glasses in the alloy system Ge1−xSx,”Phys. Rev. B, vol. 10, pp. 5134–5146, December 1974.

[51] Z. Ivanova, “Local ordering studies of semiconducting (GeS2)100−xGax,” J. ofMolecular Structure, pp. 335–340, 1991.

[52] D. Marchese, G. Kakarantzas, and A. Jha, “1G4 lifetimes, optical and ther-mal characteristics of Pr doped GeS2-chalcohalide glasses,” J. Non-Cryst. Solids,vol. 196, pp. 314–319, 1996.

[53] M. Fontana, B. Rosi, Z. Ivanova, and N. Kirov, “Raman scattering in Ge-S-Gaglasses,” Philosophical Magazine B, vol. 56, no. 4, pp. 507–517, 1987.

[54] J. Heo, J. Yoon, and S.-Y. Ryou, “Raman spectroscopic analysis on the solubilitymechanism of La3+ in GeS2—Ga2S3 glasses,” J. Non-Cryst. Solids, vol. 238,pp. 115–123, 1998.


[55] L. Riseberg and H. Moos, “Multiphonon orbit-lattice relaxation of excited statesof rare-earth ions in crystals.,” Phys. Rev., vol. 174, pp. 429–438, October 1968.

[56] R. Reisfeld, “Multiphonon relaxation in glasses,” in Radiationless processes(B. Di Bartolo, ed.), (New York), pp. 489–498, Plenum Press, 1980. ISBN 01-306-40577-6.

[57] Y. Shin, J. Heo, and H. Kim, “Modification of the local phonon modes andelectron-phonon coupling strengths in Dy3+-doped sulfide glasses for efficient 1.3µm amplification,” Chem. Phys. Lett., vol. 317, pp. 637–641, February 2000.

[58] M. Naftaly, A. Jha, and W. Jordan, “1.3 µm fluorescence quenching in Pr-dopedglasses,” J. Appl. Phys., vol. 84, no. 4, pp. 1800–1804, 1998.

[59] M. Brown, Handbook of thermal analysis and calorimetry, vol. 1. Principles andpractice. Amsterdam: Elsevier Science, 1998. ISBN 0-444-82085-X.

[60] D. Hewak and D. Brady, “Characteristic temperatures of chalcogenide glass,” inProperties, processing and applications of glass and rare earth-doped glasses foroptical fibres (D. Hewak, ed.), ch. D 2.2, pp. 309–312, INSPEC, 1998.

[61] S. Messaddeq, M. Siu Li, D. Lezal, S. Ribeiro, and Y. Messaddeq, “Abovebandgap induced photoexpansion and photobleaching in Ga-Ge-S based glasses,”J. Non-Cryst. Solids, vol. 284, pp. 282–287, 2001.

[62] J. Heo and Y. Shin, “Mid-infrared emissions and multiphonon relaxation in Dy3+-doped chalcogenide glasses,” in XVIII international congress on glass (M. Choud-hary, N. Huff, and C. I. Drummond, eds.), American Ceramic Society, 1998.

[63] L. Koudelka, M. Pisarcik, and O. Baidakova, “The effect of MnS- and MnCl2-doping on the structure of GeS2-Ga2S3 glasses,” J. Mater. Sci. Lett., vol. 8,pp. 1161–1162, 1989.

[64] Y. Ohishi, A. Mori, T. Kanamori, K. Fujiura, and S. Sudo, “Fabrication ofpraseodymium-doped arsenic sulfide chalcogenide fiber for 1.3-µm fiber ampli-fiers,” Appl. Phys. Lett., vol. 65, pp. 13–15, July 1994.

[65] J. Wang, “Glass viscosity and structural relaxation by parallel plate rheometryusing a thermo-mechanical analyser,” Mater. Lett., vol. 31, pp. 99–103, May1997.

[66] H. Scholze, Glas: Struktur und Eigenschaften. Berlin: Springer, 3rd ed., 1988.ISBN 0-387-08403-7

[67] J. Malek and J. Shanelova, “Viscosity of germanium sulfide melts,” J. Non-Cryst.Solids, vol. 243, pp. 116–122, 1999.

Chapter 3

Fibre drawing of chalcogenide

glasses

In this chapter, the fibre drawing process and the optimum drawing conditions forgermanium gallium sulphide fibres are discussed. In the fibre drawing process, piecesof glass are softened by heating the material, while a drawing force is applied on thematerial. The drawing force must be sufficiently high in order to attenuate the diam-eter of the glass into a fibre of the required dimensions. The drawn fibre is solidifiedby quenching of the glass melt. The physical properties of the fibre such as strength,optical properties and dimensions are affected by the drawing process.In the next section, the geometry of a step-index glass fibre is discussed briefly.In section 3.2, a literature overview on techniques suitable to produce chalcogenideglass fibres is given. In this study, the methods suitable for preparation of a ger-manium gallium sulphide fibre preform, based on the rod-in-tube process, are inves-tigated. In the rod-in-tube process, the fibre preform is constructed by inserting a(thin) rod of core material into a cladding tube. In this study, the core and claddingmaterials of the preform consist of germanium gallium sulphide glasses. A novelmethod for production of germanium gallium sulphide cladding glass tubes, which isthe first step in the assembly of a fibre preform, is presented. Next, a descriptionof etching techniques suitable for improvement of germanium gallium sulphide glasssurfaces is given. Etching of the surfaces of both core and cladding, prior to assemblyof the fibre preform and fibre drawing, is needed to limit the formation of defectsduring fibre drawing and obtain fibres with low optical losses.In section 3.3, the drawing of germanium gallium sulphide glasses and a mathematicalmodel for drawing of these glasses, developed in this study, is discussed. The modeldescribes material deformation, temperature profiles and stresses within the material.In this section, the model is used to determine the suitable process conditions forfibre drawing, using the physical properties of the glasses that have been determinedin this study (see e.g. chapter 2). Next, experimental results on the drawing of ger-manium gallium sulphide glasses are presented. The drawing of glass rods, using the

77


n0

n1 n2

n

rRa

2a

core

cladding

Figure 3.1: Refractive index profile n(r) and cross section of a step-index fibre witha core diameter of 2a and an outer diameter of 2R. The refractive indices of air, coreand cladding are n0, n1 and n2, respectively.

experimental fibre drawing equipment, provides information about the ability to drawfibres of this type of glass.In the last section of this chapter, the main conclusions on the preparation of preformsand the optimum conditions for fibre drawing of germanium gallium sulphide glassesare summarised.

3.1 Structure of an optical fibre

The function of an optical fibre is to confine and guide light over long distances.The optical fibre generally consists of a cylindrical core surrounded by a concentriccladding of a different composition. In a step-index fibre, the refractive index of thecore material n1 is higher than the refractive index of the cladding material n2 (seeFigure 3.1). Usually, the fibre is coated with a layer of protective (polymer) coatingin order to improve the mechanical strength and to protect the fibre against damage,caused by mechanical impact, moisture or other contamination. The optical powerof the light guided by the fibre is concentrated principally in the core region, and itsintensity decreases more or less exponentially with its distance from the axis of thefibre. The radial distribution of the optical intensity is discussed in section 4.1.3. Ifthe cladding is sufficiently thick, the effect of the protective coating on the opticalproperties is negligible [1].The optical transmission characteristics of the fibre depend on glass composition, di-mensions and the refractive index of the core and cladding. In a step index fibre, therefraction index is constant over the core radius, with a step like change at the corecladding boundary. Typically, single mode fibres have core and cladding diameters of8 and 125 µm, respectively, and the difference in the refractive index of the core and

Fibre drawing of chalcogenide glasses 79

cladding material is typically only a few percent or less [1]. However, efficient fibreamplifiers require fibres with very small core radius (∼ 2 µm) and large core claddingrefractive index differences in order to obtain high power densities of both signal andpump light in the fibre core [2] (see chapter 5).Apart from absorption of light by the host glass, dopants and impurities, losses are at-tributable to irregularities in the fibre itself. Local, microscopic variations in density,composition and small crystals in the fibre cause variations in the refractive index,which in turn bring about scattering losses. Cracks and bubbles, e.g. near the corecladding interface, can also lead to scattering. Furthermore, the performance of thefibre is influenced negatively by fluctuations in the radius, ovality and eccentricity ofthe fibre core.

3.2 Chalcogenide glass fibre drawing techniques

Many fabrication methods for various materials and fibre structures have been de-veloped to obtain low loss fibres with a core-cladding structure. Several methodsare applicable to chalcogenide glasses (e.g. germanium gallium sulphide glasses). Toobtain a fibre with core - cladding structure, fibre is either drawn directly from aglass melt using the double-crucible method, or drawn from a pre-prepared, solid pre-form [3, 4]. The double-crucible and preform methods are described in section 3.2.1and 3.2.2, respectively. In this work, the focus is on the fibre preform method. Aprocess for preparation of germanium gallium sulphide cladding tubes, which can beused to construct a fibre preform, developed in this study, is presented in section3.2.3. Improvement of the surface quality by etching of germanium gallium sulphideglasses, which is needed to obtain a high quality preform, is discussed in section 3.2.4.

3.2.1 Preform method

Fibres with a core-cladding structure can be drawn from a solid preform. Using a feedmechanism, the glass preform is lowered slowly into the furnace of the fibre drawingtower (see schematic illustration in Figure 3.2a). The preform is heated and due tothe difference in preform feeding velocity and fibre drawing velocity, a fibre (withsmaller diameter than the preform) is formed.The diameter ratio of core and cladding of the preform equals the diameter ratiowithin the fibre drawn from the preform. Usually, the fabrication of a solid preform,consists of two steps: the formation of a tube of cladding glass, which is followedby filling up the tube with the core glass, either by casting of a core glass melt orinsertion of a tightly fitting solid rod of core glass into the cladding tube.Melting and subsequent casting is a common technique for preparation of claddingglass tubes. In the so-called built-in casting technique [5], the cladding glass is castedinto a cylindrical mold (cup-like shape). After solidification of the material near thewalls of the mold, the mold is inverted to allow the remaining glass melt to drainout. The fibre preform is then obtained by casting the core glass melt immediately


Core glassCladding glass

Heater

Gas inlet

Heater

Fibre

Preform

Fibre

Crucible

a) b)

Figure 3.2: Furnace section with a) preform b) double crucible assembly. Note thedimensions are not drawn to scale.

inside the tube. The built-in casting technique, used extensively for fluoride glasses,is not suitable for most chalcogenide glasses due to the high vapour pressure of thechalcogenide melt, which lead to loss of components through volatilisation.Alternatively, the cladding tubes are formed by so-called rotational casting [5]. Thecladding tubes are formed by pouring the cladding glass inside a (sealed) cylindricalmold (e.g. ampoule). Then, the mold with the molten glass inside is spun horizon-tally, at a rotational speed of approximately 3000-5000 rev min−1, while cooling to theglass transition temperature. The internal diameter of the cladding tube is adjustedby the amount of glass melt inside the mold.Another method for preparation of the cladding tube is core drilling. This techniqueis applied for preparation of fluoride [6] and also chalcogenide [2] glass tubes usingdiamond impregnated core drills of approximately 1 mm outer diameter and lengthsof up to 150 mm.In the rod-in-tube process, the fibre preform is constructed by inserting a (thin) rodof core material into the cladding tube. The inner diameter of the cladding tube mustbe slightly larger than the core rod diameter. Ground and polished rods at the desireddiameter are prepared directly from core glass pieces or by stretching a rod of coreglass to a smaller diameter inside the drawing tower. Cladding tubes are preparedaccording to the methods described in the previous paragraphs. To remove the smallgap between core and cladding glass, i.e. encapsulate the core within the claddingtube, the rod-in-tube assembly is heated to establish collapse of the cladding tube.The rod-in-tube assembly is collapsed either prior to the fibre drawing or during thefibre drawing process itself [7].Extrusion is a technique for the preparation of rods, tubes or preforms in a singleproduction step. In this process, the molten glass is forced through a die, with theaid of high pressure at relative moderate temperature (i.e. much lower than the tem-


Core glassCladding glassDie Piston

a) b)

Figure 3.3: Schematic presentation of extrusion apparatus [11] showing the core andcladding glass discs prior and during extrusion.

perature required to melt the glass). To produce tubes, a pin is fitted in the centre ofthe die. Extrusion is carried out in a temperature region in which viscosity is typically108 Pa s [8]. An advantage is that crystal growth is unfavourable at these operatingconditions [9], which are well below the crystallisation temperature Tx.Furniss et al. [8] used extrusion to make rods and fine bore tubes of gallium lanthanumsulphide glasses. One-step extrusion of preforms with core-cladding structure wasdemonstrated for arsenic sulphide [10] and gallium lanthanum sulphide glasses [8]. Inthis process, an assembly of cladding glass and core glass discs is extruded simulta-neously through a die [11] (see Figure 3.3). The core-cladding diameter ratio can bealtered to some degree by changing the thickness of the respective discs [12].Typically, the outer diameter of a preform is 10 mm. Preforms prepared with built-inor rotational casting techniques have a typical core-cladding diameter ratio of 2–5 [5].Using the rod-in-tube method, the core-clad ratio is 3–5 [6, 12]. However, for mostapplications these diameter ratios between core and cladding are too small. Fibreswith higher diameter ratio can be obtained by drawing of a small diameter rod fromthe initial preform. Subsequently, this rod is inserted into another cladding tube (so-called overclad) and the resulting preform is drawn into a rod again or eventually intofibre. This procedure is repeated up to three times to achieve core-cladding diameterratios larger than 10.Except from melting and casting, all processing steps in the preform preparationprocess are carried out below the melting temperature and generally, the materialsare thermally reworked at a temperature well below the crystallisation temperature.However, assembly of the preform proved to be difficult due to crystallisation causedby repeated heating [12]. In the rod-in-tube method, it is difficult to form a smoothinterface between core and cladding [3]. Small imperfections of the interfaces can beadjusted by polishing and etching. For example, tetramethylammonia [2] and aque-ous solution of sodium hydroxide [13] can be used for etching arsenic sulphide andselenide glasses, respectively.The working temperatures, using the preform method for drawing of germanium gal-lium sulphide glasses, is bounded by crystallisation for Ge-rich glass compositionsand sublimation of sulphur for S-rich glass compositions [14]. Furthermore, the work-ing temperature should be sufficiently high, to prevent breakage of the fibre due tostresses within the fibre.


3.2.2 Double crucible method

Unstructured (i.e. unclad) fibres can be pulled by the single crucible method [2],while fibres with a core-cladding structure can be drawn from a double crucible as-sembly (see Figure 3.2b). The inner crucible is charged with core glass and the outerwith cladding glass. The assembly is placed in a furnace which is rinsed by an inertgas. The core and cladding glasses are melted in the crucibles and drawn into a fibrethrough two concentric nozzles at the bottom of the crucibles. Gas pressure is appliedto both crucibles independently, to control the flow rate of the melt. In this manner,fibre with moderate core-cladding diameter ratios (up to 1:10, which corresponds toa volume ratio of 1:100) can be drawn with high reproducibility [2].Commonly, vitreous silica glass crucibles are used for drawing chalcogenide fibre.Besides the applied process conditions (temperature, pressure etc.), the geometric di-mensions of the crucibles, such as length, diameter and the shape of nozzles/orifices ofboth inner and outer crucible, mainly determine the diameter of the core and claddingof the fibre. The process control is more difficult compared to preform techniques.The controlled process parameters comprise the temperature and volume of core andcladding melt, the pressure conditions over core and cladding glass melt and the ap-plied drawing force. The composition of the core and cladding glass determines theworking temperature, at which viscosity of the melts is sufficiently low for fibre draw-ing.The double crucible method allows for the preparation of fibre with high quality inter-face between the core and the cladding. However, for most applications the diameterratio between core and cladding is insufficient. Fibres with higher diameter ratio canbe obtained by drawing of a small diameter rod using the double crucible method.This rod, consisting of a core and cladding, is inserted into a cladding tube (over-clad) and the resulting preform is eventually drawn into fibre. A disadvantage ofthe double crucible method is the long residence time of the glass at temperatures,which are near crystallisation temperature. Hence, only glasses with high glass stabil-ity can be applied [14]. The long residence time at elevated temperature is partiallycompensated by the fewer high temperature processing steps needed to prepare a fibre.

3.2.3 Germanium gallium sulphide preforms

In this study, germanium gallium sulphide glass rods were obtained by melting insealed, vitreous silica ampoules. Due to the availability of glass rods, fabricated thisway, the relatively simple preform technique for fibre drawing was selected in favour ofthe crucible drawing process. The core glass rods could either be stretched to smallerdiameter rods for preparation of preforms according to the rod-in-tube method orcould be drawn into unclad fibres.The basic preparation steps in the rod-in-tube process are formation of a core rod anda cladding tube. Core glass rods at the desired diameter are prepared directly fromglass rods by stretching inside the drawing tower. In this study, an alternative processfor preparation of cladding tubes is developed. Eventually, surface imperfections in


Spindel

Needle

Cladding glass

Insulation

Heater

Mold

Figure 3.4: Schematic presentation of the furnace used for formation of cladding glasstubes.

the rod-in-tube preform will lead to scattering losses in the fibre. Therefore, polishingand etching techniques (see section 3.2.4) are applied to improve the surface qualityat the core-cladding interface prior to insertion, collapse and fibre drawing.The cladding tube is made by a hot deformation process supported by the visco-elasticproperties of the glass. In this process, a rod of cladding glass is heated inside a mould(l=100 mm, d=10 mm) and converted into a tube by penetration of a 1.6 mm thick,polished stainless steel needle (see Figure 3.4) under isothermal conditions. The nee-dle is not rotating and is moving in the vertical direction, only.Selection of the working temperature is critical to manufacture tubes by the hot de-formation process. The required viscosity of the material for the deformation processhas to be between 108 and 108.5 Pa s (region 1 in Figure 3.5). Hence, the deformationtemperature is approximately 50 K below the fibre drawing temperature (about 725 Kat µ = 107 Pa s). Under these conditions, the operating temperature is below thecrystallisation onset temperature (790 K).To prevent cracking of the material, the speed of penetration of the needle in thepenetration step has to be less than 1 cm min−1. After a few minutes of relaxation,the needle is removed from the sample at a minimum rate of 5 cm min−1 to maintainthe shape of the hole. Then, tube is immediately cooled and annealed near the glasstransition temperature, Tg, for 30 minutes.A typical course of temperature as a function of time during tube formation, of a glasstube with composition (GeS2.5)98(GaS3)2, is shown in Figure 3.6. The temperature


10 4

10 5

10 6

10 7

10 8

10 9

1010

1011

1012

1013

500 550 600 650 700 750 800

1 2

Temperature [K]

Vis

cosi

ty[P

as]

Figure 3.5: The viscosity-temperature relation for (GeS3)98(GaS3)2. The symbols (+)represent the measured data, the dashed line is obtained by fitting the experimentaldata using VFT relation (equation 2.35). The regions for cladding tube formationusing the hot deformation process and fibre drawing are indicated by the temperatureranges 1 and 2, respectively.

dependency of the viscosity for the (GeS2.5)98(GaS3)2 was not available. However,the viscosity data of (GeS3)98(GaS3)2 was used to demonstrate the trends in the vis-cosity in Figure 3.6. If the temperature is too low, and hence viscosity too high, theglass sample tends to crack. If the temperature is too high, the tube tends to collapseupon removal of the needle.As expected from the deformation working temperature, which is below the crys-tallisation onset temperature, no (surface) crystallisation is observed. Furthermore,volatilisation of glass components is prevented by the relatively low working temper-atures. A photograph (top view) of a cladding glass tube is shown in Figure 3.7.

3.2.4 Etching of germanium gallium sulphide glasses

To obtain a rod-in-tube preform with a smooth joint between core and cladding, tightfitting of the core rod within the cladding tube is required for the entire interface.Etching is a common technique to remove a small amount of surface material bydissolution. The use of liquid etching reagent is suitable for treatment of the innersurface of the tube. Ideally, the surface quality is enhanced by removal of all surfacecontamination, and improvement of the smoothness of the surface.To investigate and find a suitable etching agent, the germanium gallium sulphideglasses were subjected to both alkaline and acid solutions. The glass samples to beinvestigated (diameter approx. 8 mm) were cut into discs using a diamond saw. One


250

350

450

550

650

750

0 50 100 150 200 250 300 35010 0

10 5

1010

1015

1020

1025

In Out

Annealing

(Spindle)

viscositytemperature

Time [min]

Tem

per

ature

[K]

Vis

cosi

ty[P

as]

Figure 3.6: The temperature and viscosity as function of time during formation of acladding glass tube with composition (GeS2.5)98(GaS3)2. The dashed line representsthe estimated viscosity using equation 2.35 for (GeS3)98(GaS3)2. The regions formoving the needle into and out of the cladding glass are indicated by the arrows.

1 mm

Cladding glass

Cylindrical opening

Figure 3.7: Photograph showing top view of a cladding glass tube prepared by hotdeformation (with composition (GeS2.5)98(GaS3)2).


of the surfaces of the cylindrical disc was polished mechanically, while no improve-ments were made to the rough surface on the other side of the disc. This untreatedsurface resembles a ground surface, due to the scratches resulting from the cutting us-ing the diamond saw. After polishing the thickness of the sample was approximately4 mm. The samples were completely immersed in the etching solution. The mass lossper unit time is taken as measure for the etching rate. Moderate etching rates arerequired to control and limit material removal by the etching process.No mass loss of germanium gallium sulphide glass samples was observed in concen-trated nitric acid (HNO3, 65%), sulphuric acid (H2SO4, 96%), hydrochloric acid (HCl,37%) or hydrofluoric acid (HF, 48%). Therefore, these acids can be used to clean con-taminated glass surfaces, without impairments to the glass surface.Tetramethylammonia [2] and aqueous solution of sodium hydroxide [13] are used foretching arsenic sulphide and selenide glasses, respectively. Most likely, aqueous alka-line solutions can be used for etching germanium gallium sulphide glass samples aswell.Aqueous solutions of sodium carbonate (Na2CO3), caustic soda (NaOH) and am-monia (NH3) are capable of etching germanium gallium sulphide glasses. However,etching with sodium carbonate resulted in a hazy surface. The etching rate by con-centrated solutions (>0.5 M) is too high for controllable etching.The relative mass loss in diluted caustic soda vs etching time is shown in Figure 3.8a.The samples were immersed in 150 ml of 0.1 M and 0.21 M caustic soda during 4hour intervals. The samples were weighed and measured after each interval. Theetching rate is determined by the concentration of the reagent (see Figure 3.8b) andthe surface area of the sample. During the course of the etching, the surface areaof the cylindrical sample discs is reduced. Hence, the etching rate is slowed down.Furthermore, the activity of the reagent decreases during the course of the etching.In Figure 3.9, the etching rate by using 0.02 M ammonia and 0.02 M caustic sodasolutions are shown. The samples were immersed in 150 ml solution during 3 × 16hour. After each interval, the samples were weighed and its dimensions were mea-sured. The etching solution was reused during the whole experiment. Under theseconditions, the mass loss of the sample is limited and can be well controlled due tothe relatively low etching rate.The photographs in Figure 3.10 demonstrate the effect of etching on both polished anduntreated surfaces. Each photograph represents a surface of 1×1 mm. The surfacesprior to etching are shown on the left-hand side of Figure 3.10. The untreated surface(a) resembles a ground surface, due to the scratches resulting from the cutting usingthe diamond saw. The polished surface (d) contains a number of small imperfectionsand scratches.The samples were treated with diluted ammonia (0.02 M, middle) and caustic soda(0.02 M, right). After 48 hours etching, the appearance of the rough surface (top row)has improved, however the surface is covered with lumps. Increment of the etchingtime will not improve the surface smoothness. The differences between diluted am-monia (b) and caustic soda (c) are small.The clarity of the polished surfaces is not affected by the etching. The surface iscovered with lumps, too. Especially in the case of ammonia (e), the small scratches


0.50

0.60

0.70

0.80

0.90

1.00

0 4 8 12 16

Rel

ativ

e m

ass

[-]

time [h]

a)

0.10 M

0.21 M

0.00

0.01

0.02

0.03

0.04

0.05

0 4 8 12 16

Etc

hing

rat

e [m

m3 /m

m2 /h

]

time [h]

b)

0.10 M

0.21 M

Figure 3.8: Relative mass loss of (GeS2.25)98(Ga2S3)2 glass vs etching time in 0.10and 0.21 M caustic soda.

0.90

0.92

0.94

0.96

0.98

1.00

0 8 16 24 32 40 48

Rel

ativ

e m

ass

[-]

time [h]

0.02 M NaOH0.02 M NH3

Figure 3.9: Relative mass loss of (GeS2.25)98(Ga2S3)2 glass vs etching time in 0.02 Mammonia and 0.02 M caustic soda.


a b c

d e f

Figure 3.10: Effects of etching. Rough surface before (a) and after 48 hours etchingin 0.02 M ammonia (b) and 0.02 M caustic soda (c). Polished surface before (d) andafter 48 hours etching in ammonia (e) and caustic soda (f).

have become more pronounced compared to caustic soda (f).Aqueous, alkaline solutions can be used to etch the surface of germanium galliumsulphide glasses. The clarity of rough surfaces is improved, at the expense of theformation of a lumpy surface. The best etching results are obtained using dilutedcaustic soda (c and f).

3.3 Fibre drawing of germanium gallium sulphide

glasses

In this section, the focus is on drawing of germanium gallium sulphide fibres. A math-ematical model for fibre drawing, using fibre preforms, is presented in section 3.3.1.The model is used to establish and find suitable process conditions (i.e. temperatureand fibre drawing velocity) for fibre drawing of germanium gallium sulphide glasses.The working range for fibre drawing is determined by the thermal and rheologicalproperties of glass, which were derived in chapter 2. The working range for fibredrawing is discussed in section 3.3.2. In the last section, the equipment and exper-imental techniques for fibre drawing of germanium gallium sulphide glasses, used inthis study, are discussed. In this section, some results of the drawing of unstructured(i.e. unclad) germanium gallium sulphide fibre are given, also.


3.3.1 Fibre drawing model

In this section, the fibre drawing process of glass rods is investigated, using a twodimensional axi-symmetric simulation model. First, the governing equations andboundary conditions for motion and heat transfer are presented. Next, a descriptionof the solver, used to solve the model equations by finite element methods [15], isdiscussed. Finally, the results are presented and discussed.A schematic description of the fibre formation process, which occurs within the fur-nace section, is depicted in Figure 3.11. A cylindrical co-ordinate system, z, r, θ isapplied. At each position, the radial velocity u and the axial velocity v of the ma-terial are given by the velocity vector u = (u, v). The motion is considered to be asteady state flow, that is, the velocity components at a fixed position are independentof time [16]. The temperature at a fixed location is independent of time, also. Afibre preform with initial velocity v0 is inserted into the furnace, where it is heatedto a temperature at which the glass softens. While the fibre is pulled down with aconstant velocity vf , the material (melt) of the softened preform is attenuated andelongated. The intermediate structure between preform and fibre is denoted as theneckdown region.The shape of the neckdown is determined by the furnace temperature, the (tempera-ture dependent) material properties (e.g. viscosity) and the forces acting on the glass.The drawing force and gravity force are working in the z-direction only. A drag forceoriginating from the purge gas flow is directed parallel to the surface in upward ordownward direction, while the surface tension is perpendicular to the surface, directedinto the material domain.The heat transfer processes within the furnace involve conduction, convection, andradiation. At the temperatures involved in the fibre drawing process, the radiativeheat exchange between the furnace and the preform is dominant. In addition, a smallamount of heat is transferred from the furnace via the gas to the glass surface by con-vection. Inside the glass material, the heat transfer occurs by convection, conductionand radiation (see e.g. Purnode et al. [16]).

Mathematical modelling

The motion of the glass in the neckdown region can be described using the equationsof conservation of mass, momentum and energy1, along with initial and boundaryconditions. The glasses are assumed to satisfy Newton’s law of viscosity (i.e. theviscosity does not depend on the deformation rate, so-called Newtonian fluids [17]),while the viscosity is a function of temperature only. All other physical propertiesof the glass (see Table 3.2) are taken constant, and the material is considered to beisotropic.The equation of continuity for a fluid (in the material domain i.e. the fibre preform)of constant density ρ (incompressible fluid) is given by

(∇ · u) = 0 (3.1)

1A full derivation of these equations can be found in Bird et al. [17]. In this literature, a summaryof vector and tensor operations, used in this chapter, can be found, also.


rz

H

R

v0

vf

vu

0

θ

R0

Rf

Lf

furnace

fibre

preform

heat

gas flow

F d

F f

F s

F g n

z = 0

z = Z

Figure 3.11: Furnace section with a preform inside, which is drawn into a fibre. Thefurnace has a height H and radius R. The preform of radius R0 is entering the furnaceat velocity v0, while the fibre of final radius Rf is drawn at velocity vf . The length ofthe fibre below the end of the furnace section is Lf . The forces acting on the materialare the fibre drawing force F f , the drag force F d and the forces due to surface tensionF s and gravity F g. The directions of the velocities, forces and the normal vector n

perpendicular to the surface are indicated by arrows.


where the velocity of the molten glass is denoted by the velocity vector u = (u, v) andthe velocity components in the radial and the axial directions are u and v, respectively.The equation of motion is given by

ρ∂u

∂t+ ρ(u · ∇u) = −∇p + −[∇ · τ ] + ρg (3.2)

where ρ is the density, p is the fluid pressure, g is the acceleration due to gravity, and τ

is the stress tensor (see equation 3.3). The terms on the left hand side of the equationdescribes the accumulation of momentum and transport of inertial momentum dueto material flow. The first term on the right hand side represents the momentumchange due to pressure gradients, the second term describes the rate of momentumgain by viscous transfer (see Annex A for the stress tensor components in cylindricalcoordinates) and the effect of gravity (acting on the glass) is taken into account bythe last term.The stress tensor is given by

τ =

τzz τrz 0τzr τrr 00 0 τθθ

(3.3)

where the subscripts i,j of the elements of the stress tensor τ refer to a stress compo-nent acting in the ith direction on the plane perpendicular to the jth direction. Thecomponents of the stress tensor for incompressible, Newtonian fluids are given by

τrr = −µ

(

2∂u

∂r

)

(3.4)

τθθ = −µ(

2u

r

)

(3.5)

τzz = −µ

(

2∂v

∂z

)

(3.6)

τrz = τzr = −µ

(

∂v

∂r+

∂u

∂z

)

(3.7)

In these equations, the viscosity µ depends on the temperature only. For fluids ofconstant density ρ and with the viscosity µ independent of the deformation rate,equation 3.2 reduces and yields the Navier-Stokes equation

ρ∂u

∂t+ ρ(u · ∇u) = −∇p + µ∇2u + ρg (3.8)

The definition of the Laplacian operator ∇2, in cylindrical coordinates, is given inAnnex A. The boundary conditions for the equations 3.1 and 3.8 are determined bythe symmetry conditions at the axis, the material flow along the glass surface and thefeed rate.The axial component v of the velocity u reaches a minimum at the axis of symmetry


through the centre of the neckdown. At the axis of symmetry, the radial velocitycomponent u is zero.

r = 0 : u = 0,dv

dr= 0 (3.9)

The position of the glass surface (free boundary) is determined by the kinetic bound-ary condition. It states that, in a steady state situation, the velocity vector u isalways perpendicular to the vector normal to the surface n

r = R : u · n = 0 (3.10)

The preform enters the top of the furnace at a constant feed rate v0 and the fibreleaves the furnace at velocity vf . Due to the rigid nature of the preform at thisposition, the velocity u comprises non-zero component in the axial direction, only.

z = 0 : u = 0, v(r) = v0 (3.11)

z = Z = −H : u = 0, v(r) = vf (3.12)

Furthermore, the stresses due to surface tension and purge gas drag force are incor-porated in the boundary conditions. The stress due to surface tension equals theproduct of surface curvature and the surface tension.

|τs| =γ

R∗(3.13)

where γ denotes the surface tension coefficient and R∗ is local radius of curvature ofthe surface. The radius of surface curvature R∗ is approximated by the local fibreradius R, since the radius of the fibre (which equals the radius of curvature in the r,θplane) is much smaller than the radius of curvature in the r,z plane. The stress dueto surface tension is directed into the material (fibre preform) domain. The stressdue to purge gas drag force on the free surface [16] is computed using the empiricalrelation for axi-symmetric flow over a cylinder

|τd| = 0.13ρau2rel

(

Red

2

)−0.734

(3.14)

where ρa is the density of the purge gas. Here it is assumed that the purge gas isflowing in the same direction as the fibre preform. If the local gas velocity is less thanthe local velocity of the glass material, the direction of the stress due to the drag forceis opposite to the direction of movement of the glass and parallel to the surface. Themagnitude of the relative gas velocity urel at the surface is given by

urel = |u − ua| (3.15)

where ua is the local gas velocity. Analogous to the direction of the stress due tothe drag force, the direction of the relative gas velocity is opposite to the direction ofmovement of the glass material and parallel to the surface, if the local gas velocity


is less than the local velocity of the glass material. The Reynolds number, for axi-symmetric gas flow along a cylinder, Re (dimensionless) is given by

Red(z) =2R(z)urel

νa(3.16)

where νa is the kinematic viscosity of the purge gas at the local temperature.The viscosity µ of the glass, included in the equation of motion 3.8, is a function oftemperature. The equation of conservation of energy is used to determine the localtemperature T within the material. The equation of energy for an incompressible,Newtonian fluid with constant heat capacity Cp [17] is given by

ρCp∂T

∂t+ ρCpu · ∇T = −(∇ · qc) − (∇ · qr) + µΦv (3.17)

where the deratives on left hand side describe the rate of gain of energy, the heat trans-fer by conduction and radiation (inside the glass) are given by qc and qr, respectively.The viscous dissipation function Φv [17] is given by

Φv = 2

[

(

∂u

∂r

)2

+(u

r

)2

+

(

∂v

∂z

)2]

+

(

∂v

∂r+

∂u

∂z

)2

(3.18)

Viscous dissipation of mechanical energy may usually be neglected, except for systemswith large velocity gradients [17].The heat transfer inside the glass is governed by convection, conduction and radiation.The conductive energy flux qc is determined by Fourier’s law

qc = −k∇T (3.19)

where k is the thermal conductivity.At elevated temperatures, the glass is a source of radiative energy itself. The radia-tive heat flux qr in equation 3.17 at an arbitrary point confined within the materialis the difference between energy radiated from the volume and the energy arriving byradiation from all distant points taking the reflection of radiation at the surface intoaccount.Due to the complexity of radiative heat transfer, which involves the emission, absorp-tion and transmission of rays in all directions, the exact solution procedure of theequations for radiative heat transfer is very complex and hence approximations forthe radiative heat transfer are widely used [18]. The formulation and solution of theequations, necessary for exact calculation of the radiative heat transfer between thefurnace and the glass material and the within glass material, are beyond the scope ofthis thesis. Here, the radiative heat transfer within the material is either neglected(assuming the material is transparent for the radiation) or estimated using the Rosse-land approximation (which is in principle only valid for optical thick media). Notethat neglecting the radiative heat transfer for relatively long time periods will resultin deviations of the local temperature from the exact solution [18]. This will resultin an underestimation of the local temperature when neglecting the radiative heat


transfer. The local temperature calculated using the Rosseland approximation differsfrom the exact solution [18], too, as the absorption of radiation during heating isoverestimated for materials which do not satisfy the assumption of an optical thickmaterial.If the absorption coefficient of the material α is large or αrl >> 1, where rl is the av-erage optical path length, then all far field effects can be neglected and the Rosselandapproximation can be applied. (The appropriateness of the Rosseland approxima-tion, in fibre drawing of germanium gallium sulphide glass preforms, will be discussedbelow.) In the Rosseland or diffusion approximation, the radiative heat transfer istreated as a heat diffusion process. The radiative conductivity for optical thick ma-terials [19] is highly temperature dependent and is estimated by

krad =16n2σ

3αT 3 (3.20)

where α is the absorption coefficient of the material, n is the refractive index of theglass at the wavelength of radiation and σ is the Stefan-Boltzmann constant.The radiative heat flux is incorporated into the equation of energy by an effectivethermal conductivity coefficient keff composed of the thermal conductivity of theglass k and a radiative contribution krad.

keff = k + krad (3.21)

The equation of energy becomes

ρCp∂T

∂t+ ρCpu · ∇T = keff∇2T + µΦv (3.22)

Equation 3.22 describes the total heat transfer inside the glass as a diffusion process.The equations 3.20–3.22 are only valid for materials with a large optical thickness.When the Rosseland approximation is applied, the heating of the material is usuallyoverestimated (compared to the actual contribution of radiation to the heating of thematerial), because the optical thickness of the glass is too low to achieve diffusion-likebehaviour in the material [18]. Due to the small diameter of the preform and fibre,this probably applies for glass fibre drawing, also. For example, if the thickness of thepreform is 0.01 m and the absorption coefficient α equals 75 m−1 then approximately47% of the radiation is absorbed by the glass. This result indicates that the Rosselandapproximation overestimates the absorption of radiation by the preform. Van derLinden [18] proposes to omit the radiative terms in equation 3.17, i.e. krad=0, in casethe dimensions of the material are small compared to the optical thickness and thetime scale involved is small. However neglecting radiative heat transfer in the glasscan result in severe errors, especially after longer radiation times [18]. The impactof both simplifications of radiative heat transfer within the material on the materialtemperature is discussed in the results and discussion section.The heat exchange between the heating element and the glass is mainly caused byradiation, while heat exchange between the glass surface and the purge gas is caused byconvection. The heat-exchange with the environment, the symmetry conditions at the


axis, and the initial temperature of the material entering the furnace are incorporatedin the boundary conditions solution of the equation of conservation of energy 3.17 (oralternatively equation 3.22).The temperature profile in the material entering the furnace is mainly a result ofradiative heat exchange in the section above the furnace. It is assumed that at thefurnace entrance, a parabolic temperature profile2 T0(r) will exists inside the preform.

z = 0 : T0 = T0(r) (3.23)

At the axis of symmetry through the centre of the neckdown, the temperature gradientin the axial direction is zero.

r = 0 :dT

dr= 0 (3.24)

The heat flux at the surface of the glass (free-boundary) qfb, equals the heat flux byconvection qcon and the heat flux due to radiative heat transfer qrad.

r = R : qfb = qcon + qrad (3.25)

The convective heat flux qcon is a function of the difference between the surfacetemperature of the glass and the temperature of the purge gas.

|qcon| = ±h (Tsurf − Ta) (3.26)

where h is the heat transfer coefficient, Tsurf is the local surface temperature and Ta

is the temperature of the purge gas.The heat transfer coefficient by forced convection is described by an empirical relationfor axi-symmetric flow along a cylinder [16, 20]

Nud(z) = 0.42 (Red(z))0.334

(3.27)

where Nud and Red are dimensionless numbers for heat transfer (Nusselt) and axi-symmetric flow along a cylinder (Reynolds), respectively. The Nusselt number Nu isgiven by

Nud(z) =2R(z)h

ka(3.28)

where 2R is the local diameter and ka is the thermal conductivity of the purge gas atthe local temperature T. An expression for the local heat transfer coefficient is foundby combination of equations 3.16, 3.28 and 3.27.The net radiative flux through the boundary qrad, at position (z, R), equals thedifference between the emission by the glass and the radiation to the glass originatingfrom the furnace, taking reflections into account.

2Due to the slow movement and the cylindrical geometry of the preform, the heat diffusion can beapproximated by heat diffusion into a static cylinder (outside the furnace, radiative heat transfer isneglected). The solution of the differential equations describing heat diffusion into a cylinder resultsin a parabolic temperature profile along a horizontal cross section of the static cylinder [17] untilsteady state is achieved.


The preform is mainly heated by radiation originating from the furnace, while thepurge gas (e.g. argon) inside the furnace will not emit or absorb radiation. Theradiative properties of the furnace are accurately modelled as so-called black bodyradiation [18]. Hence, the radiant energy emitted by the heating element is wavelengthindependent and a function of temperature alone [17]. The emission coefficient of thefurnace ǫfur is equal to unity for a black body.The radiative properties of the glass are assumed to resemble a radiating grey body,that is the emission coefficient of the glass ǫglass is less than unity and assumed to beindependent of wavelength and temperature. Furthermore, the emissivity of the glassequals the absorption coefficient. In general, the emission coefficient is dependent onthe diameter of the neckdown [21]. Here, the emission coefficient of the glass ǫglass istaken constant over the entire wavelength range for all temperatures of the glass atall positions.The radiation, which is emitted by the furnace, is partly absorbed by the glass andpartly reflected on the outer surface of the neck down. The fraction of radiation, thatis reflected by the preform surface, is ζext. Although the reflectivity of the glass ishighly dependent on angle of incidence, surface curvature, polarisation of the incidentradiation, surface temperature and index of refraction, for the purpose of this analysisa constant reflectivity is assumed.Under the assumption of an optical thick medium (e.g. the Rosseland approximation),the absorption of radiation is assumed to occur at the surface, only. Since radiation isassumed to be not transmitted through the material, neither reflections nor radiationinside the material take place. The radiation emitted by the furnace is either reflectedor absorbed on the glass surface. In this case, the condition of energy conservationon the glass surface is given by

ζext + ǫglass = 1 (3.29)

in which ζext is the reflection coefficient and ǫglass is the (apparent) emission coefficientof the glass, which (in general) depends on the thickness of the glass. The net radiativeheat flux |qrad| to the surface is given by [22]

|qrad| = ±σ(T 4

fur − T 4surf )

1ǫglass

+1−ǫfur

ǫfur

RRf

(3.30)

where Tsurf is the surface temperature of the glass and the emission coefficient andthe absolute furnace temperature are given by ǫfur and Tfur, respectively. In thisequation, R is the local radius of the neckdown and the furnace inner radius is Rf .Substitution of ǫfur = 1 in equation 3.30 yields

|qrad| = ±σ[

(1 − ζext)T 4fur − ǫglassT

4surf

]

(3.31)

The magnitude of the heat flux at the surface |qfb| is found by substitution of equation3.26 and 3.31 into equation 3.25, which results in the boundary condition of the free-surface

|qfb| = h (Tsurf − Ta) + σ[

(1 − ζext)T 4fur − ǫglassT

4surf

]

(3.32)


The forces acting on the neckdown during fibre drawing are schematically shown inFigure 3.11 on page 90. After solution of the equations of continuity 3.1, momentum3.2 and energy 3.22 (i.e. equations of state) together with the appropriate boundaryconditions, the forces are computed based on the local temperature and velocity pro-file in the material.The rheological behaviour of the glass in the drawing process and the stresses occur-ring within the glass are governed by the stress tensor τ and are due to gravity andthe local force at height z exerted to elongate the preform (F f ). The components ofthe stress tensor τ describe the axial stress (τzz) due to elongation of the preform,the radial stress (τrr) occurring due to the contraction of the fibre diameter, as wellas the shear stress (τrz) that occurs due to internal friction. The balance of the forcesacting on a slice of material in the neckdown, at height z, is given by [23]

F f + F g + F µ + F s + F d + F i = 0 (3.33)

in which F f is the force exerted to elongate the preform, F g is the gravity force, F µ

is the force due to viscous friction, F s is the total force due to surface tension (at thesurface only), F d is the drag force due to shear exerted by the purge gas and F i isthe force due to inertia (i.e. change in velocity of the material).In this equation, F µ and F i are body forces. The forces F s are F d act at the freesurface only and are taken into account in the boundary conditions (equation 3.13,3.14) for the Navier-Stokes equation 3.8 [24].Here, the emphasis will be on order of magnitude of the dominant forces at height zwith components operating in either the z or the r direction, instead of calculationof the full force balance presented in equation 3.33. Due to the gradual reduction ofthe diameter of the preform in the neckdown region (so-called attenuation), the forcesare predominantly directed in either z or the r direction. The error by neglecting theminor components of the forces in the perpendicular directions, is estimated usingthe fibre drawing model and is found to be less than 5 percent.The total force due to the axial stress (τzz) at height z operating in the z direction,caused by the viscous friction, is given by

Fµ,z(z) = (πR2)τzz = (πR2)2µ∂v

∂z(3.34)

The force, due to surface tension is directed perpendicular (normal) to the surface,directed into the material domain, i.e. it is mainly directed in the r direction. Thecomponent of the force due to surface tension [23], at height z operating in the zdirection is given by [24]

Fs,z(z) =

[

(

1 + (dRdz )2

)2 − R d2Rdz2

(

1 + (dRdz ))3/2

]

πγR (3.35)

If the radius of the neckdown decreases gradually, the deratives dRdz and d2R

dz2 may beneglected. In this case, the force due to surface tension, operating in the z directionis [23]

Fs,z(z) = πR2 γ

R∗≈ πRγ (3.36)


where γ denotes the surface tension coefficient and R∗ is the radius of surface curvatureR∗, which is approximately equal to the local fibre radius R, since the radius ofcurvature in the cross-sectional plane of the fibre (i.e. the fibre radius) is muchsmaller than the radius of curvature in the drawing plane.The force due to air drag is mainly directed in the tangential direction. The forcedue to air drag on the free surface [16, 23], at height z operating in the z direction,is approximately

Fd,z(z) ≈ |Fd(z)| = 2π

∫ Z−Lf

z

0.13ρau2rel(z)

(

Red(z)

2

)−0.734

rdz (3.37)

where ρa is the density of air and Red is the Reynolds number for axi-symmetric flowover a cylinder with radius R. The integration is carried out over a length betweenz and Z − Lf , which accounts for the drag force imposed on a fibre of length z − Zwithin the furnace and Lf below the furnace exit (at z = Z).The total force due to inertia Fi,z [23], at height z operating in the z direction, is

Fi,z(z) = πρ

∫ Z−Lf

z

r2v∂v

∂zdz (3.38)

where the integration over length between z and Z −Lf also accounts for the inertiaof a fibre of length z −Z within the furnace and of length Lf below the furnace exit.The gravity force Fg,z, at height z operating in the z direction, is given by

Fg,z(z) = πρg

∫ Z−Lf

z

r2dz (3.39)

in which the mass of the fibre of length z−Z within the furnace and of length Lf be-low the furnace exit is accounted for by integrating over length between z and Z−Lf .

Overview of main assumptions for the fibre drawing model

The main assumptions made in the derivation and construction of the fibre drawingmodel are summarised below:

• two dimensional, axi-symmetric;

• steady state;

• viscous dissipation is neglected i.e. Φv=0;

• apart form heat transfer inside the material by conduction, the radiative heattransfer inside the material is either neglected or the Rosseland approximationis applied;

• the radiative properties of the furnace are modelled as black body radiation.

The material, involved in the fibre drawing process, is considered to be


a)

b)

Figure 3.12: Shape of the mesh used in the simulations of the fibre drawing processa) initial shape b) final shape, i.e. the calculated shape of the neckdown region insteady-state.

• isotropic;

• incompressible fluid;

• Newtonian fluid;

• its viscosity is a function of temperature only;

• its radiative properties are approximated by grey body radiation;

• when the Rosseland approximation is applied, the material is assumed to be anoptical thick medium, and the effective thermal conductivity keff is a functionof temperature;

• all other material properties are assumed to be constants.

The heat transfer inside the material by normal (phonon) conduction, radiative con-duction (Rosseland approximation, only) and convection are incorporated in themodel.

Method of solution

The equations of continuity 3.1, momentum 3.2 and energy 3.22 (i.e. equations ofstate) together with the appropriate boundary conditions are solved using finite el-ement methods to obtain the temperature and velocity profiles in the fibre drawingprocess. The equations are solved for the steady-state situation (i.e. at any positioninside the neckdown ∂u

∂t = 0 and ∂T∂t = 0).

The equations are numerically solved using SEPRAN [15], which is a finite elementsoftware package for computational fluid dynamics. The equations of state of thefibre drawing process are calculated in the so-called quasi-stationary approach (i.e.assuming a stationary solution of the model equations after each calculation step). Inthis approach, a time-stepping procedure is applied, until the final solution describing


Figure 3.13: Grid element, consisting of 9 nodes, used in the simulations of the fibredrawing process.

the fibre drawing process in steady state is obtained. The algorithm, used in thecomputational process, is outlined below.Since the neckdown is axi-symmetric, an axial cross section (e.g. in the r, z plane)is considered. The cross section is discretised by a grid or so-called mesh of 20×120(initially) rectangular elements (see Figure 3.12a). Each element of the grid consistsof 9 nodal points (see Figure 3.13), forming the basis on which the equations of stateare discretised and solved.The shape of the mesh is adapted after every computation of the equations of conti-nuity, motion and energy. The radius of the neckdown at the top (z = 0) and bottom(z = Z) of the furnace obey the boundary conditions, that is the radius of the preformR0 and the fibre Rf , respectively. The shape of the free boundary is derived from thekinetic boundary condition u · n = 0. Automatic adaptation of the mesh, applied tomatch the calculated shape, is integrated in the SEPRAN software package. Eventu-ally, the shape of the mesh reflects the shape of the neckdown in the steady state (seeFigure 3.12b).The solver for the mathematical description of drawing process of a glass fibre froma preform in a cylindrical furnace3, as used in this study, is based on finite elementcode and is shortly outlined below.The equations of state are co-called coupled equations, commonly these equations are(numerically) solved by first solving the coupled momentum and continuity equationsusing an estimate of temperature. Then the temperature is calculated from the en-ergy equation, based on the just calculated velocity profile [15, 25]. Large changes invelocity, temperature and viscosity between two consecutive computation steps affectthe stability of the solver. Therefore, the equations of state are solved by slowly in-creasing the drawing velocity, the viscosity and contribution of radiative heat transferto the heat conductivity (in the Rosseland approximation, only). In each calculationstep, first the temperature profile is calculated, then the velocity is computed. Inthe calculation procedure of the velocity, the calculated temperature profile is usedto determine the variables that are functions of temperature i.e. the viscosity.Typically, in the first ten calculation steps (with a duration of about 1 s each), theequations of state are solved, while the fibre velocity vf is kept equal to the preform

3The proper functioning of the solver was checked by comparison of the analytical solution andmodel. In this evaluation the isothermal fibre drawing of a Newtonian liquid was considered [25].


Table 3.1: Process conditions and geometry of the furnace section and preform.

parameter magnitude

R0 preform radius 5 10−3 mTp preform temperature 550–650 Kv0 preform feed rate 0.1–5.0 10−4 m s−1

Rf fibre radius 70 10−6 mvf fibre drawing velocity 0.05–2.5 m s−1

H furnace height 5 10−2 mRfur furnace inner radius 17.5 10−3 mTfur furnace temperature 600–1000 K

velocity v0. Note that in these calculation steps, the shape of the preform (and themesh) does not change. To maintain stability of the solver, the temperature depen-dence of the viscosity can be slowly increased. Inertia terms (µ∇2u) in the momentumequation are neglected in these calculation steps. The contribution of radiative heattransfer to the heat conductivity (in the Rosseland approximation, only) is not in-cluded in equation of energy, yet.Then, in the following calculation steps (100 × 1 s), the fibre drawing velocity vf isincreased stepwise to the desired rate. Furthermore, the inertia terms of the momen-tum equation are included. The contribution of radiative heat transfer to the heatconductivity (in the Rosseland approximation, only) is also increased stepwise.After that, the calculations proceed for another 150 steps of 1 s each, until the finalsolution including stationary temperature profile and shape of the neckdown is ob-tained. In these computations, the mesh is adapted (after each step) to match thecalculated shape.Finally, the steady-state solution is obtained. The output of the calculations com-prises temperature and velocity profiles, local stresses and local viscosity. Thermallyinduced stresses, due to cooling of the fibre, are not included in the model.

Model parameters

The geometry of the furnace section is depicted in Figure 3.11 and the dimensionslisted in Table 3.1. The equations of continuity, motion and energy are solved forthe entire neckdown within in the furnace. The shape of the neckdown is calculated,while the radius of the preform entering the furnace section and the radius of the fibreat the exit of the furnace section are prescribed. The process conditions, used in thecalculations, are also summarised in Table 3.1.The temperature of the preform at the entrance of the furnace (z=0) is a result ofradiative heat transfer and conduction. The estimated temperature profile of thepreform at the entrance of the furnace (assuming an estimated 50 K temperaturedifference between the surface (r=R0) and the axis of symmetry (r=0) of the preform)


is given by

T0(r) = 50

(

r

R0

)2

+ Tp(v0) (3.40)

where Tp is the minimum temperature of the preform at the entrance of the furnace.As the preform feed rate v0 is increased, the initial temperature T0(r) will becomelower, due to the shorter time available for (pre-) heating of the preform. The tem-perature difference between the surface and the axis of symmetry of the preform isestimated on basis of the calculated heating rate of the preform in the furnace be-tween z=0 and z=-1 cm.The material properties of the glass are summarised in Table 3.2. The density ρ ofthe germanium gallium sulphide glasses is approximately 2650 kg m−3 [26] at roomtemperature, while the thermal expansion coefficient αl is approximately 20 10−6 K−1

(see section 2.5.2). In this analysis, thermally induced stresses are not included in themodel. Hence, the density of the glass is taken to be independent of temperature4.Here, the experimentally determined relation given by equation 2.35 between the vis-cosity and the temperature for (GeS3)98(GaS3)2 glasses, in the range 107–1010 Pa sis used.The values for the other material parameters (listed in Table 3.2) are unknown forgermanium gallium sulphide glasses and estimated values will be used instead. In gen-eral, the emission coefficient is dependent on the diameter of the neckdown [21]. Here,the emission coefficient of the glass ǫglass is taken 0.3 [16] over the entire wavelengthrange for all temperatures of the glass at all positions. If the radiative heat transferinside the glass is not neglected, the Rosseland approximation is applied. In this case,all incident radiation is assumed to be either absorbed or reflected at the surface (seeequation 3.29) and the effective reflection coefficient ζext of the glass equals 0.7. Inpractice, the reflection coefficient is much smaller, due to the large transmittance ofthe glass. As the refractive index of germanium gallium sulphide glass at room tem-perature is approximately 2.07 (see section 2.2), the estimated reflection coefficientζext, using Fresnell’s equations [27], is 0.12. However, for the purpose of this analysis,the use of a realistic value for the emission coefficient is preferred at the expense of anerroneous value for the reflection coefficient. The thermal conductivity k (not takingthe radiative conduction into account) is estimated based on the thermal conductivityof Ge38As2S60 [28].In practice, a small flow rate of purge gas is applied to remove oxygen from the furnace.The surface of the neckdown may be somewhat cooled by this small gas flow, which iscompensated by increasing the furnace temperature. The incorporation of the effectot this flow of the purge gas provokes stability problems of the solver. Therefore, thecalculations are performed in a stagnant atmosphere of purge gas (i.e. without flowof the purge gas, ua=0). As the (small) gas flow is not intended for cooling pur-poses, this assumption has a minor effect the heat transfer between the preform andthe furnace area. Within the temperature range and fibre drawing velocities beingconsidered, the stress due to drag force of the purge gas is small compared to the

4For a typical temperature difference between the minimum and maximum temperature withinthe neckdown, of 250 K, the change in density is maximum 1.5 %


Table 3.2: Material properties of the preform.

parameter magnitude

ρ glass density 2650 kg m−3

Cp heat capacity of glass 1000 J kg−1K−1

k thermal conductivity of glass 0.93 W m−1K−1

γ surface tension 0.36 N m−1

n refractive index 2.07α absorption coefficient 75 m−1

ǫ emission coefficient 0.3ζ reflection coefficient 0.7

other forces acting on the neckdown. For small Red (e.g. near the furnace entrance,v = v0), equation 3.27 for turbulent flow should be replaced by a similar relationshipdescribing laminar flow. However, at these local Reynolds numbers radiative heattransfer is at least an order of magnitude more important than forced convection [29].The furnace (wall) temperature Tfur is taken homogeneous over the height of thefurnace. The temperature of the purge gas Ta, inside the furnace, is assumed to be200 K below the furnace temperature.In general, an inert atmosphere (i.e. nitrogen or argon gas) is required for the draw-ing of chalcogenide glasses. Reactions between the glass and the purge gas are notincorporated in the model. For the simulations, the properties (e.g. density, viscosityand thermal conductivity) of the argon gas at elevated temperature are needed. Inthis study, the properties of air were used instead. The temperature dependence ofthe kinematic viscosity νa and thermal conductivity ka of the gas are described bythird order polynomial equations [16].

νa = ν0 + ν1 (Ta − Ta,ref ) + ν2 (Ta − Ta,ref )2

+ ν3 (Ta − Ta,ref )3

(3.41)

ka = k0 + k1 (Ta − Ta,ref ) + k2 (Ta − Ta,ref )2 + k3 (Ta − Ta,ref )3 (3.42)


For a preform of given initial diameter R0 and prescribed fibre diameter Rf , thefibre drawing process is controlled by the furnace temperature Tfur and the glassvolume flow rate Q (i.e. preform feed rate). In the fibre drawing model, used here,the glass volume flow rate (which determines the required fibre drawing force) is pre-scribed. The forces, occurring in the neckdown region and required for fibre drawing,are computed from the resultant temperature, viscosity and velocity profiles. In thecalculations, the preform enters the furnace at height z=0, while the fibre leaves thefurnace at height z=Z=-0.05 m. The process conditions and material properties,


Table 3.3: Properties of the purge gas (air) including parameters for kinematic vis-cosity (see equation 3.41) and thermal conductivity (see equation 3.42) of air.

parameter magnitude

ν0 1.1512 10−5 m2 s−1

ν1 8.9 10−8 m2 s−1K−1

ν2 8.262 10−11 m2 s−1K−2

ν3 -1.3655 10−14 m2 s−1K−3

k0 2.2899 10−2 W m−1K−1

k1 7.8264 10−5 W m−1K−2

k2 -3.06 10−8 W m−1K−3

k3 7.866 10−12 W m−1K−4

Ta,ref 255.37 Kρa 1.29 kg m−3 at T=293.15 K

which are used to model the fibre drawing of germanium gallium sulphide glass pre-forms, were presented in Tables 3.1, 3.2 and 3.3.In this section, the fibre drawing process is simulated for two cases, differing fromeach other by the modelling of the radiative heat transfer within the material. Theradiative heat transfer within the material is either neglected or estimated using theRosseland approximation. The Rosseland approximation overestimates the energyabsorption within the glass [18], while omitting the radiative heat transfer will resultin an underestimation of the total heat transfer (due to conduction and radiation)within the material, compared to the exact solution of the equations for radiativeheat transfer, which involves the calculation of emission, absorption and transmissionof rays in all directions for all points within the glass domain.In Figure 3.14, the shape of the neckdown region is depicted as function of glassvolume flow rate Q for a fixed final fibre diameter. The shape of the neckdown is de-termined by the local temperature, viscosity and stresses occurring in the neckdownregion. In Figure 3.14a, the shape of the neckdown is computed while the internal ra-diation is not taken into account. The furnace temperature Tfur is 765 K. The shapeof the neckdown region, when the Rosseland approximation is applied (i.e. absorptionof radiation and radiative conductivity), is shown in Figure 3.14b. In this case, theassumed furnace temperature Tfur is 825 K. The furnace temperature was adjusted inorder to obtain approximately the same fibre temperatures Tf at the furnace exit, inboth cases. When the glass volume flow rate Q is increased, a lower fibre temperatureTf is obtained at the furnace exit. This results in an increased viscosity µ and hencethe stress in the axial direction τzz is much higher, too.The calculated, local temperature levels in the neckdown are strongly related to theheat transfer mechanism in the glass. In Figure 3.15, the calculated temperatures inthe centre of the neckdown (i.e. r=0) and surface of the neckdown (r=R) are shown.It is assumed that the preform is already slightly warmed by the furnace, before it


a)

0

0.002

0.004

0.006

0.008

0.010

0 0.01 0.02 0.03 0.04 0.05

Volume flow rate Q7.85e-10 m3/s3.93e- 9 m3/s7.85e- 9 m3/s

Rad

ius

R[m

]

Axial distance from furnace top [m]

b)

0

0.002

0.004

0.006

0.008

0.010

0 0.01 0.02 0.03 0.04 0.05


Rad

ius

R[m

]


Figure 3.14: Shape of the neckdown region for different volume flow rates Q. a)Internal radiation is neglected. The furnace temperature Tfur is set to 765 K forall three glass volume flow rates. b) Internal radiation is accounted for by using theRosseland approximation. Here, the furnace temperature Tfur is set to 825 K for allthree glass volume flow rates.


enters the furnace (at z=0). Hence, at the furnace entrance (z=0), a radial tempera-ture distribution is present within the preform (see equation 3.40). The temperatureof the neckdown gradually increases as the preform descents into the furnace. At thebottom of the furnace, it is observed that the fibre temperature slightly decreases,probably due to cooling of the fibre by the purge gas.In Figure 3.15a, the temperature in the centre (r=0) and at the surface (r=R) ofthe neckdown are depicted, in case internal radiative heat transfer is neglected. Thecentre of the preform is slowly heated due to normal (phonon) conduction of heat.When the Rosseland approximation is applied, the inside of preform is heated muchfaster (see Figure 3.15b) compared to calculations neglecting internal radiation (seeFigure 3.15a), due to the combined heat transfer by conduction and radiation. Inthis case, the temperature difference between centre (r=0) and surface r=R of theneckdown is negligible for z ≤ -0.005 m. The increased heating rate in the case theRosseland approximation is applied is mainly explained by the higher effective con-ductivy (which includes the radiative conductivity). The effect of the higher furnacetemperature is small, as the temperature of the surface of the preform is similar tothe surface temperature when internal radiative heat transfer is neglected.A remarkable difference in the computed temperature profile (in the radial direction)within the preform is observed comparing the case where radiative energy transportwithin the material is neglected with the case where the Rosseland approximation isapplied. However, in both approaches for the radiative heat transfer, the observedtrends as a function of furnace temperature (not shown) of the other parameters (e.q.neckdown radius, stress, etc.) are comparable although the absolute value of the as-sumed furnace temperature is different. In practice, the required furnace temperatureis even higher, because the radiant energy emitted by the furnace (modelled as blackbody) determines an upper limit for the radiant energy emitted by a real furnace.Hence, in the remainder of this section, the results for the Rosseland approximationare shown, only.The maximum temperature of the fibre at the bottom of the furnace is strongly depen-dent on the glass volume flow rate Q. The temperature in the centre of the neckdown(r=0) in the axial direction of the neckdown is shown in Figure 3.16 for three glassvolume flow rates Q. The viscosity in the neckdown is shown in Figure 3.17. Theviscosity decreases as the material descents into the furnace due to the increase oftemperature.For fibre drawing starting from a preform, typically viscosities below 106–107 Pa sare required. If the viscosity drops below 105 Pa s, the glass can start flowing spon-taneously under the influence of gravity, and the fibre drawing process becomes fastuncontrollable.Approximately similar viscosity levels can be obtained in the tip of the neckdown (i.e.the fibre exiting the furnace) from a whole range of combinations of process condi-tions. In Figure 3.18, the shapes of the neckdown region for three combinations offurnace temperature Tfur and glass volume flow rate Q are shown. In all three cases,the resulting fibre temperatures Tf are equal and hence the viscosities in the tip ofthe neckdown are equal. The differences in the shape of the neckdown are originatingfrom differences in the local temperature distribution and stresses occurring during


a)

500

550

600

650

700

750

800

0 0.01 0.02 0.03 0.04 0.05

surfacecore

Fib

rete

mper

ature

Tf

[K]


b)

500

550

600

650

700

750

800

0 0.01 0.02 0.03 0.04 0.05

surfacecore

Fib

rete

mper

ature

Tf

[K]


Figure 3.15: Calculated temperature (at height z) in the centre of the neckdown (r=0)and surface of the neckdown (r=R). The glass volume flow rate Q is 3.93 10−9 m3 s−1.a) Internal radiation is neglected. The furnace temperature Tfur is set to 765 K. b)Internal radiation is accounted for by using the Rosseland approximation. Here, theassumed furnace temperature Tfur is 825 K.


500

550

600

650

700

750

800

850

900

0 0.01 0.02 0.03 0.04 0.05


PSfrag

replacem

en

Tem

per

ature

T[K

]


Figure 3.16: Calculated temperature in the neckdown region as function of glassvolume flow rate Q at constant furnace temperature Tfur = 825 K. The Rosselandapproximation is applied.

10 0

10 2

10 4

10 6

10 8

1010

1012

1014

0 0.01 0.02 0.03 0.04 0.05


Vis

cosi

tyµ

[Pa

s]


Figure 3.17: Calculated viscosity in the neckdown region as function of glass volumeflow rate Q at constant furnace temperature Tfur = 825 K. The Rosseland approxi-mation is applied.


0

0.002

0.004

0.006

0.008

0.010

0 0.01 0.02 0.03 0.04 0.05

Volume flow rate Q,Furnace temperature Tfur7.85e-10 m3/s, 825 K3.93e- 9 m3/s, 855 K7.85e- 9 m3/s, 885 K

Rad

ius

R[m

]


Figure 3.18: The shape of the neckdown region at equal fibre temperature Tf forthree combinations of furnace temperature Tfur and glass volume flow rate Q. TheRosseland approximation is applied.

the fibre drawing. The axial stress inside the neckdown reaches its maximum valueat a position close to the end of the furnace section, where the neck down radius isclose to the final fibre radius (see Figure 3.19). The axial stress in the neckdown isproportional to the viscosity µ and the deformation rate dv/dz (see equation 3.4). Inthe upper region of the furnace, the deformation rate in the axial direction is small.At the bottom end (z=-0.025 – -0.05 m), the deformation rate tends to increases veryrapidly. This causes the stress to increase near the furnace exit. The axial stress,local viscosity and deformation rate are shown in Figure 3.19 as function of the axialdistance from the furnace entrance.In Figure 3.20, the absolute values of the main forces acting on the preform at heightz, as given by equations 3.34, 3.36 and 3.39 are shown. Note, both the force due toviscous friction Fµ,z and the force due to gravity Fg,z are in the axial direction, whilethe force due to surface tension Fs,r is mainly in the radial direction. The oscillationsin the calculated values of the force (see Figure 3.20) are caused by small numericalerrors, which are caused by the applied numerical methods used for the calculationsof both stress and radius.In the upper part of the neck down, where the temperature is relatively low, the draw-ing force F f is mainly determined by the force due to axial stress caused by viscousfriction F µ. The fibre drawing process can become uncontrollable at low viscosity, ifthe order of magnitude of drawing tension becomes comparable to the gravity forceF g. In this case, the fibre drawing continues under the influence of the weight ofthe material itself. The significance of the forces due to inertia F i and drag F d (notshown) decreases at lower drawing velocity. The magnitude of these forces is at leastthree orders smaller than the force due to gravity. In the lower part of the neck down,


10-6

10-4

10-2

10 0

10 2

10 4

10 6

10 8

1010

1012

0 0.01 0.02 0.03 0.04 0.05

stress τzz

viscosity µdeformation rate dv/dz

τ zz

[Pa]

,µ

[Pa

s],dv/d

z[s−

1]


τzz

µ

dv/dz

Figure 3.19: The stress τzz (in the axial direction) at the surface of the neckdown. Thefurnace temperature Tfur equals 825 K and the glass volume flow rate Q is 7.9 10−10

m3 s−1. The stress is proportional to the local viscosity µ and the deformation ratedv/dz (see equation 3.4). The Rosseland approximation is applied.

0

1

2

3

4

5

6

7

0 0.01 0.02 0.03 0.04 0.050

0.01

0.02

0.03

0.04

0.05

0.06

0.07Fµ,z

Fµ,z

Fg,z

Fg,z

Fs,z

Fs,z

Fµ

,z[N

]

Fg,z

,F

s,z

[N]


Figure 3.20: The magnitude of the main forces, i.e. forces due to viscous friction Fµ,z,gravity Fg,z and surface tension Fs,z, acting on the neckdown in the axial directionat height z . The Rosseland approximation is applied.


107

108

109

1010

1011

1012

1013

1014

1015

600 650 700 750 800

Volume flow rate Q1.75 10- 8 m3/s7.85 10- 9 m3/s3.93 10- 9 m3/s7.85 10-10 m3/s3.93 10-10 m3/s

Max

.Str

ess

τ zz

[Pa]

Fibre temperature Tf [K]

Figure 3.21: Maximum axial stress in the neckdown region as function of fibre tem-perature Tf for several glass volume flow rates Q. The Rosseland approximation isapplied.

the force due to axial stress F µ, caused by viscous friction, is the main contributionto the required drawing force F f , also.In Figure 3.21, the maximum axial stress occurring in the neckdown region is plottedfor several glass volume flow rates Q as function of the fibre temperature Tf (i.e. atthe bottom of the furnace). The maximum obtained stress is decreased by loweringthe glass volume flow rate (i.e. lowering the deformation rates) and lowering the vis-cosity by increasing the temperature.The fibre temperature Tf is mainly determined by the furnace temperature Tfur andthe glass volume flow rate Q. The maximum axial stress occurring in the neckdownregion for several glass volume flow rates Q is depicted in Figure 3.22 as function offurnace temperature Tfur. As the glass volume flow rate increases, a higher furnacetemperature is needed to accommodate the required increased heating rate of thepreform. Additional heating is required to lower the viscosity in the neckdown toenable the higher deformation rate and to limit the stress in the axial direction.For a preform of given diameter 2R0 and prescribed fibre diameter 2Rf , the residencetime of the glass inside the furnace is inversely proportional to the flow rate or fibrevelocity (see Figure 3.23). For a given glass volume flow rate, the points in Figure 3.23represent the residence time at different furnace temperatures for the fibre drawingof a preform of diameter 2R0=0.01 m into a fibre with diameter 2Rf=140 10−6 m.The furnace temperature was varied between 865 and 925 K for inverted glass volumeflow rates of approximately 5.71 107 s m−3 and between 730 and 805 K for invertedglass volume flow rates of approximately 2.55 109 s m−3.


107

108

109

1010

1011

1012

1013

1014

1015

700 750 800 850 900 950 1000

Q= 1.75 10- 8 m3/s7.85 10- 9 m3/s3.93 10- 9 m3/s7.85 10-10 m3/s3.93 10-10 m3/s

stress

Max

.Str

ess

τ zz

[Pa]

Furnace temperature Tfur [K]

Figure 3.22: Maximum axial stress in the neckdown region as function of furnacetemperature Tfur for several volume flow rates Q. The Rosseland approximation isapplied.

0

1000

2000

3000

4000

5000

6000

0 0.5 109 1.0 109 1.5 109 2.0 109 2.5 109 3.0 109

Res

iden

ceti

me

τ r[s

]

Inverted volume flow rate 1/Q [s m−3]

Figure 3.23: Residence time τr as function of the inverted volume flow rate Q of theglass within the furnace, for the fibre drawing of a preform of diameter 2R0=0.01 minto a fibre with diameter 2Rf=140 10−6 m.


10-1

10+0

10+1

10+2

10+3

10+4

10+5

700 800 900 1000 1100 1200 1300

Fibredrawingwindow

Stresses too high

Crystallisation

Viscosity too lowA

B

C

Volume flow rate Q1.75 10- 8 m3/s7.85 10- 9 m3/s3.93 10- 9 m3/s7.85 10-10 m3/s3.93 10-10 m3/s

For

cedue

toax

ialst

ress

Fµ

[N]

Furnace temperature Tfur [K]

Figure 3.24: The operating window for fibre drawing of germanium gallium sulphideglasses. The operating window is bounded by the maximum allowed stresses τ inthe fibre and the on-set crystallisation temperature Tx. The almost straight, parallelcurves represent the fibre drawing force, approximated by the maximum force due tostress in the axial direction in the neckdown region, as function of furnace temperatureTfur for several glass volume flow rates Q. The glass volume flow rate Q and furnacetemperature Tfur, at which the viscosity becomes too low, the stresses become toohigh or crystallisation can occur, is indicated by curves A, B and C, respectively.

3.3.2 Fibre drawing operating conditions

The operating window for the drawing of germanium gallium sulphide glasses is givenby the allowed temperature (i.e. where the glass temperature is below the crystalli-sation onset temperature) and viscosity ranges and the maximum stresses permittedin the glass during the fibre drawing process. For a given diameter of both preformand fibre, the process is controlled by the furnace temperature and the preform feedrate (residence time). The required fibre drawing force is determined by these processconditions.The operating window (based on the model results, using the Rosseland approxima-tion to account for radiative heat transfer in the glass domain, as presented in theprevious section) is shown in Figure 3.24.The almost straight, parallel lines represent the required fibre drawing force, approx-imated by the maximum force due to axial stress in the neckdown region, as functionof furnace temperature Tfur for several glass volume flow rates Q. In practice, glassvolume flow rates of at least 3.93 10−10 m3 s−1 (i.e. vf= 0.025 m s−1) are desired tohave a suitable production rate.The maximum furnace temperature is bound by the local temperature inside the glasspreform, which may exceed neither on-set crystallisation temperature nor the tem-


perature at which the viscosity is too low for fibre drawing. As the glass temperatureexceeds 800 K, the viscosity µ becomes less than 105 Pas and the glass can start flow-ing under the influence of gravity. Under these conditions, the fibre drawing processbecomes uncontrollable. To determine this minimum viscosity limit, for each glassvolume flow rate the corresponding furnace temperature at which the viscosity equals105 Pas was calculated. The viscosity limit is indicated by curve A in Figure 3.24.Below the curve (i.e. at higher temperatures), the viscosity is too low for fibre draw-ing.The crystallisation temperature for the germanium gallium sulphide glasses is ap-proximately 750 K (i.e. 200 K above the glass transition temperature). The furnacetemperature at which the local temperature inside the neckdown attains the crys-tallisation temperature, was calculated for each glass volume flow rate and depictedin Figure 3.24, curve C. At a certain temperature of the furnace, the crystallisationcurve C shows, for a certain glass volume flow rate, whether crystallisation takes placeor not. Below the curve (i.e. at higher temperatures), crystallisation can occur. FromFigure 3.24, it is concluded that the on-set crystallisation temperature is determiningthe maximum allowed furnace temperature at a given preform feed rate.The lower furnace temperature limit is governed by the local temperature at whichthe stresses occurring inside the fibre become too high, resulting in rupture of thefibre. Typically, the strength of a glass fibre is in the order of 10 MPa. This value ismuch lower than its theoretical strength (in the order of 1 GPa), due to surface im-perfections. The maximum applicable fibre drawing force, for a fibre with a diameterof 140 µm, is approximately 5 N. The maximum force is indicated in Figure 3.24 byline B.The fibre temperature, which is mainly determined by furnace temperature and theresidence time within the furnace, must be well controlled to prevent rupture of thefibre due to stress or crystallisation. The working range is limited, due to the steepviscosity-temperature relationship and the low on-set crystallisation temperature ofthe glass. Precise control of the furnace temperature becomes more critical as thefibre drawing speed increases.In practice, the required furnace temperature is higher than the furnace temperatureTfur obtained by the fibre drawing model, because, the radiant energy emitted bythe furnace (modelled as black body, ǫfur=1) at any furnace temperature Tfur deter-mines an upper limit for the radiant energy emitted by the real furnace.From Figure 3.24, it is concluded that the fibre drawing of germanium gallium sul-phide glasses is possible, however the narrow working area is bound by crystallisation(which limits the furnace temperature) and the axial stresses occurring in the fibre(which limit the applicable fibre drawing speed). A practical approach to find suitablefibre drawing conditions is to increase the furnace temperature until the onset crys-tallisation temperature (approximately 750 K) is nearly attained for the glass fibre.Then the fibre drawing speed is increased until the maximum allowed stresses in thefibre are achieved.


3.3.3 Experimental fibre drawing

In this section, the experimental drawing of germanium gallium sulphide glasses isdiscussed. The uniformity of the fibre is strongly dependent upon process conditionsduring fibre drawing. For a given size geometry of both preform and fibre, the processis controlled by both preform feed and fibre draw velocities and the furnace temper-ature. First, the setup of the pilot scale fibre drawing machine, used in this study,is described. Then, the applied process conditions for drawing of germanium galliumsulphide glass preforms are discussed. The observations during elongation of glassrods, by this experimental method, provides information about the ability to drawfibres of this type of glass, successfully.

Setup of the pilot scale fibre drawing machine

Using a feed mechanism, a cylindrical glass preform is lowered slowly into a (cylin-drical) furnace. The furnace section (see Figure 3.25) is shielded by a vitreous silicatube and is flushed (purged) with argon in order to prevent oxidation of the carbonheating element. The carbon heating element with inner diameter of 35 mm andheight of 50 mm is heated by the current induced by the alternating electromagneticfield provided by a radio frequency (RF) generator. The preform (lmax=200 mm,Dmax=10 mm) is heated and due to the difference in preform feeding velocity andfibre drawing velocity, a fibre is formed. After leaving the furnace the fibre passesa cooling section and a laser-diameter monitor. The fresh drawn fibre is put on awinding drum.The pilot scale fibre drawing machine, used in this study, was not equipped with anautomatic control system. The set-points for furnace temperature, preform feedingvelocity and fibre drawing velocity are controlled manually.The velocity of the preform feeding mechanism and the winding drum are controlledby separate motor drives equipped with tachometers. Due to the lack of an automaticcontrol system, the preform feeding rate is maintained independent from the drawingvelocity. The diameter of the fibre is controlled by adjustment of the individual set-points of the preform feeding velocity and the fibre drawing velocity.The fibre drawing force is provided by the motor of the winding drum. A lateral mov-ing mechanism is used to move the winding drum in axial direction in order to placethe fibre side by side and prevent the fibre from fracture. The diameter monitor isused to control the fibre diameter by adapting the ratio between drawing and preformvelocity.Optionally, on-line coating systems can be installed between the diameter monitorand the winding drum. However, process start-up and control is more complicatedwhen coating systems are applied [30].The temperature of the neckdown gradually increases as the preform descents intothe furnace. Near the exit of the furnace, the attenuation of the neckdown continuesat a more gradual rate (so-called draw-down zone), before solidifying into the finishedfibre. A cooling section is located downstream of the furnace exit in order to increasethe cooling rate of the fresh fibre.The temperature profile within the furnace exhibits steep temperature gradients in


Figure 3.25: The drawing section of the experimental drawing tower.


both axial and radial directions. A symmetrical temperature distribution around thepreform is required in order to draw an uniform shaped fibre with an uniform distri-bution of the residual stresses. The temperature within the furnace is controlled by athermocouple located between the preform and the heating element. Due to the steepaxial and radial temperature gradients caused by the short heat zone and the heattransport by the purge gas flow [2], a large difference between control temperatureand effective drawing temperature (i.e. maximum temperature in the middle of thefurnace) is obtained. In the pilot scale fibre drawing machine, the measured maximumtemperature in the centre of the heating zone is 975 K and the temperature gradient(axial direction) around the maximum temperature is approximately 150 K cm−1.The response of the process to changes in the balance between preform and fibre ve-locities is fast, whereas effects of changes in furnace temperature are relatively slow.Hence, the fibre diameter should be controlled primary by the fibre drawing veloc-ity. However, precise temperature control in the drawing zone is necessary, becausefluctuations in the thermal gradient in the drawing zone (including the temperaturedistribution around the preform) may cause instability affecting diameter and con-centricity of the fibre.

Fibre drawing starting from germanium gallium sulphide glass rods

An assembly of a germanium gallium sulphide glass rod (or preform) mounted be-tween two vitreous silica supports5 is positioned within the furnace. Due to thelimited length (approximately 70 mm) of the germanium gallium sulphide glass rods,the weight of the material is too low to initiate the formation of the neckdown attemperature near the fibre drawing temperature. A weight of approximately 500 g isattached to the lower support, in order to initiate the attenuation of the glass (i.e.formation of the neckdown shape). The glass is heated slowly in the fibre drawing fur-nace until softening is observed. As soon as the glass starts to flow under the weight,the temperature of the furnace is slightly reduced. The weight is removed and thebeginning of the fibre is attached to the winding drum. The velocity of the wind-ing drum is increased until the preferred fibre drawing speed is obtained, while thepreform feed is operated manually to maintain the neckdown well positioned withinthe centre of the furnace. After (lateral en tangential) alignment of the fibre andthe diameter monitor, the diameter of the drawn fibre is measured. Based on thediameter measurement, the ratio between fibre drawing rate and preform feed rate isset.A typical course of a fibre drawing experiment is depicted in Figure 3.26. The diame-ter of the glass rod was 8 mm. The heating of the glass within the furnace is shown onthe left hand side (indicating the calculated temperature in the centre of the furnace,which is derived from temperature measurement using a thermocouple near the wallof the furnace). The point of softening of the glass rod is indicated by the drop offurnace temperature around t= 6100 s. The fibre drawing is shown on the right handside of Figure 3.26. The time to draw the fibre was approximately 15 minutes. The

5Vitreous silica supports at both sides of the germanium gallium sulphide glass rod are usedbecause metal parts are strongly heated by the electro-magnetic fields applied to heat the furnace.


300

400

500

600

700

800

900

1000

0 1000 2000 3000 4000 5000 6000

Tem

pera

ture

T [

K]

Time [s]

heating

300

400

500

600

700

800

900

1000

6000 6250 6500 6750 7000 72500

100

200

300

400

500

600

700

Tem

pera

ture

T [

K]

Fibr

e di

amet

er 2

R [

µm]

Time [s]

drawing

start coolingof furnace

runawaymonitordiameter

start drawing

Figure 3.26: The drawing of germanium gallium sulphide glasses. On the left handside the heating of the rod/preform, indicated by the temperature in the centre ofthe furnace is shown, while the same temperature and diameter monitor signal duringdrawing are shown on the right hand side.

starting and ending points (due to fibre rupture) of the drawing are indicated in thefigure. The applied fibre drawing speed was 1.35 m min−1.The mutual alignment of the fibre and diameter monitor is critical. A small (lateral ortangential) displacement of the fibre will result in a run away of the diameter signal.Furthermore, the diameter signal tends to have large deviations, due to vibrations ofthe fibre. Hence, the diameter monitor signal was only available for 200 s.The diameter of the fibre shown in Figure 3.26 was between 200 and 300 µm, whilethe obtained fibre length was approximately 17.5 m. The optical properties of apraseodymium doped fibre, drawn from a germanium gallium sulphide glass rod arediscussed in section 5.2.The working range (as derived in section 3.3.2) for drawing of germanium galliumsulphide glass fibre appears to be very small. At increased drawing velocity, accu-rate temperature control and monitoring of the drawing force becomes more impor-tant [30]. Currently, the fibre drawing tower is not equipped with a diagnostic toolfor measuring the drawing tension (e.g. torque measurement on winding drum [24]).It is expected that fibres smaller diameters (up to 150 µm) can be drawn using thepilot scale fibre drawing tower, by improved process control (i.e. automatic controlof the fibre drawing velocity and monitoring of the drawing force).In section 3.3.1, it is shown that the maximum glass temperature is obtained nearthe bottom of the furnace. During drawing of the germanium gallium sulphide glass,the temperature in the centre of the furnace (hot spot) is approximately 875 K (seeFigure 3.26b). Due to the short length of the furnace and the heat transport by thepurge gas flow, steep temperature gradients in the axial direction exist within the fur-nace. For the fibre drawing process of germanium gallium sulphide glasses, the use ofa short furnace is advantageous, because the glass is exposed shortly to temperatures


close to the crystallisation temperature, only. The temperature at the bottom of thefurnace is at least 150 K below the hot spot temperature. Hence, the experimentalconditions used for drawing of 200–300 µm germanium gallium sulphide fibre are inclose agreement with the optimum temperature for fibre drawing of about 750 K (atµ = 107 to 106 Pa s) as estimated from the viscosity-temperature equation 2.35 (seeregion 2 in Figure 3.5).

3.4 Conclusions

Germanium gallium sulphide fibres can be prepared from solid preforms with core-cladding structure. In the rod-in-tube process, the fibre preform is constructed byinserting a (thin) rod of core material into the cladding tube. Thin core glass rodscould be prepared by stretching of core glass rods (as melted) to the desired diameterin the fibre drawing tower. Cladding glass tubes can be prepared by a hot deforma-tion process, developed in this study.Selection of the working temperature range, for the hot deformation process, is crit-ical to prevent cracking of the material (at low temperature and high viscosity),crystallisation (due to high temperatures) or collapse upon removal of the needle(at low viscosity). The required viscosity of the material for the deformation pro-cess has to be between 108 and 108.5 Pa s. Cladding glass tubes, with composition(GeS2.5)98(GaS3)2, can be prepared around 675 K.Etching of the glass surfaces, prior to assembly of the fibre preform and fibre draw-ing, is needed to limit the formation of defects at the core-cladding interface duringfibre drawing and obtain fibres with low optical losses. Aqueous, alkaline solutions(e.g. caustic soda or ammonia) can be used to etch the surface of germanium gal-lium sulphide glasses. The best etching results are obtained using diluted causticsoda (0.02 M). The etching rate of more concentrated solutions (>0.5 M) is too highfor controllable etching. Due to negligible reactivity between (concentrated) acidsand germanium gallium sulphide glasses, these glasses can not be etched with acids.Hence, (concentrated) acids (e.g. nitric, sulphuric, hydrochloric or hydrofluoric acid)can be used only to clean contaminated glass surfaces, without impairments to theglass surface.The working range for fibre drawing of germanium gallium sulphide glass rods, withan initial diameter of 0.01 m, into fibre with a final diameter of 140 µm, is derivedusing a mathematical model. The maximum furnace temperature is bound by thelocal temperature inside the neckdown, which may not exceed either the tempera-ture at which the viscosity is too low for fibre drawing (approximately 800 K) or theon-set crystallisation temperature (approximately 750 K). The maximum applicablefibre drawing force, for a fibre with a diameter of 140 µm, is approximately 5 N. Inpractice, the minimum required fibre drawing velocity is 0.025 m s−1.Based on the modelling results, these conditions are met if the furnace temperature(modelled as a black body radiator) is between 800 and 830 K. Then the workingarea is bound by crystallisation (which limits the furnace temperature) and the axialstresses occurring in the fibre (which limit the maximum fibre drawing velocity to


0.075 m s−1). Precise control of the furnace temperature becomes more critical asthe fibre drawing speed increases. In practice, the required furnace temperature ishigher, because the radiant energy emitted by the furnace (modelled as black body)determines an upper limit for the radiant energy emitted by a real furnace.Unclad germanium gallium sulphide fibres with a diameter between 200 and 300 µmand a length of 17.5 m were obtained using the pilot scale fibre drawing tower. Basedon the modelling results, it is expected that germanium gallium sulphide fibres withdiameter less than 150 µm can be drawn using this equipment by improved processcontrol (i.e. automatic control of the fibre drawing velocity and monitoring of thedrawing force).

3.5 Nomenclature

VectorsF d Drag force due to purge gas flow on neckdown surface NF f Fibre drawing force NF g Force due to gravity NF i Force due to inertia acting on neckdown NF s Force due to surface tension at the surface of the neckdown NF µ Force due to stress Ng gravitational acceleration m s−2

n vector normal to surface -qcon energy flux at free boundary by conduction W m−2

qfb energy flux at free boundary W m−2

qrad energy flux at free boundary by radiation W m−2

u velocity m s−1

urel relative gas velocity m s−1

ua gas velocity m s−1

τ i,j stress tensor kg s−2m−1

τ d stress due to purge gas drag force on the free surface kg s−2m−1

τ s stress due to surface tension kg s−2m−1

Scalarsa radius of fibre core mA surface area m2

Cp heat capacity at constant pressure J kg−1K−1

d diameter mh heat transfer coefficient (convection) W m−2K−1

H height of the furnace mk thermal conductivity of glass W m−1K−1

ka thermal conductivity of purge gas W m−1K−1

keff Effective thermal conductivity (Rosseland approximation) W m−1K−1

krad Radiative contribution to the effective W m−1K−1

thermal conductivity (Rosseland approximation)


l length mLf fibre length mn index of refraction -n0 refractive index of air -n1 refractive index of fibre core -n2 refractive index of fibre cladding -p pressure PaQ volume flow rate of the glass m3 s−1

r radial distance in cylindrical coordinates mrl optical path length mR radius of preform/neckdown/fibre mR∗ radius of curvature of the surface (radial direction, only) mR0 radius of preform mRf radius of fibre mRfur (inner) radius of furnace mT absolute temperature KTa ambient temperature KTf fibre temperature KTfur furnace temperature KTg glass transition temperature KTp preform temperature KTsurf surface temperature KTx crystallisation temperature Kt time su radial velocity m s−1

v axial velocity m s−1

vf axial velocity of the fibre m s−1

v0 axial velocity of the preform m s−1

z axial distance in cylindrical coordinates mZ axial distance at the furnace exit m

α linear absorption coefficient m−1

ǫfur emission coefficient of furnace -ǫglass (apparent) emission coefficient of glass -γ surface tension N m−1

ζext reflection coefficient -µ dynamic viscosity Pa sνa kinematic viscosity of purge gas νa = µ

ρ m2s−1

Φv viscous dissipation s−2

ρ density kg m−3

ρa density of purge gas kg m−3

σ Stefan-Boltzmann’s constant = 5.67033 10−8 W m−2K−4

τr residence time sθ azimuthal angle in cylindrical coordinates rad


Dimensionless numbersNu Nusselt number -Nud Nusselt number axi-symmetric flow over cylinder -Re Reynolds’ number -Red Reynolds’ number axi-symmetric flow over cylinder -

3.6 Bibliography


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[20] L. Glicksman, “The cooling of glass fibres,” Glass Technol., vol. 9, pp. 131–138,October 1968.

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[23] V. Vasiljev, G. Dulnec, and V. Naumchic, “The flow of a highly viscous liquidwith a free surface,” Glass Technol., vol. 30, pp. 83–90, April 1989.

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[27] H. Tompkins and W. McGahan, Spectroscopic ellipsometry and reflectometry :a user’s guide. New York: John Wiley & Sons, Inc., 1999. ISBN 0-471-18172-2.


[28] T. B., H. Misiorek, E. Vateva, A. Jezyowski, and D. Arsova, “Low-temperaturethermal conductivity of GexAs40−xS60 glasses,” Solid State Comm., vol. 134,pp. 349–353, 2005.

[29] G. Homsy and K. Walker, “Heat transfer in laser drawing of optical fibres,” GlassTechnol., vol. 20, pp. 20–26, February 1979.

[30] R. Jaeger, A. Pearson, J. Williams, and H. Presby, “Fiber drawing and control,”in Optical fiber telecommunications (S. Miller and A. Chynoweth, eds.), ch. 9,pp. 263–298, Academic press, 1979.

Chapter 4

Modelling light amplification

in praseodymium doped

single-mode fibres

In this chapter, a model, describing amplification of optical signals using a praseody-mium doped fibre amplifier, is presented. The model is used to study the amplifiercharacteristics (e.g. gain and noise) of the praseodymium doped fibre (so-called ac-tive fibre). The model input parameters incorporate the optical properties of thepraseodymium doped glasses, the geometry of the fibre and the configuration (e.g.co-propagating, counter-propagating and bi-directional pumping schemes) of the am-plifier.In the first section, the principle of operation of a praseodymium doped amplifieris described. Next, the governing equations for a spatially and spectrally resolvedamplifier model will be presented.In section 4.2, the outcome of the model is compared with measurement results ob-tained with a praseodymium doped fibre amplifier, in order to verify the validity ofthe model. This is done, to ensure that the model is suitable for the design and de-velopment of PDFA’s based on other glass compositions (such as germanium galliumsulphide glasses) or geometry of the fibre, also. The PDFA, used for validation ofthe model, was based on praseodymium doped fluoride glass fibre modules and wasbuilt using commercially available components. Due to the modular set-up of thePDFA, the amplifier characteristics in different operation conditions, can be assessedin different configurations of the amplifier.In section 4.3, the outcome of the amplifier model and the experimental results arediscussed in relation to experimental errors and the effect of amplifier configurationon gain and amplified spontaneous emission noise. The model can also be used tooptimise the design elements such as fibre length and core radius of Pr-doped fibreamplifiers. The use of the amplifier model, as a tool for design of praseodymium dopedfibre amplifiers based on praseodymium doped germanium gallium sulfide glasses, is

125


discussed in chapter 5.Finally, some concluding remarks are given in the last section of this chapter.

4.1 Praseodymium doped fibre amplifier model

In this section, the governing equations of a steady-state model for the praseodymiumdoped fibre amplifier are presented. Steady-state models describing the properties ofthe praseodymium system were proposed independently around 1992 by Karasek [1],Pedersen [2], and Urquhart [3]. The application of the steady-state assumption inamplifier model is discussed in section 4.1.1. The amplifier model, presented here, ismainly based on the work by Karasek [4] and the numerical solver developed by VanOsch [5]. The amplifier noise analysis is based on the work of Olsson [6].The light in the amplifier is modelled as a number of optical beams i, with fre-quency νi, travelling through the fibre. The frequency of the (monochromatic) pumpand signal light is νs and νp, respectively. In addition, amplified spontaneous emission(ASE) is travelling through the fibre. The ASE is caused by amplification of photonsoriginating from spontaneous decay of the excited state (see section 1.2.1). In orderto compute the amplified spontaneous emission (ASE) spectra, the spectrum is di-vided into a number of wavelength bands of frequency bandwidth ∆ν centred arounda wavelength1 λi = c/νi. A typical output spectrum, as determined by the amplifiermodel, is shown in Figure 4.1.In order to calculate the power of signal, ASE and pump light, propagating in thelongitudinal direction of the fibre, the fibre is considered as a concatenation of seg-ments of length ∆z (see Figure 4.2). In each segment, the distribution of the opticalintensity (as a function of frequency ν) of the signal, ASE and pump light in theradial direction is taken into account. The praseodymium dopant is assumed to bedistributed uniformly in the fibre core.The interaction of the light with the praseodymium dopant is discussed in sec-tion 4.1.1. These interactions are described by the population density of each energylevel, the electronic transitions and the transition rates between the energy levels ofthe Pr3+ ions. The transition rates are related to the emission and absorption crosssections, as determined using Judd-Ofelt theory (see chapter 2). The (steady state)population densities of both ground state (3H4) and excited state (1G4) are obtainedfrom the calculated transition rates between the energy levels of praseodymium.Due to the interactions of the light with the praseodymium, the intensity of the signal,ASE and pump light changes, as the light travels through the fibre. The power ofthe light, at each frequency ν, in the longitudinal direction of the fibre is modelled byso-called propagation equations, which are presented in section 4.1.2.The distribution of the optical intensity of the light in the radial direction of the fibreis discussed in section 4.1.3. The distribution (so-called mode-profile) is a function ofthe wavelength of the signal, ASE and pump light and the geometry of the fibre.

1In this work, the wavelength λ is referred to as if the wavelength was determined in free space [18].The wavelength of light is given by λ = c/ν, where ν is the frequency of the light.

Modelling light amplification in praseodymium doped single-mode fibres 127

signalASE

λmin λmaxWavelength [a.u.]

Pow

er[a

.u.]

Figure 4.1: Typical output spectrum, showing the amplified signal and the amplifiedspontaneous emission, as determined by the amplifier model. The amplified sponta-neous emission spectrum is divided into a number of wavelength bands.

r

z

z = zz = z + ∆z

2a

l

Ps

P+p P−

p

P+ASE

P−ASE

Figure 4.2: The fibre with a core diameter of 2a and a length l is considered as a con-catenation of segments of length ∆z. The direction of the signal Ps, co-propagatingP+

p and counter propagating P−p pump power are indicated by the arrows. Further-

more the directions of co-propagating P+ASE and counter propagating P−

ASE amplifiedspontaneous emission are shown.


0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0

1

2

3

4

Pr

Pum

pG

SA

Sig

nal

Em

issi

on

Sig

nal

ESA

Sig

nal

GSAEner

gy[c

m−

1]

3H4

3H5

3H6

3F2

3F3

3F4

1G4

1D2

Figure 4.3: Energy level diagram of praseodymium, indicating the electronic transi-tions for stimulated emission, pump and signal ground state absorption (GSA) andsignal excited state absorption (ESA) which are used in the model. Furthermore,several (non-radiative) transitions are shown (dashed lines).

The praseodymium doped fibre amplifier adds amplified spontaneous emission to theoptical signal, which results in noise. In section 4.1.4, a model for the characterisationof the signal to noise ratio (SNR) and the amplifier noise figure is described.The model equations cannot be solved analytically. The numerical methods, whichare applied to find a solution for the model equations, are presented in section 4.1.5.

4.1.1 Operation principle of the PDFA

The (general) principle of operation of a praseodymium doped fibre amplifier is dis-cussed in section 1.2.1. In this paragraph, the electronic transitions incorporated inthe amplifier model are discussed. In the remainder of this chapter, the energy levelswill be denoted by the numbers 0–4, as indicated on the left hand side of Figure 4.3.The transition rates between the various energy levels in the doped material causedby absorption, stimulated emission and spontaneous emission are described by rateequations [4]. The number of electronic transitions from level i to level j per unittime is given by the transition rateWij .The Pr3+ ions are pumped at a frequency νp of about 1.03 µm from the groundstate 0 (3H4) into the excited state 3 (1G4). The pump ground state absorption rateW03(r, z, νp) for this transition, at frequency νp, is

W03(r, z, νp) = σ03(νp)P+

p (z) + P−p (z)

hνpI(r, νp) (4.1)


where σ03(νp) is the pump absorption cross section at frequency νp, P+p (z) and P−

p (z)are the local pump power in the forward (co-propagating) and backward (counter-propagating) directions, respectively, h is Planck’s constant and I(r, νp) is the nor-malised intensity distribution of the pump power in the radial direction at frequencyνp. The derivation of the normalised intensity distribution function is discussed insection 4.1.3.Stimulated or spontaneous emission of photons can occur between level 3 (1G4) andlevel 1 (3H5). Note that photons, caused by stimulated emission, have exactly thesame frequency, phase and direction as the incident photons of the signal [7, 8], i.e.are coherent with respect to the incoming signal. Spontaneous emitted photons haveno coherence characteristics with respect to the signal light. The spontaneously emit-ted photons, which are captured by the fibre (i.e. coupled into the fibre mode), travelalong the fibre and are amplified resulting in amplified spontaneous emission (ASE).The (total) transition rate for stimulated emission W31 due to a signal at frequencyνs plus ASE in a frequency range between c/λmin and c/λmax is given by

W31(r, z, νs, ν) = σ31(νs)Ps(z)

hνsI(r, νs)

+

∫ c/λmax

c/λmin

σ31(ν)P+

ASE(z, ν) + P−ASE(z, ν)

hνI(r, ν) dν (4.2)

where the first term on the right hand side describes the transition rate due to stim-ulated emission by the signal and the second term accounts for the transition ratedue to ASE. In this equation, σ31(ν) is the signal emission cross section at frequencyνs and Ps is the signal power. The normalised intensity distribution at the signalfrequency νs is denoted by I(r, νs). The ASE is evaluated in the wavelength rangeλmin–λmax. P+

ASE(z, ν), P−ASE(z, ν) are the ASE power spectral density in the for-

ward (co-propagating) and backward (counter-propagating) directions respectively,the corresponding normalised intensity of the ASE is I(r, ν).Apart from the fundamental transitions, which are responsible for amplification, themodel accounts for competing transitions in which the signal photon will be lost re-sulting in decreased gain.Both signal and ASE photons can be absorbed in the signal excited state absorption(ESA) process. The signal excited state absorption rate W34 is given by

W34(r, z, νs, ν) = σ34(νs)Ps(z)

hνsI(r, νs)

+

∫ c/λmax

c/λmin

σ34(ν)P+

ASE(z, ν) + P−ASE(z, ν)

hνI(r, ν) dν (4.3)

where σ34(νs) is the signal excited state absorption cross section. The first term onthe right hand side describes the transition rate due to excited state absorption of thesignal and the second term accounts for the excited state absorption transition ratedue to ASE.Furthermore, electrons decay from level 3 (1G4) via non-radiative, phonon relaxation.


This non-radiative decay to the ground state (level 0) occurs either directly or viasome of the intermediate 3F4,

3F3,3F2,

3H6 and 3H5 levels. The lifetime of level 3(1G4) is called the emission lifetime τe.Due to both signal and ASE ground state absorption (GSA), the Pr3+ ions are ele-vated from the ground state 0 (3H4) to level 2 (3F4). The transition rate for signalground state absorption is not evaluated, because of the fast (non-radiative) decayto the ground-state. However, these losses of signal and ASE photons by signal GSAare accounted for by a wavelength dependent absorption factor (see equation 4.12).The intermediate level 1 (3H5) is depopulated by non-radiative decay to the groundstate (level 0). It is assumed that due to this fast depopulation, the population den-sity of level 1 (3H5) can be neglected (Λ1(r, z)=0).For continuous wave (CW) signal beams, and for those signals modulated at frequen-cies greater than approximately 10–100 kHz [9, 10], equilibrium between the varioustransition rates is obtained (steady state situation). The amplifier response to amodulated light wave (so-called transient gain modulation) is dependent on the timedependent changes of the population inversion. The time dependent changes of thepopulation inversion will vanish for modulation frequencies above 10–100 kHz. Thischaracteristic frequency range is largely determined by the emission lifetime τe of theexcited state [9, 11].In the steady state situation, the population densities of the excited state Λ3(r, z)and the ground state level Λ0(r, z) can be derived from the rate equations, under theassumption that the population densities of the other exited states is negligible.

Λ3(r, z) = ΛPr(r, z)W03(r, z)

W03(r, z) + W34(r, z) + W31(r, z) + 1/τe(4.4)

Λ0(r, z) ≈ ΛPr(r, z) − Λ3(r, z) (4.5)

where ΛPr(r, z) is the dopant distribution (expressed in the number of praseodymiumions per unit volume) across the fibre core cross section and the τe is the emissionlifetime of the excited state level 3 (1G4).When the population densities Λ0 and Λ3 are known, the propagation of pump, signaland ASE can be determined (see section 4.1.2.The population inversion (which is necessary for amplification by stimulated emis-sion) is defined as the number of ions in the excited state level 3 (1G4) relative tothose those in the intermediate level 1 (3H5). At low pump powers, the populationinversion of a four-level system increases linearly with pump power [12]. Signal GSAis negligible when a high level of population inversion is achieved.

4.1.2 Propagation equations

The fibre is considered as a concatenation of segments of length ∆z, each of them withuniform praseodymium distribution in the fibre core. Propagation equations describethe evolution of optical power versus distance. As discussed in [5], signal, ASE andpump power are subject to attenuation due to intrinsic fibre absorption and scattering


losses α(ν) and due to absorption by the praseodymium dopant. The absorption bypraseodymium is dependent on the (local) population inversion.The propagation of pump power P±

p , in both in the co-propagating (+) and counter-propagation (–) directions is described by

dP±p (z, νp)

dz= ∓ [gp(z, νp) + α(νp)]P

±p (z) (4.6)

where gp(z, νp) is the pump ground state absorption factor and α(νp) is the loss due tointrinsic fibre absorption and scattering losses at the pump frequency νp. The pumpground-state absorption factor gp(z) is given by

gp(z, νp) = 2πσ03(νp)

∫ a

0

Λ0(r, z)I(r, νp)r dr (4.7)

where a is the core radius.The propagation of the signal power Ps is

dPs(z, νs)

dz= [ge(z, νs) − ga(z, νs) − gg(z, νs) − α(νs)]Ps(z) (4.8)

where ge(z, νs) is the signal/ASE stimulated emission factor for the transition fromlevel 3 to level 1, ga(z, νs) is the signal/ASE excited-state absorption factor for thetransition from level 3 to level 4, gg(z, νs) is the signal/ASE ground-state absorptionfactor for the transition from level 0 to level 2 and α(νs) is the loss due to intrinsicfibre absorption and scattering losses at signal frequency νs.The propagation of amplified spontaneous emission P±

ASE with frequency νi and band-width ∆ν (in both co-propagating and counter propagating directions) is given by

dP±ASE(z, νi)

dz= ± [ge(z, νi) − ga(z, νi) − gg(z, νi) − α(νi)] P

±ASE(z, νi)

±2hν∆νige(z, νi) (4.9)

where ±2hνi∆νige(z, νi) is the contribution of spontaneous emission in both propaga-tion directions [13]. In this term, the factor of 2 reflects that (amplified) spontaneousemission power occurs in polarisation modes which are parallel and orthogonal tothat of the signal [11]. It is assumed that the probability for spontaneous emissionwithin in a single-mode (guided by the fibre) is the same as the probability of a stimu-lated emission event for a single photon [7]. A description of the underlying quantummechanics of the occurrence of spontaneous emission is beyond the scope of this thesis.

In equations 4.8 and 4.9, the signal/ASE stimulated emission factor ge(z, ν) for thetransition from level 3 to level 1 is given by

ge(z, ν) = 2πσ31(ν)

∫ a

0

Λ3(r, z)I(r, ν)r dr (4.10)


0

pump

signal

I(r)

r

a

2acore

cladding

Figure 4.4: Distribution of the optical power (intensity) in the fibre core at bothpump and signal wavelength (single-mode condition).

the signal/ASE excited-state absorption factor ga(z, ν) for the transition from level 3to level 4 is given by

ga(z, ν) = 2πσ34(ν)

∫ a

0

Λ3(r, z)I(r, ν)r dr (4.11)

the signal/ASE ground-state absorption factor gg(z, ν) for the transition from level 0to level 2 is given by

gg(z, ν) = 2πσ02(ν)

∫ a

0

Λ0(r, z)I(r, ν)r dr (4.12)

where σ02 is the signal ground state absorption cross section at frequency ν.

4.1.3 Light guiding in single-mode fibres

The propagation of light through a step index single-mode fibre is determined usingMaxwell’s equations. A comprehensive derivation of the characteristic equation (so-lution of the wave equations) for a step index fibre can be found in e.g. Van Ettenet al. [14] and is beyond the scope of this thesis. In a single-mode fibre, the electro-magnetic field is concentrated in the waveguide’s core and decreases exponentially inthe cladding. Maximum intensity at each wavelength is located near the axis of thefibre ( [15], see Figure 4.4). In a multi-mode fibre, several modes are available for thepropagation of light. In a multi-mode fibre, each mode has its own characteristic fielddistribution (not shown).The electro-magnetic field that is associated with a particular (transmission) modeof a step index fibre depends on the normalised frequency V of the light, which is


defined [14] as

V =2πa

λ

√

n21 − n2

2 (4.13)

in which λ is the wavelength, a is the core radius and n1, n2 are the refractive indicesof the core and cladding respectively. The factor

√

n21 − n2

2 is called the numericalaperture NA. The normalised frequency V can be adjusted by the NA and the coreradius. The NA is determined by the refractive indices of the core and cladding glass,which in turn are related to the glass composition. The core radius is set in the fibredrawing process.For values of V , which are smaller than 2.405, only one transmission mode can existin the waveguide [14]. Hence, the fibre is single-mode for wavelengths longer than thecut-off wavelength of the fibre. The cut-off wavelength λc is given by [14]:

λc =2πa

√

n21 − n2

2

2.405(4.14)

In the case of a weakly guiding fibre, i.e. the relative difference between the indexof refraction of the core and cladding material is small, the optical intensities of thepump and signal modes can be calculated (see Van Etten et al. [14] and Annex C).The normalised intensity I(r, ν) in the fibre core [13, 14], for a single-mode is

I(r, ν) =1

π

[

wt

aV

J0(utr/a)

J1(ut)

]2

(4.15)

in which ut is the transverse propagation constant and wt is the transverse decayconstant (see e.g. [14, 16]), r is the radial distance and ν is the frequency of the light.At the interface between core and cladding (r = a), the magnitude of the electro-magnetic field in the core is equal to the magnitude of the field in the cladding. Thiscondition is satisfied when [14]

V 2 = u2t + w2

t (4.16)

The value of the transverse propagation constant wt as a function of V is tabulatedby Jeunhomme [16]. The Bessel functions of the first kind J0, J1 are given in AnnexC.Equation 4.15 is used to determine the intensity distribution of pump, signal and ASElight in the fibre core in the radial direction.

4.1.4 Amplifier noise analysis

In optical communication systems, amplifiers along the transmission link add ampli-fied spontaneous emission to the optical signal, which results in noise. At the receiver,the optical signal and the amplified spontaneous emission (around the signal wave-length) are converted simultaneously into an electrical signal. The signal to noiseratio (SNR) at the receiver is an important figure to evaluate the performance of acommunication system.


The amplifier noise analysis, presented here, is based on the work by Olsson [6] andevaluates the electrical noise resulting from ASE after conversion of the output spec-trum into an electrical signal (i.e. photo-electric current from the photo detector) atthe receiver.The signal power and the spontaneous emission spectrum at the output of the PDFAcan be determined from equations 4.8 and 4.9 (see section 4.1.2).The electrical signal power S originating from the detector in the receiver is propor-tional to the square of the signal current is (so-called square law detection).

S ∝ (is)2 (4.17)

The photo-electric current i originating from the optical power P (ν) at frequency νentering the detector is given by

i =eηd(ν)

hνP (ν) = RdP (ν) (4.18)

with detector responsivity

Rd =eηd(ν)

hν(4.19)

where e is the elementary charge, ηd(ν) is the photodiode quantum efficiency, h isPlanck’s constant and ν the signal frequency. Note, all photons (within a broadwavelength range) are converted into electrons by the detector.A detailed description of the amplifier noise terms from the (total) intensity of theelectric field, based on the derivation by Olsson [6], is given in Appendix D2.The total noise contribution to the receiver, consists of shot noise Nshot, signal-spontaneous beat noise Ns−sp and spontaneous-spontaneous beat noise Nsp−sp [6].

Ntot = Nshot + Ns−sp + Nsp−sp (4.20)

The thermal noise contribution of the receiver (i.e. power generated by the receiverin the absence of an optical signal) is assumed negligible compared to the signal- andspontaneous-spontaneous beat noise [17].Shot noise originates from statistical fluctuations in the detected optical power, dueto random arrival in time of photons (with discrete energy quanta). The magnitudeof the shot noise is proportional to the current i through the detector and depends onthe electrical bandwidth Be of the detector [17]. A detailed derivation of shot noiseis given in e.g. Yariv [7]. The power of the shot noise Nshot, related simultaneousdetection of the signal and ASE, is given by [6]

Nshot = 2e(is + isp)Be (4.21)

2Note that in contrast to the noise terms as presented by Olsson [6], the noise terms as presentedhere are based on the photo current equivalents of the signal and amplified spontaneous emissionpower at the amplifier output. For the purpose of the noise analysis of the PDFA, the amplifierproperties such as signal output power and amplified spontaneous emission power will be treateddifferently.


a) b)Pin Pin

BPF BPFPDFARx Rx

Bo Bo

SNRin SNRout

ηd, Beηd, Be ηin, G, PASE, ηout

Pout, PASE, αc

Figure 4.5: Set-up for determination of the SNR at both the amplifier input (a) andoutput (b) using an opto-electronic receiver (Rx) with electrical bandwidth Be. Anoptical bandpass filter (BPF) with bandwidth Bo is inserted in front of the photodetector.

where the equivalent photo-electric currents of the signal and amplified spontaneousemission powers are denoted by is and isp, respectively. Upon opto-electronic conver-sion at the detector, interference between light of different frequencies occurs. Theinterference (so-called beating or mixing) of ASE components with the signal at theoptical detector generates signal-spontaneous beat noise (see Appendix D). The powerof the signal-spontaneous beat noise Ns−sp is given by [6]

Ns−sp =4(isisp)Be

Bo(4.22)

where Bo is the optical bandwidth of a filter, which is inserted between the amplifierand the detector. Spontaneous-spontaneous beat noise is due to the mixing of theASE with itself. The power of the spontaneous-spontaneous beat noise Nsp−sp is [6]

Nsp−sp =2i2sp(BoBe − 1

2B2e )

B2o

(4.23)

The performance of the PDFA added to a telecommunication system is described byits noise figure F , which is defined as

F =SNRin

SNRout(4.24)

where the signal to noise ratio (SNR) at the input and output of the PDFA are givenby SNRin and SNRout, respectively. Hence, the noise figure is a measure of the signalto noise ratio degradation caused by the amplifier. Usually, the noise figure is de-termined (experimentally) using a probe signal without the presence of spontaneousemission originating from the light source (e.g. laser). In this case, no beat noise ispresent, i.e. the probe signal is shot noise limited.The SNRin is defined as the SNR at the output of the detector photodiode, afterdetection of the (shot noise limited) optical input signal Ps in the receiver (see Fig-ure 4.5a). The SNR at the amplifier input is given by the signal power Sin and theshot noise generated at the detector Nshot,in. Note that isp equals zero for shot noise


Pr-doped fibre

Ytterbium dopedfibre laser

(pump laser)

Powermeter(pump monitor)

WSC1030/1300nm


(pump laser)


WSC1030/1300nm

Isolator Isolator

PDFA

PDFA

GGff

Gff

ηin ηout

Figure 4.6: The PDFA (considered as a single device with input and output fibre,left hand side) and its components (i.e. pump laser, wavelength selective couplers(WSC), isolators and praseodymium doped fibre, right hand side). The definitions ofthe measurable, fibre-to-fibre gain Gff , the gain of the praseodymium doped fibre G(active fibre) and the losses between the active fibre and the input and output of thedevice ηin and ηout are indicated by the arrows.

limited signals.

SNRin =

(

S

Nshot

)

in

=i2s,in

2e(is,in)Be=

αcηdPs

2hνBe(4.25)

in which the photo-electric current originating from the signal is given by is,in =RdαcPs, where αc accounts for the connection losses between the amplifier and thereceiver.The SNRout is defined as the SNR at the output of the detector photodiode, whenthe optical output signal of the PDFA is fed to this detector (see Figure 4.5b). TheSNR at the amplifier output is given by

SNRout =

(

S

Ntot

)

out

(4.26)

=i2s,out

Nshot,out + Ns−sp,out + Nsp−sp,out

The photo-electric currents generated by the amplified signal is,out and the ASE isp

are given by

is,out = ηinGPsηoutαcRd (4.27)

isp = PspηoutαcRd (4.28)

where G is the gain provided by the amplifier, Ps is the signal power (at the PDFAinput) and the amplifier input and output coupling efficiencies are represented by ηin

and ηout, respectively. This is shown schematically in Figure 4.6.The shot noise Nshot,out, signal-spontaneous beat noise Ns−sp,out and spontaneous-


spontaneous beat noise Nsp−sp,out at the output of the amplifier are obtained bysubstitution of equation 4.27 and 4.28 into equations 4.21–4.23:

Nshot,out = 2e(ηinGPs + Psp)ηoutαcRdBe (4.29)

Ns−sp,out =4(ηoutαc)

2ηinGPsPspR2dBe

Bo(4.30)

Nsp−sp,out =2(ηoutαcPspRd)

2(BoBe − 12B2

e )

B2o

(4.31)

Substitution of equations 4.25, 4.26 and 4.29–4.31 into 4.24 yields the noise figure F(for shot noise limited input signals) of the PDFA

F =

[

αc

η2in

(

ηinGPs + Psp

αcG2Psηout+

2ηdηinPsp

GhνBo+

(Bo − 12Be)ηdP

2sp

G2PshνB2o

)]

(4.32)

In this equation, the input signal power is Ps af frequency νs, the gain of the amplifieris G and power of the ASE at the amplifier output (within the optical bandwidth Bo)is given by Psp. The three successive terms account for the contributions of shotnoise, signal-spontaneous beat noise and spontaneous-spontaneous beat noise to thenoise figure, respectively.

4.1.5 Numerical solution of the model equations

The model equations, as presented in the previous sections, can only be solved nu-merically. In this work, the solver developed by Van Osch [5] is used. The solver isprogrammed in FORTRAN using the NAG Fortran Library.Using the transition rates obtained from equations 4.1 to 4.3 as a starting point, thepopulation densities in the ground state and the excited state are calculated usingequations 4.4 and 4.5. Then the set of emission and absorption factors is calculatedusing equation 4.7 and 4.10–4.12. The evolution of the pump, signal and ASE powersis obtained from simultaneous integration of the coupled set of ordinary differentialequations 4.6, 4.8 and 4.9.In order to solve the set of equations, boundary conditions for pump, signal and ASEpowers have to be determined at z = 0. For the counter-propagating pump and ASEbeams, the boundary conditions are only known at z=L and therefore an initial guessis made in order to determine the conditions at z = 0. A Newtonian iteration tech-nique is used to correct the estimated boundary conditions of the pump, signal andASE power. The simultaneous integration of the coupled set of ordinary differentialequations 4.6, 4.8 and 4.9 and adaptation of the boundary conditions at z=0 is re-peated until the final solution of the equations is obtained.The known boundary conditions for the co-propagating and counter-propagatingpump powers are P+

p (0) = ΓPp,in and P−p (L) = (1 − Γ)Pp,in where Γ is the frac-

tion of pump power in the co-propagating direction. The boundary condition for thesignal power is Ps(0) = Ps,in, while the bounds for ASE are set to zero P+

ASE(0) = 0


and P−ASE(L) = 0.

After solving the model equations, the noise figure (at the signal frequency) is calcu-lated according to equation 4.32, using the obtained signal output power (Ps(L)) andthe power of the ASE propagating in the co-propagating direction (P+

ASE(L)).

4.2 Model validation

In this section, the results obtained from the fibre amplifier model (simulated data) arecompared with experimental data. For the purpose of this analysis, a praseodymiumdoped fibre amplifier based on two commercially available praseodymium doped fi-bre modules (NEL type FFM–I–R–1000–A–7–F) is used. Each module contains 7 m,1000 ppm Pr-doped indium-based fluoride glass fibre between the two silica fibre pig-tails (see Appendix A for detailed specifications). The input of the fibre amplifiermodel includes the amplifier operating conditions and the physical properties of thepraseodymium doped fibre. The model is verified by measuring amplifier input andoutput signals and comparing them to the corresponding simulation results for differ-ent operation conditions.In sections 4.2.1 and 4.2.2, the method used for experimental determination of the gainand noise characteristics of the PDFA and the experimental set-up are described. Theamplifier characteristics were determined for the co-propagating, counter-propagatingand bi-directional pumping configurations. The model outcome and the experimentaldata are compared in section 4.2.3–4.2.5.

4.2.1 Experimental determination of gain and noise

In this section, the determination of gain and noise figures from the experimentaldata is described. The measurement set-up is shown schematically in Figure 4.7.Continuous wave (CW) probe signals are generated by a combination of a tuneablelaser source (TLS) and an optical attenuator. Using this set-up, spontaneous emission(originating from the tuneable laser source) is reduced by the optical attenuator. Theremaining spontaneous emission at the output of the optical attenuator is negligible.At the PDFA output, the amplified signal is observed in the presence of amplifiedspontaneous emission (ASE) noise. The input and output power spectra are mea-sured by an optical spectrum analyser (OSA).In the remainder of this chapter, the PDFA (containing pump laser, wavelength se-lective couplers (WSC), isolators and praseodymium doped fibre) is considered as asingle device. Due to internal losses of the PDFA (i.e. coupling losses, mode mis-matches (due to different fibre types) and internal losses of the components e.g. dueto scattering and absorption), the measurable gain of the PDFA (or fibre-to-fibregain) Gff is always lower than the gain of the praseodymium doped fibre G insidethe PDFA. This is shown schematically in Figure 4.6. The fibre-to-fibre gain Gff isrelated to the gain of the praseodymium doped fibre G (active fibre) as

Gff = ηinGηout (4.33)


α

PDFAAttenuator OSATLS

Figure 4.7: Measurement set-up. Signals are generated by a tuneable laser source(TLS) and an optical attenuator. The output power of the PDFA is measured withan optical spectrum analyser (OSA).

BRB

Ptot

Pout

2Psp,f

λs

PASE(∨)

PASE(∧)

P[d

Bm

]

λ [m]

Figure 4.8: Application of the interpolation-subtraction technique on experimentaldata taken from an optical spectrum analyser. The power Ptot is measured within asmall wavelength range determined by the resolution bandwidth BRB of the OSA.

where ηin and ηout are the losses at the input and output of the praseodymium dopedfibre, respectively. These losses are calculated from the (wavelength dependent) lossesof the individual components (i.e. isolators and WSC’s) used to construct the PDFA.The interpolation-subtraction technique (see Figure 4.8) can be applied to obtain thefibre-to-fibre signal gain Gff . The signal power Pout equals the total measured powerPtot at the signal wavelength minus the ASE noise contribution at this wavelength:

Pout = Ptot − 2Psp,f (4.34)

where the factor of 2 reflects that (amplified) spontaneous emission power occurs inboth polarisation modes, which are quided by the fibre. These polarisation modesare parallel and orthogonal to that of the signal [11]. Hence, Psp,f equals the ASEpower, which has the same polarisation state as the signal. The ASE power Psp,f


can be approximated by the harmonic average of the total ASE powers PASE(∨) andPASE(∧) adjacent to the signal wavelength:

Psp,f =

√

PASE(∨)PASE(∧)

2(4.35)

The gain is given by

Gff =Pout

Pin=

Ptot −√

PASE(∨)PASE(∧)

Ps(4.36)

where Pin is the (measurable) signal input power at the signal wavelength λs.Using the experimentally determined signal and ASE power, the noise figure can beestimated. The SNR at the input of the amplifier is given by

SNRin =

(

S

Nshot

)

in

(4.37)

where the input signal power is given by

Sin = (iin)2 = (RdPin)2 (4.38)

and the noise power of the (shot noise limited) input signal equals

Nin = Nshot = 2eiinBe = 2eRdPinBe (4.39)

The optical power Pin of the (shot noise limited) input signal, used in these equations,is measured using the OSA.If the ASE power at the amplifier output Psp is much smaller than the amplifieroutput power Pout, the spontaneous-spontaneous beat noise can be neglected (i.e.the output signal is signal-spontaneous beat noise limited). The SNR at the outputof the amplifier is given by

SNRout =

(

S

Ns−sp

)

out

(4.40)

where the signal power at the amplifier output is

Sout = (iout)2 = (RdηinGPinηout)

2 (4.41)

and the noise power of the (signal-spontaneous beat noise limited) output is given by

Nout = Ns−sp = 4ioutispBe

Bo= 4R2

dηinGPinηoutPspηoutBe

Bo(4.42)

The operational noise figure Fs−sp is given by the ratio between the shot noise limitedinput SNR (equation 4.37) and the signal-spontaneous beat noise limited output SNR(equation 4.40).

Fs−sp =SNRin

SNRout=

2Rd

eBo

Psp

ηinG(4.43)


This result can be related to measurable parameters Pin, Ptot, PASE(∨) and PASE(∧)

assuming the detector quantum efficiency ηd equals 1. The ASE power Psp is deter-mined from the measurable ASE power Psp,f by

Psp,f = Pspηout (4.44)

while the relation between the fibre-to-fibre gain Gff and the active fibre gain Gis given by equation 4.33. The power Ptot is measured within a small wavelengthrange determined by the resolution bandwidth BRB of the OSA. Hence, the opticalbandwidth Bo (in equations 4.42 and 4.43) equals the resolution bandwidth BRB ofthe optical spectrum analyser. Substitution of equations 4.33 and 4.44 into equation4.43 gives

Fs−sp =2

hνBRB

Psp,f

Gff(4.45)

This experimentally obtained noise figure describes noise behaviour of the amplifier,if the amplifier output power Pout exceeds the ASE power Psp by at least one order ofmagnitude. When this condition is satisfied, the spontaneous-spontaneous beat noisecan be neglected. In section 5.1.3, the gain and noise figure (given by equation 4.32)for the application of the experimental PDFA as a pre-amplifier is discussed.

4.2.2 Experimental set-up used for amplifier model validation

The experimental set-ups of the praseodymium doped fibre amplifier for co-propaga-ting, bi-directional, and counter-propagating pumping configurations are shown sche-matically in Figure 4.9.The continuous wave (CW) signals, with wavelengths between 1250 and 1350 nm, aregenerated by a combination of a tuneable laser source (TLS, type HP 8167B) and anoptical attenuator (HP 8156A).A dual output ytterbium doped fibre laser (IPG Laser YLM–1030–500×2) was usedas a pump source for the praseodymium doped fibre amplifier (see Appendix A fordetailed specifications). The maximum output power of each output of this laseris 500 mW at a wavelength of 1030 nm. The signal and pump powers are com-bined/splitted in 1030/1300 WSCs, which are connected to the Pr-doped fibre mod-ules (NEL FFM–I–R–1000–A–7–F). Each module contains 7 m, 1000 ppm Pr-dopedfluoride fibre between the two silica fibre pigtails (see Appendix A for detailed speci-fications). Optical isolators3 are applied at the amplifier input and output to preventinstability of the output power due to reflections of signal and ASE.The input and output powers are measured with an optical spectrum analyser (OSA,type HP 86145A). The wavelength selective grating inside the spectrum analyser actsas a tuneable filter, which allows for measurement of the power as a function of wave-length.As the model only considers the active fibre section, the experimental data must be

3Optical isolators allow transmission of light, within a small wavelength range, in a single directiononly by blocking transmission in the other direction [18].


7 m Pr-dopedfibre module


(pump laser)


WSC1030/1300nm



(pump laser)


WSC1030/1300nm


(pump laser)


WSC1030/1300nm


(pump laser)


WSC1030/1300nm

α

Tuneable laser source

Attenuator OSA

α


Attenuator

α


Attenuator

OSA

OSA

a)

b)

c)

Isolator Isolator

Isolator

Isolator

Isolator

Isolator

Figure 4.9: Experimental set-up showing the PDFA incorporating a 2×7 m ofpraseodymium doped fibre in a) co-propagating pump configuration b) bi-directionalpump configuration and c) counter-propagating pump configuration.


0

5

10

15

20

25

301260 1280 1300 1320 1340

Los

s [d

B]

Wavelength [nm]

simulated 7mmeasured 7msimulated 14mmeasured 14m

Figure 4.10: Simulated and measured wavelength dependent loss (when no pumppower is applied) for 1 praseodymium doped fibre module (7 m) and 2 modules(14 m). The probe signal power is -30 dBm.

compensated for all power losses at both active fibre input and output. In the fol-lowing discussion, coupling losses, mode conversion losses (due to mismatches of themodes when connecting different fibre types) and internal losses of the optical compo-nents itself (e.g. scattering and absorption) are taken into account. The magnitudeof these losses was either determined from the specifications by the supplier or mea-sured separately. Hence, the (re-calculated) gain G of the active fibre is used in thevalidation of the amplifier model instead of the measurable gain Gff .The coupling of two 7 m Pr-doped fibre modules to each other introduces additionalsplicing and mode conversion losses (of approximately 1 dB, in total). In the simula-tions these extra losses were not taken into account.The measured and predicted signal loss (when no pump power is applied), in thewavelength range between 1250 and 1350 nm, for a single and for two concatenatedPr-doped fibre modules are shown in Figure 4.10. The probe signal input power is-30 dBm (1 µW). In an unpumped system (i.e. negligible inversion), the main lossesare caused by the fibre attenuation and coupling losses. The additional losses at higherwavelengths are caused by the signal ground state absorption (GSA) (see equation4.8).The simulated signal loss (in units of dB) is proportional to the fibre length. The mea-sured losses (at short wavelengths) of the two combined modules are slightly largerthan the values obtained from simulations due to the additional coupling and con-version losses (which are not accounted for in the model calculations). Additionalmeasurements also indicate a slight difference in the loss when comparing the twomodules to each other.

4.2.3 Co-propagating pumping scheme

The measured and calculated signal gain spectra in the wavelength range between1250 and 1350 nm, for the co-propagating pumping scheme, are depicted in Fig-


-25

-20

-15

-10

-5

0

5

10

15

20

25

1260 1280 1300 1320 1340

Gai

n [d

B]

Wavelength [nm]

7 m

simulated 100 mWmeasured 100 mWsimulated 200 mWmeasured 200 mWsimulated 300 mWmeasured 300 mW

-25

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-15

-10

-5

0

5

10

15

20

25

1260 1280 1300 1320 1340

Gai

n [d

B]

Wavelength [nm]

14 m


Figure 4.11: Simulated and measured wavelength dependent gain G (in co-propagating pump configuration for 1 module (7 m) and 2 modules (14 m). Theprobe signal power is -30 dBm.) The applied pump power is 100, 200, and 300 mW.

ure 4.11. A co-propagating pumping scheme is applied and the pump power is 100,200, and 300 mW, respectively. The probe signal power is -30 dBm.The gain values determined by the amplifier model are slightly lower than the mea-sured gain G, but the shape of the calculated spectra resemble the measured spectra.Extending the active fibre from 7 to 14 m, and hence increasing the losses, results ina slightly reduced gain. The large difference in the gain for 1 module (7 m) and 2modules (14 m), at longer wavelengths, is mainly caused by the additional losses dueto the signal ground state absorption (GSA).The (small signal) gain as a function of applied pump power is shown in Figure 4.12.Here, the wavelength of the probe signal is 1310 nm, which corresponds to the gainpeak of the amplifier. The model outcome has an almost constant slope, while mea-surement shows a small decrease of the slope for higher pump power. This slopeequals the amplifier gain efficiency, which is defined as the ratio between small signalgain (expressed in units of decibels) and the launched pump power (in milliwatts) [17].At the signal input level of -30 dBm, and rather low pump powers (up to 300 mW),the amplifier is saturated. (Gain saturation is the phenomenon that the gain of anamplifier decreases when the signal input power increases, due to the limited avail-ability of pump power.)The gain versus signal input power is shown in Figure 4.13. For small signal power,the gain is almost independent of the signal power, while the signal gain becomessaturated at larger signal input powers. The 3 dB saturation output power (i.e. thesignal output power at which the amplifier gain is decreased by a factor 2 with respectto the unsaturated gain, not shown) is approximately 13 dBm (20 mW) and 10 dBm(10 mW) for 1 module (7 m) and 2 modules (14 m), respectively.On the left hand side of Figure 4.14, the experimental signal gain and noise figure(using equations 4.36 and 4.45) are depicted for a probe signal power of -30 dBm. Theresolution bandwidth of the optical spectrum analyser was 0.1 nm (or equivalently17.5 GHz at 1310 nm). The noise figure increases with increasing signal wavelength


-10

-5

0

5

10

15

20

0 0.05 0.10 0.15 0.20 0.25 0.30

Gai

n [d

B]

Pump power [W]

simulated 7 mmeasured 7 msimulated 14 mmeasured 14 m

Figure 4.12: Simulated and measured gain as a function of applied pump power inco-propagating pump configuration for 1 module (7 m) and 2 modules (14 m). Theprobe signal power is -30 dBm at a wavelength of 1310 nm.

-5

0

5

10

15

20

-60 -50 -40 -30 -20 -10 0 10

Gai

n [d

B]

Signal input power [dBm]

7 m

100 mW

200 mW

300 mW

-5

0

5

10

15

20

-60 -50 -40 -30 -20 -10 0 10

Gai

n [d

B]


14 m

100 mW

200 mW

300 mW

Figure 4.13: Simulated (curves) and measured (symbols +, × and ) signal gain vssignal input power in co-propagating pump configuration for 1 module (7 m) and 2modules (14 m). The applied pump power is 100, 200, and 300 mW. The probe signalwavelength is 1310 nm.


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-10

-5

0

5

10

15

20

1260 1280 1300 1320 1340

Gai

n, n

oise

fig

ure

[dB

]

Wavelength [nm]

measured

G 7 mF 7 m G 14 mF 14 m

-15

-10

-5

0

5

10

15

20

1260 1280 1300 1320 1340

Gai

n, n

oise

fig

ure

[dB

]

Wavelength [nm]

simulated

G 7 mF 7 m G 14 mF 14 m

Figure 4.14: Measured and simulated signal gain (G) and noise figure (F ) vs wave-length in co-propagating pump configuration for 1 module (7 m) and 2 modules (14 m).The probe signal power is -30 dBm. The applied pump power is 300 mW.

due to ground state absorption [19].On the right hand side of Figure 4.14, the simulated gain and noise figure (accordingto equation 4.32) are shown. This equation was derived for shot noise limited inputsignal. The optical bandwidth Bo was 0.1 nm (or equivalently 17.5 GHz at 1310nm) in order to obtain a signal-spontaneous beat noise limited output signal (see alsosection 4.2.1). Under these conditions, the noise figure is dominated by the secondterm of equation 4.32 (signal-spontaneous beat noise) and can be compared with theexperimental noise figure.

4.2.4 Counter-propagating pumping scheme

The signal gain spectra, for the counter-propagating pumping scheme, are depictedin Figure 4.15. For small input signals (circa -30 dBm), the gain (per module) inthe counter-propagating pumping configuration is comparable with the gain in co-propagating pumping configuration.The gain efficiency (slope of the curves in Figure 4.16) of the counter-propagating con-figuration is comparable with the efficiency of the co-propagating pumping scheme.At relatively low pump power, the higher gain is obtained for the single module (7 m)amplifier. Approximately 75 mW extra pump power is needed to overcome the lossesintroduced by the additional module and to achieve equal gain. The gain as a functionof signal input power is plotted in Figure 4.17. For small signal power, the signal gainis almost independent of the signal power, however for large signals gain saturationoccurs. According to the amplifier model, the 3 dB saturation output power (notshown) is approximately 15.5 dBm (35 mW) and 15 dBm (32 mW) for 1 module(7 m) and 2 modules (14 m), respectively.The amplifier model results show a somewhat stronger gain saturation in the co-propagating configuration (see Figure 4.13) compared to the counter-propagatingpumping scheme (see Figure 4.17).


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5

10

15

20

25

1260 1280 1300 1320 1340

Gai

n [d

B]

Wavelength [nm]

7 m


-25

-20

-15

-10

-5

0

5

10

15

20

25

1260 1280 1300 1320 1340G

ain

[dB

]

Wavelength [nm]

14 m


Figure 4.15: Simulated and measured wavelength dependent gain in counter-propagating pump configuration for 1 module (7 m) and 2 modules (14 m). Theprobe signal power is -30 dBm. The applied pump power is 100, 200, and 300 mW.

-10

-5

0

5

10

15

20

0 0.05 0.10 0.15 0.20 0.25 0.30

Gai

n [d

B]

Pump power [W]

simulated 7 mmeasured 7 msimulated 14 mmeasured 14 m

Figure 4.16: Simulated and measured gain as a function of applied pump power incounter-propagating pump configuration for 1 module (7 m) and 2 modules (14 m).The probe signal power is -30 dBm at a wavelength of 1310 nm.


-5

0

5

10

15

20

-60 -50 -40 -30 -20 -10 0 10

Gai

n [d

B]


7 m

100 mW

200 mW

300 mW

-5

0

5

10

15

20

-60 -50 -40 -30 -20 -10 0 10

Gai

n [d

B]


14 m

100 mW

200 mW

300 mW

Figure 4.17: Simulated (curves) and measured (symbols +, × and ) signal gain vssignal input power in counter-propagating pump configuration for 1 module (7 m)and 2 modules (14 m). The applied pump power is 100, 200, and 300 mW. The probesignal wavelength is 1310 nm.

In Figure 4.18, the signal gain and noise figure for the counter-propagating amplifierconfiguration are shown. For the longer Pr-doped fibre (e.q. two modules instead ofone single module) the noise figure is slightly larger, because less pump power (perunit fibre length) is available. The available pump power is not sufficient to achievehigh population inversion (i.e. a large fraction of the praseodymium ions are in theground state instead of the excited state 1G4) over the complete fibre length. Thenoise figure increases with increasing signal wavelength due to ground state absorp-tion [19]. The increase of the noise figure is more pronounced for the longer Pr-dopedfibre (e.q. two modules instead of one single module), because the available pumppower per unit fibre length is lower in this case.The noise figure of the counter-propagating amplifier is higher (worse) than the noisefigure of the co-propagating amplifier (see Figure 4.14). This is explained by thedependence of the noise figure on population inversion. The highest population in-version is obtained in the section of the fibre where the pump power is launched. Inthe co-propagating pumping scheme, the highest amplification of the signal occursat the amplifier input, where the (amplified spontaneous) noise level is low. As thespontaneous emission rate is proportional to the population inversion, less sponta-neous emission is generated in the remainder of the fibre. In the counter-propagatingscheme, the population inversion near the the amplifier output is high compared tothe co-propagating amplifier. Hence, more spontaneous emission is generated in thisarea and the signal and spontaneous emission are amplified simultaneously. In gen-eral, the increased ASE level will cause a minor difference in signal gain because thesignal power exceeds the ASE power by several orders of magnitude.


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-5

0

5

10

15

20

1260 1280 1300 1320 1340

Gai

n, n

oise

fig

ure

[dB

]

Wavelength [nm]

measured

G 7 mF 7 m G 14 mF 14 m

-15

-10

-5

0

5

10

15

20

1260 1280 1300 1320 1340

Gai

n, n

oise

fig

ure

[dB

]

Wavelength [nm]

simulated

G 7 mF 7 m G 14 mF 14 m

Figure 4.18: Measured and simulated signal gain (G) and noise figure (F ) vs wave-length in counter-propagating pump configuration for 1 module (7 m) and 2 modules(14 m). The probe signal power is -30 dBm. The applied pump power is 300 mW.

4.2.5 Bi-directional pumping scheme

The measured and calculated signal gain spectra, for the bi-directional pumpingscheme, are depicted in Figure 4.19. The pump power is 300, 400, and 500 mW,respectively. The pump power is equally divided over co-propagating and counter-propagating directions (so-called balanced pumping). The probe signal power is -30 dBm. Similar to the co-propagating and counter propagating cases, the gainvalues determined by the amplifier model are slightly lower than the measured gainspectra, but the shape of the calculated spectra resemble the measured spectra.The gain efficiency (slope of the curve in Figure 4.20) as determined by the amplifiermodel of the bi-directional configuration is comparable with the efficiency of the co-propagating and counter-propagating pumping schemes. However, the measurementsindicate a slightly larger gain efficiency for the bi-directional pumped amplifier.The gain as a function of signal input power is shown in Figure 4.21. For small signalpower, the signal gain is almost independent of the signal power, however for largesignals gain saturation occurs. According to the amplifier model, the signal saturationoutput power (not shown) is approx. 13 dBm (20 mW) for 300 mW of pump powerand 14 dBm (25 mW) for 500 mW of pump power.In Figure 4.22, the signal gain and noise figure for the bi-directional pumped amplifierconfiguration are shown. The applied pump power is 500 mW.Generally, the noise figure of the bi-directional pumped amplifier is between the resultsof the co-propagating and counter-propagating amplifier when equal (total) pumppower is applied.

4.3 Discussion

In section 4.2, the outcome of the spatially and spectrally resolved amplifier modelwas compared with experimental results for different amplifier configurations using


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-5

0

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10

15

20

25

30

1260 1280 1300 1320 1340

Gai

n [d

B]

Wavelength [nm]


Figure 4.19: Simulated and measured wavelength dependent gain in bi-directionalpump configuration 2 modules (14 m). The probe signal power is -30 dBm. The(total) applied pump power is 300, 400, and 500 mW.

-10

-5

0

5

10

15

20

25

30

0 0.10 0.20 0.30 0.40 0.50

Gai

n [d

B]

Pump power [W]

simulated 14 mmeasured 14 m

Figure 4.20: Simulated and measured gain as a function of applied pump power in bi-directional pump configuration 2 modules (14 m). The probe signal power is -30 dBmat a wavelength of 1310 nm.


5

10

15

20

25

30

-60 -50 -40 -30 -20 -10 0 10

Gai

n [d

B]


14 m

300 mW

400 mW

500 mW

Figure 4.21: Simulated (curves) and measured (symbols +, × and ) signal gain vssignal input power in bi-directional-propagating pump configuration for 2 modules(14 m). The (total) applied pump power is 300, 400, and 500 mW, respectively. Theprobe signal wavelength is 1310 nm.

-5

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5

10

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20

25

30

1260 1280 1300 1320 1340

Gai

n, n

oise

fig

ure

[dB

]

Wavelength [nm]

measured

G 14 mF 14 m

-5

0

5

10

15

20

25

30

1260 1280 1300 1320 1340

Gai

n, n

oise

fig

ure

[dB

]

Wavelength [nm]

simulated

G 14 mF 14 m

Figure 4.22: Measured and simulated signal gain (G) and noise figure (F ) vs wave-length in bi-directional-propagating pump configuration for 2 modules (14 m). Theprobe signal power is -30 dBm. The applied pump power is 500 mW.


an experimental PDFA based on commercially available praseodymium doped fluo-ride fibre modules. This is done, to ensure that the model is suitable for the designand development of PDFA’s which are based on other glass compositions (such asgermanium gallium sulphide glasses) or on another geometry of the fibre.In the validation of the model outcome, the accuracy of the data, which is used asinput for the amplifier model, is of major importance. The use of the amplifier model,as described in this chapter, is not necessarily limited to the applications as describedin the previous sections. It can also be used for the design and development of PDFA’sbased on other glass compositions or geometrical configurations.In the next sections, the inaccuracies of the experimental input data will be evalu-ated. Secondly, the experimentally observed amplifier characteristics are discussed, inrelation to results obtained by the amplifier model. Finally, the usage of the amplifiermodel for other applications with respect to underlying assumptions is discussed.

4.3.1 Amplifier model input data

The accuracy of the model outcome is strongly dependent on the accuracy of thedata determined for the Pr-doped fibre modules (see Appendix A). The error in thecross section (σ31, σ03, σ02, σ34) and emission lifetime (τe) data, which is obtainedfrom photoluminescence and absorption spectroscopy, can be rather large. In thecalculations shown in this chapter, excited state absorption (ESA) was not taken intoaccount, because no ESA data are specified for the Pr-doped fibre modules. Incorpo-ration of ESA results in gain reduction at the long wavelength side of the modelledgain spectrum.The inaccuracy of the signal input power, determined by the tuneable laser sourceand attenuator, is 0.5 dB. The pump power inaccuracy is within 0.4 dB. The mea-surement of signal and ASE power with the OSA introduces an additional uncertaintyof 0.2 dB.In addition, the losses of the amplifier components (i.e. WSC’s and isolators) areslightly wavelength dependent, resulting in a maximum uncertainty of 0.7 dB in thesignal power at input of the praseodymium doped fibre and 0.4 dB at the outputof the praseodymium doped fibre (both co-propagating and bi-directional configura-tions). Experimentally, the conversion of the amplifier from co-propagating pumpingscheme into the counter-propagating pumping scheme was accomplished by reversingthe signal direction. Hence, the input and output uncertainties are reversed in thisconfiguration.The mentioned inaccuracies for the measurement of signal input and output poweradd to an inaccuracy of approximately 1.5–2 dB for the observed gain, while the in-accuracy in the pump power (0.4 dB) results in an inaccuracy of the obtained gain ofapproximately 1 dB.Furthermore, the coupling of two 7 m Pr-doped fibre modules introduces additionalsplicing and mode conversion losses of approximately 1 dB. These losses affect bothsignal and pump power, and will result in smaller gain and worse noise figure. In thesimulations these extra losses were not taken into account.


4.3.2 Amplifier model results

The measured losses (due to intrinsic absorption and scattering in the fibre) of thesignal, at wavelengths less than 1300 nm, of a single and two concatenated Pr-dopedfibre modules are higher than the losses derived by the amplifier model (see Fig-ure 4.10). The additional coupling and mode conversion losses (approximately 1 dB)of the two concatenated modules are not accounted for in the model calculations. Theincrease of the losses at higher wavelengths (as measured and determined using themodel) is caused by the signal ground state absorption (GSA).Generally, the gain as determined by the amplifier model is lower than the measuredgain. The gain as calculated by the amplifier model, is dependent on the intensity dis-tribution of pump, signal and ASE power in the radial direction of the fibre core (i.e.the so-called overlap between the doped fibre core, signal and pump light). Hence,the gain is very sensitive to the fibre geometry (e.g. core diameter and numericalaperture

√

n21 − n2

2). Small differences between the actual fibre parameters and theused model input data result in substantial deviations in the calculated gain. Here,the specifications of the geometry of the praseodymium doped fibre provided by thesupplier were used.

Gain

The measured gain efficiency of the amplifier is slightly larger than the efficiencyderived from the model results. The saturation of the experimental amplifier (i.e.the measured gain efficiency decreases as the the applied pump power increases) isstronger than the decrease of gain efficiency observed by the amplifier model.For small input signals (less than -20 dBm), the gain efficiency of the counter-propaga-ting configuration is comparable with the efficiency of the co-propagating pumpingscheme. The gain, provided in the counter-propagating pump scheme, is slightly largerwhen the signal input power exceeds -20 dBm. For identical (total) pump power andthe same fibre length, the highest gain is obtained in the bi-directional pumpingscheme. This effect is more pronounced as the signal power exceeds -10 dBm, and isconfirmed by both model results and gain measurements.The difference in gain efficiency is explained by the evolution of pump, signal andASE (in both directions) along the fibre. In general, the available pump power islimited. Note that stimulated emission is proportional to the intensity of the light,whereas spontaneous emission is not related to the intensity of the light [7]. Hence,the local signal gain within the fibre will reduce when the (local) power of the ASE(generated by spontaneous emission) increases. The evolution of the optical power inthe forward direction, along a fibre of length L, is depicted in Figures 4.23a and b inco-propagating, bi-directional and counter-propagating pump configurations.In the co-propagating pumping scheme, the population inversion decreases along thefibre (as the pump power decreases). Near the output of the fibre, the increment ofboth signal and forward-propagating ASE power is limited by the decreased popula-tion inversion. The backward-propagating ASE is amplified significantly at the fibreentrance, where the population inversion is high. Hence, the power of the backward-propagating ASE (not shown) is larger than the power of the forward-propagating


0 L

Sign

al p

ower

[a.

u.]

Distance [a.u.]

a)Signal powerPs Co-prop.Ps Bi-direct.Ps Cou-prop.

0 L

ASE

pow

er [

a.u.

]

Distance [a.u.]

b)ASE powerPsp Co-prop.Psp Bi-direct.Psp Cou-prop.

0 L 2L

Sign

al P

ower

[a.

u.]

Distance [a.u.]

c)Signal powerPs Co-prop.Ps Bi-direct.Ps Cou-prop.

0 L 2L

ASE

pow

er [

a.u.

]

Distance [a.u.]

d)ASE powerPsp Co-prop.Psp Bi-direct.Psp Cou-prop.

Figure 4.23: Signal power Ps and forward propagating ASE power Psp in co-propagating, bi-directional and counter-propagating pump configuration as a functionof distance in a weakly pumped fibre. a) and c) signal power in a fibre of length Land 2L, respectively. b) and d) forward ASE power in a fibre of length L and 2L,respectively.


ASE.In the counter-propagating pumping scheme, the population inversion increases inthe propagation direction of the signal. The amplification of the signal and forwardpropagating ASE is located near the fibre output, where the population inversion ishigh. Due to the low population inversion at the amplifier input, the gain in thispart of the fibre is small and hence less ASE in the forward propagating directionis developed along the fibre. As a result, the signal gain in the counter-propagatingpumping scheme will be higher than in the co-propagating pumping scheme.In the bi-directional pumping scheme, signal amplification is located near both fibreends, where the population inversion is high. The power of the forward propagatingASE increases mainly at the fibre output. Due to the higher signal power at the fibreoutput, the increase of the ASE power is limited. Hence, the power of the ASE, inthe bi-directional pumping scheme, is between the ASE power in the co-propagatingand counter-propagating pump schemes, respectively.If the available pump power is limited, eventually the amplifier gain will decrease withincreasing fibre length, irrespective of the applied pump scheme (see Figure 4.23).

Noise figure

The noise figure is dependent on both signal power and the power of the amplifiedspontaneous emission (within the optical bandwidth of the applied filter the electricalbandwidth of the photo detector) and is linked to the population inversion, which inturn is dependent on the pumping configuration of the amplifier. Complete inversionresults in the lowest optical noise figure [20].The evolution of the optical power, along a fibre of length 2L is depicted in Fig-ures 4.23c and d. When compared to the output power for the fibre of length L, thesignal output power and ASE power are significantly smaller. The signal power andASE power decrease within the fibre, however the decrease in signal power is largerthan the decrease of the forward-propagating ASE. Consequently, the signal to noiseratio (SNR) in a fibre of length L is better than that of the fibre with length 2L. Theworst noise performance is obtained by the counter-propagating pump scheme, whilethe best noise figure is obtained for the co-propagating amplifier. The noise figure ofthe bi-directional amplifier is slightly worse than the noise figure of the co-propagatingamplifier [21, 22].When a co-propagating pumping scheme is applied, the amplification of the signaldirectly starts at the amplifier input. If the pump power is too weak to accomplishcomplete inversion over the entire active fibre, internal attenuation due to intrinsicabsorption and scattering losses in the fibre and signal ground state absorption canpossibly take place (see Figure 4.23c). In this case, the noise originating from ampli-fied spontaneous emission will be relatively small.However, when the counter-propagating configuration is applied, the amplification ofthe signal and noise is located near the amplifier output. In the weakly pumped case,the signal can be slightly attenuated prior to amplification in the presence of ASE(see Figure 4.23d). This degradation of the input SNR causes a worse noise figure.The noise figure depends heavily on inversion level at amplifier input, therefore the


co-propagating scheme is in favour of counter-propagating configuration. The noisecontribution of a (balanced) bi-directional pumped amplifier is between the contribu-tions of the co- and counter-propagating configurations.Furthermore, the noise figure increases with increasing signal wavelength due to signalground state absorption [19].The operational noise figure Fs−sp (calculated by equation 4.45) is obtained from themeasured optical spectrum at the amplifier output, which contains both amplifiedsignal and amplified spontaneous emission (ASE). In equation 4.45, the optical band-width Bo is determined by the resolution bandwidth BRB of the spectrum analyser(0.1 nm), which acts as a (tuneable) optical filter. The equation for the operationalnoise figure Fs−sp was derived for shot noise limited input signals, while the outputsignal is signal-spontaneous beat noise limited.The noise figure (equation 4.32), as calculated by the amplifier model, describes noiseoriginating from a PDFA used as an optical preamplifier at the receiver of a direct-detection system. Equation 4.32 was derived for shot noise limited input signals. Anoptical bandwidth Bo of 0.1 nm (or equivalently 17.5 GHz at 1310 nm) results in anoise figure which is dominated by signal-spontaneous beat noise (second term at theright hand side of equation 4.32). In this case, the noise figure is virtually independentof the electrical bandwidth Be and the noise figure, calculated by the amplifier model,can be compared with the experimentally obtained operational noise figure Fs−sp.For the tested amplifier configurations, the noise figure as determined by the am-plifier model, as a function of wavelength, is slightly lower than the experimentallyobtained operational noise figure. The shape of the calculated noise figure resemblesthe measured operational noise figure.

Wavelength dependence of the gain

The wavelength dependence of the gain is dependent on the stimulated emission,signal ground state absorption (GSA) and signal exited state absorption (ESA) crosssections. The signal GSA, due to the 3H4 – 3F4 transition, peaks at approximately1440 nm, while the signal ESA due to the 1G4 – 1D2 transition attains maximumintensity around 1375 nm [2]. Hence, both signal GSA and ESA reduce the gain inthe wavelength region beyond 1300 nm. The relative importance of signal GSA andsignal ESA is determined by the (local) population inversion.The applied pump power was not sufficient to cause complete population inversion(i.e. depletion of the ground level) in the PDFA based on either 7 m or 14 m offibre. Hence the gain, at wavelengths longer than 1300 nm, was reduced by signalGSA. When no pump power is applied the wavelength dependent losses caused bysignal GSA are slightly overestimated by the amplifier model. This results in anunderestimation of the gain by the model, especially at lower pump powers.The maximum measured gain is located at shorter wavelengths than the maximumgain calculated by the amplifier model. Although (signal) excited state absorption(ESA) is incorporated in the model, the ESA cross section data was not availablefor the praseodymium doped fibre modules used in this study. Hence, in the modelcalculations ESA was neglected. This could cause the difference between the measured


and calculated gain maximum. Due to the lack of data for the excited state absorptioncross section, the wavelength dependence of the signal gain can be determined onlyqualitatively by the amplifier model.

4.3.3 Validity of the amplifier model

The amplifier model can be used to optimise the design of praseodymium dopedamplifiers based on the optical properties of the praseodymium doped glasses, thedimensions of the fibre and the configuration of the amplifier. The model equationsare based on the optical properties (such as emission and absorption around the sig-nal wavelength) and concentration of the praseodymium dopant, which in turn aredependent on glass composition. When using different glass compositions and dopantconcentrations in the design process, the underlying assumptions of the model mustbe re-examined. For some applications (e.g. optical communications systems deploy-ing intensity (amplitude) modulation techniques to transmit data), time dependentsolution of the model equations, or the inclusion of additional transitions betweenenergy levels must be considered.The model equations are applicable to single-mode praseodymium doped fibre ampli-fiers. Single-mode operation provides the best overlap between the doped fibre core,signal and pump light. High efficiency (i.e. high signal gain per unit pump power) isobtained when the fibre amplifier is based on single-mode fibre [23]. The active fibrepreferably should be designed for single-mode operation at pump and signal wave-lengths. As standard single mode fibre (SMF) is not single-moded for wavelengthssmaller than approximately 1.2 µm, a special fibre is needed to connect the pumplaser (with a wavelength of about 1030 nm) to the fibre amplifier.For the derivation of equation 4.4 and 4.5, fast non-radiative decay of the Pr3+ ionsfrom the 3H5 state to the 3H4 state is assumed. Due to this fast depopulation, thepopulation density of the 3H5 level can be neglected. However, in low phonon energyglass hosts, depopulation rate may become too small to justify this assumption, dueto the longer lifetime of the 3H4 state [3, 24, 25].Depopulation of the 1G4 level by so-called cooperative upconversion (caused by thecoupled 1G4–

1D2 and 1G4–3H5 transition) is not included in the model. Co-operative

upconversion is negligible for praseodymium dopant concentrations less than 500 ppm[22].The amplifier model, presented here, is based on a steady state solution of the rateequations. This condition is applicable for continuous wave beams, and for thosesignals which are (amplitude) modulated at frequencies greater than approximately10–100 kHz [9, 10]. Hence, the results are also applicable to modern telecommunica-tion systems which operate at much higher modulation frequencies [23]. In general,the amplifier response to a (amplitude) modulated light wave (i.e. transient gainmodulation) is dependent on the time dependent changes of the population inver-sion. The characteristic frequency range, at which the time dependent changes of thepopulation inversion vanish, is largely determined by the emission lifetime τe of theexcited state [9, 11].


4.4 Conclusions

The spatially and spectrally resolved amplifier model, based on the four-level opera-tion of praseodymium, presented in this chapter can be used to study the operation ofpraseodymium doped fibre amplifiers in different configurations. The (steady state)amplifier model describes the evolution of signal, ASE, and pump power within thepraseodymium doped fibre. The model can be used to calculate the amplification ofboth continuous wave signals and signals which are (amplitude) modulated at highfrequencies (i.e. greater than approximately 10–100 kHz).The model requires high accuracy of the input data (i.e. signal input power andcoupling efficiency), the optical properties of praseodymium (i.e. cross sections andemission lifetimes) and the fibre geometry (i.e. core radius and refractive indices ofcore and cladding).The inaccuracies in the experimentally determined coupling efficiency, signal inputand output power result in an inaccuracy of approximately 1.5–2 dB for the observedgain, while the maximum inaccuracy in the pump power (0.4 dB) results in an in-accuracy of the obtained gain of approximately 1 dB. Furthermore, the accuracy ofthe model outcome is strongly dependent on the accuracy of the data specified forthe praseodymium-doped fibre. The error in the cross section (σ31, σ03, σ02, σ34)and emission lifetime (τe) data, which is obtained from photoluminescence and ab-sorption spectroscopy, can be rather large. Taking the limited accuracy of the opticalproperties and the gain measurements into account, the results of the model havebeen found in trendwise agreement with the experimental data. An error of 1.5 dB inthe model results (e.g. gain) is in the order of what is usually obtained with erbiumdoped fibre amplifier models [26].The outcome of the model was compared with measurement data. In general, thegain as determined by the amplifier model is lower than the measured gain. Whenno pump power is applied the wavelength dependent losses caused by signal GSA isslightly overestimated by the amplifier model, which may be caused by the inaccuracyof the signal GSA cross section data. This also results in an underestimation of thegain by the model, especially at lower pump powers.In general, the trends in the amplifier characteristics are well described by the model.The maximum measured gain is located at somewhat shorter wavelengths than themaximum gain calculated by the amplifier model. Signal GSA and ESA reduce thegain in the wavelength region beyond 1300 nm. In the validation of the model, theeffect of ESA is not included in the analysis, due to the lack of data for the excitedstate absorption cross section. Hence, the wavelength dependence of the signal gainonly could be determined qualitatively using the amplifier model.In addition, the model can be used to evaluate the noise figure (in direct-detectionsystems). The model confirmed the small differences observed in the measurementsof the gain and noise figure for the amplifier in co-propagating, counter-propagatingand bi-directional configurations.The model is considered to be suitable for the design and development of new types ofPDFA’s based on other glass compositions or geometrical configurations. The modelmakes use of the experimentally obtained data for optical properties of praseodymium


for a given glass composition (i.e. cross sections and emission lifetimes). The modelcan be used to optimise the fibre parameters such as length, core radius, numericalaperture, cut-off wavelength, praseodymium concentration and distribution in orderto obtain e.g. maximum gain efficiency for a given configuration (e.g. co-propagatingamplifier). In the next chapter, the model is used to design praseodymium doped fibreamplifiers, based on germanium gallium sulphide host glasses for some applications(e.g. booster, pre-amplifier).

4.5 Nomenclature

VectorsE electric field N C−1

Es electric field of signal light N C−1

Esp electric field of (amplified) spontaneously emitted light N C−1

Etot total electric field of signal and spontaneously emitted N C−1

light

Scalarsa core radius mBe electrical bandwidth HzBo optical bandwidth HzBRB resolution bandwidth of the OSA Hzc speed of light in vacuum = 2.99792108 m s−1

e elementary charge = 1.60210−19 CF noise figure -Fs−sp signal-spontaneous beat noise limited noise figure -ga signal/ASE excited-state absorption factor m−1

ge signal/ASE stimulated emission factor m−1

gg signal/ASE ground-state absorption factor m−1

gp pump ground-state absorption factor m−1

G gain -Gff fibre to fibre gain -h Plank’s constant = 6.6255910−34 J si photo-electric current Aiout photo-electric current due to amplified signal Ais signal current Aisp noise current AI normalised optical intensity distribution within fibre core m−2

l fibre length mn refractive index -n1 refractive index of fibre core -n2 refractive index of fibre cladding -N electrical noise power at receiver A2

Nin noise power at receiver (shot noise limited) A2


Ntot total noise A2

Nshot shot noise A2

Ns−sp signal-spontaneous beat noise A2

Nsp−sp spontaneous-spontaneous beat noise A2

P optical power WP+

ASE power spectral density of co-directionalpropagating ASE W Hz−1

P−ASE power spectral density of counter-directional

propagating ASE W Hz−1

Pin signal input power WPout signal output power WP+

p co-directional propagating pump power WP−

p counter-directional propagating pump power WPs signal power WPsp noise power WPsp,f noise power at fibre output WPtot signal power plus ASE power Wr axial co-ordinate mRd detector responsivity A W−1

S electrical signal power at receiver A2

Sin electrical signal input power at receiver A2

Sout electrical signal output power at receiver A2

ut transverse propagation constant -wt transverse decay constant -V normalised frequency -Wij transition rate between level i and j s−1

W03 pump GSA transition rate s−1

W31 stimulated emission transition rate s−1

W34 signal ESA transition rate s−1

z longitudinal co-ordinate m


αc connection losses -Γ co-propagating pump fraction -ηd photodiode quantum efficiency -ηin input coupling efficiency (i.e. loss) -ηout output coupling efficiency (i.e. loss) -λ wavelength mλc cut-off wavelength mλmax upper wavelength bound for ASE mλmin lower wavelength bound for ASE mλs signal wavelength mΛPr number of praseodymium dopant ions per unit volume m−3

Λi population density of praseodymium ions in level i m−3

Λ0 population density of Pr in the ground state (3H4) m−3


Λ3 population density of Pr in the excited state (1G4) m−3

ν frequency of light wave Hzνp pump frequency Hzνs signal frequency Hzσij cross section of transition from level i to j m2

σ02 signal GSA cross section m2

σ03 pump GSA cross section m2

σ31 stimulated emission cross section m2

σ34 signal ESA cross section m2

τe emission lifetime s

4.6 Bibliography

[1] M. Karasek, “Numerical analysis of Pr3+-doped fluoride fibre amplifier,” IEEEPhoton. Technol. Lett., vol. 4, pp. 1266–1269, November 1992.

[2] B. Pedersen, W. Miniscalco, and R. Quimby, “Optimization of Pr3+:ZBLANfiber amplifiers,” IEEE Photon. Technol. Lett., vol. 4, pp. 446–448, May 1992.

[3] P. Urquhart, “Praseodymium-doped fiber amplifiers: theory of 1.3 µm opera-tion,” IEEE J. Quant. Electron., vol. 28, pp. 1962–1965, October 1992.

[4] M. Karasek, “Theoretical investigation of Pr3+-doped fluoride fibre amplifiers,”Frequenz, vol. 47, no. 7–8, pp. 197–201, 1993.

[5] A. v. Osch, “Modelling of praseodymium-doped fluoride and sulfide doped fibreamplifiers for the 1.3µm wavelength region,” EUT Report 95-E-294, EindhovenUniversity of Technology, October 1995.

[6] N. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol.,vol. 7, pp. 1071–1082, July 1989.


[8] L. Mandel and E. Wolf, Optical coherence and quantum optics. Cambridge:Cambridge University Press, 1995. ISBN 0-521-41711-2.

[9] S. Fleming, “Crosstalk in 1.3 µm praseodymium fluoride fiber amplifiers,” J.Lightwave Technol., vol. 14, pp. 66–71, January 1996.

[10] J. Valles, M. Hotoleanu, and E. Voiculescu, “Modelling of the temporal responseof Pr3+-doped fluoride fibre amplifiers,” Pure Appl. Opt., vol. 6, pp. 779–792,1997.




[13] C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Light-wave Technol., vol. 9, pp. 271–283, February 1991.

[14] W. Etten and J. Plaats, Fundamentals of optical fiber communications. London:Prentice Hall, 1991. ISBN 0-13-717521-3.


[16] L. Jeunhomme, Single-mode fiber optics - principles and applications. MarcelDekker, Inc., 1983. ISBN 0-8247-7020-X.

[17] P. Becker, N. Olsson, and J. Simpson, Erbium-doped fiber amplifiers. Fundamen-tals and Technology. Optics and photonics, San Diego, CA: Academic Press,1999. ISBN 0-1208-4590-3.


[19] Y. Nishada, M. Yamada, T. Kanamori, K. Kobayashi, J. Temmyo, S. Sudo, andY. Ohishi, “Development of an efficient praseodymium-doped fiber amplifier,”IEEE J. Quant. Electron., vol. 34, pp. 1332–1339, August 1998.

[20] D. Derickson, Fiber optics test and measurement. Upper Saddle River, NJ: Pren-tice Hall, 1998. ISBN 0-13-534330-5.

[21] M. Karasek, “Analysis of gain improvement of Pr3+-doped fluoride fibre ampli-fiers using an optical filter or isolator,” Opt. Communications, vol. 107, pp. 235–239, April 1994.

[22] S. Wannenmacher, “Praseodymium doped fibre amplifier for optical amplificationat 1300 nm,” in Global telecommunications conference, vol. 3, pp. 1618–1623,IEEE, 1996.

[23] M. Artiglia, P. d. Vita, and M. Potenza, “Optical fibre amplifiers: physical modeland design issues,” Optical and Quantum Electronics, vol. 26, pp. 585–608, 1994.

[24] R. Quimby and B. Zheng, “New excited-state absorption measurement techniqueand application to Pr3+ doped fluorozirconate glass,” Appl. Phys. Lett., vol. 60,pp. 1055–1057, March 1992.

[25] R. Quimby and B. Aitken, “Effect of population bottlenecking in Pr fiber ampli-fiers with low-phonon hosts,” IEEE Photon. Technol. Lett., vol. 11, pp. 313–315,March 1999.

[26] V. Morin and E. Taufflieb, “High output-power praseodymium-doped fiber am-plifier single-pumped at 1030 nm: Analysis and results.,” IEEE J. Sel. TopicsQuant. Electron., vol. 3, pp. 1112–1118, August 1997.

Chapter 5

Performance and design of

the PDFA for

telecommunication systems

In this chapter, the performance and design of praseodymium doped fibre amplifiersin optical telecommunication systems operating at wavelengths around 1.3 µm arediscussed. Usually, gain, saturation, and noise characteristics are referred to as theamplifier performance. In the first section, the performance of an experimental PDFA,based on commercially available components, in booster, in-line and pre-amplifier ap-plications is evaluated based on measurements.In the next section, the optical properties (i.e. the attenuation at both pump andsignal wavelengths and the spontaneous emission spectra) of a praseodymium dopedgermanium gallium sulphide glass fibre, prepared in this study, are described.In practise, the amplifiers have to be designed to have optimum performance in thedesired application. In section 5.3, the design of the amplifier, based on germaniumgallium sulphide glasses, is optimised using the fibre amplifier model as derived inchapter 4. In this section, the design criteria, used in this study, for booster, in-lineand pre-amplifier are summarised. Not all amplifier characteristics can be influencedby the design of the amplifier. The possible pump and operating wavelengths of thePDFA (and other rare earth doped amplifiers) are mainly determined by the host ma-terial of the fibre. In fibre amplifiers, the propagation direction of the pump and signallight are important parameters to influence gain and noise properties (see chapter 4).The main parameters involved in the optimisation of the praseodymium doped fibreitself are length, core radius, numerical aperture, cut-off wavelength, praseodymiumconcentration and distribution.Section 5.3 is concluded by a comparison of the differences in performance of thepraseodymium doped fibre amplifier based on a) germanium gallium sulphide hostmaterial and b) fluoride host materials using the amplifier model. Here, the proper-ties of the amplifier, based the proposed design for the sulphide fibre are compared

163


Binary data

NRZ format

RZ format

1 0 0 11 1

Figure 5.1: Non-return-to-zero (NRZ) and return-to-zero (RZ) formats for modulationof binary data signal [1].

with those of an amplifier based on fluoride fibre.In the last section of this chapter, the main conclusions on the performance of thePDFA in telecommunication systems, the optical properties of the germanium galliumsulphide glass fibre and the optimum design of the amplifier based on sulphide hostglasses are given.

5.1 PDFAs in communication systems

In this section, the performance of an experimental PDFA, based on commerciallyavailable components is evaluated. Booster, in-line and pre-amplifier applicationsfor the PDFA in optical telecommunication systems are discussed. In the previouschapter, the time dependency of optical signal power was not taken into account. Totransmit data bits over an optical fibre, the transmitter converts data in electronicform into an optical signal by the process of modulation [1]. The most commonlyused modulation schemes are the non-return-to-zero (NRZ) and return-to-zero (RZ)formats (see Figure 5.1). In both modulation schemes, on–off switching modulatesthe intensity of the optical signal. In the non-return-to-zero (NRZ) format, a lightpulse is transmitted for a mark (1) bit, which occupies the entire bit interval. Fora space (0) bit, no power is transmitted [1]. In the return-to-zero (RZ) format, thetransmitted power occupies only a fraction of the bit time. For a mark bit, an opticalpulse is transmitted, while no optical power is transmitted for a space bit [1].At the receiver, the optical signal is converted into an electrical signal, succeeded byextraction of the data (demodulation). Decisions about the transmitted bits (markor space) based on the received signal are subject to error [1], due to the presence ofnoise, timing jitter and intersymbol interference. The bit-error-rate (BER), definedas the probability of erroneous identification of a bit by the receiver, is a measurefor the performance of a telecommunication system. The sensitivity of the receiveris defined as the minimum received average optical power, incident on the receiver,needed to achieve a bit-error-rate of 10−9 [2], i.e. on average one error occurs forevery 109 received bits. Receiver sensitivity and the probability of error is thoroughlydiscussed in e.g. Agrawal [2] and Ramaswami [1]. Usually, the BER is determined

Performance and design of the PDFA for telecommunication systems 165

1 0 0

1

1

1

00

0 0

0 0

00

0 0 0 0

1 1

111 1

1 1 1 1

11

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

Data stream:

Eye diagram on oscilloscope:

Figure 5.2: The eye diagram, formed by superposing many short sequences of bits,originating from the data stream on top of each other.

using a data stream based on a so-called Pseudo Random Bit Sequence (PRBS).The shape of the optical pulses can be determined from a so-called eye diagram,formed by superposing sequences of 2–3 bits each, originating from the data streamon top of each other (see Figure 5.2). Degradation of the pulse shape due to noiseand timing jitter results in partial closing of the eye.In section 5.1.1, the experimental evaluation of the amplifier performance, based onBit-Error-Rate (BER) measurements will be presented for both NRZ and RZ formatsat a bit rate of 10 Gbit/s. The influence of the applied pump configurations (co-,counter- and bi-directional) will be discussed.Then the results of an experimental analysis of the PDFA in an optical recirculatingloop will be presented. The loop was used to estimate, in a laboratory environment,the transmission performance over a long transmission distance incorporating multi-ple, cascaded praseodymium doped fibre amplifiers.Finally the application of a PDFA as an optical pre-amplifier in the receiver is evalu-ated. The noise figure of the pre-amplifier is derived directly from system experimentsby evaluation of the receiver sensitivity improvement, caused by the pre-amplifier.


5.1.1 Booster amplifier

In this section, the experimental performance of an PDFA is investigated as a func-tion of wavelength and optical input power. Large signal power was applied totest the characteristics of the PDFA as a booster amplifier in co-propagating andbi-directional pumping schemes. The sensitivity of the receiver was determined inthe so-called Back-to-Back (B2B) configuration, i.e. without the device under test(PDFA) installed between transmitter and receiver sections. The sensitivity improve-ment was determined from bit-error-rate measurements for 3 different signal inputpowers (-5 dBm, -10 dBm and -15 dBm) and for four different wavelengths (1290 nm,1300 nm, 1310 nm and 1320 nm).

Experimental set-up

The experimental configuration for the NRZ experiments is schematically shown inFigure 5.3. The continuous wave (CW) light from the HP 8167B tuneable laser is am-plified by a semiconductor optical amplifier (SOA, Philips CQF 882/e) and modulatedby a LiNbO3 external modulator. A 10 Gbit/s NRZ, pseudo random bit sequence(PRBS) of 231 − 1 bits is generated by a HP 70843 electrical pulse pattern generator(PPG) which drives the external modulator. Directly after the SOA, in the case ofNRZ modulation, a tuneable optical bandpass filter with a 3 dB bandwidth of 1 nmis used to reduce the ASE noise from the amplifier. The optical input level of thePDFA, is adjusted by the variable optical attenuator (HP 8156A). At the receiverend, a tuneable optical bandpass filter with a 3 dB bandwidth of 1 nm is used toreduce the ASE of the PDFA. In the NRZ experiments, a 10 Gbit/s NRZ receiver(NEL MOS43CM) with clock and data regeneration functions is used. The (electri-cal) clock and data signals are fed to a HP 70843 Bit-Error-Rate Test set (BERT).Bit-Error-Rate (BER) measurements were performed by comparing the detected bitsto the transmitted bits as a function of received average optical power incident on thereceiver (Preceiver), adjusted by a second variable optical attenuator (HP 8157A).In Figure 5.3 the modified set-up for the RZ experiments is also shown. The 10 GHzoptical pulse stream is generated by an external-cavity tuneable mode-locked laser.The wavelength of the pulse laser can be tuned over more than 30 nm and the gen-erated soliton shaped optical pulses have a pulse width of less than 4 ps (FWHM).The same transmitter configuration is used, but without the 1 nm tuneable opticalbandpass filter which would broaden the pulses. At the receiver end, a 3 nm tuneableoptical bandpass filter is used to reduce the ASE of the PDFA and SOA. For the RZexperiments, a custom 10 Gbit/s RZ receiver, with clock and data regeneration and1:4 Electronic Time Domain Demultiplexing functions is used.

Layout of the praseodymium doped fibre amplifier

The co-propagating and bi-directional configurations of the amplifier under investiga-tion are shown in Figure 5.4a and b respectively. An ytterbium fibre laser operating at1030 nm is used as pump source (providing 350 mW and 2×290 mW of pump powerin the co-propagating and bi-directional schemes respectively). The signal and pump


co-prop 2x7m PDFA

α

Pol.

Pol.

SOA BPF 1 nm

10 Gbit/s Modulator

Pol. SOA

35+15 m

HP tuneable laser 8167BPout = +2.5 [dBm]

Tuneable mode-lockedlaser. Pout = -4 [dBm]

PPG

RZ

NRZ

35+15 m

BPF 1 nm (NRZ)3 nm (RZ)

α

E-DEMUX1:4

BERAnalyzer

Powermeter

NRZ

RZ

AttenuatorHP 8156 A

AttenuatorHP 8157A



WSC 1030/1300nm


To adjust thesignal input powerPin at the PDFA.

To adjust the optical powerPreceiver at the receiver in

BER measurements.

Figure 5.3: Set-up used for performance assessment of the PDFA booster amplifier.The electrical data signal for the RZ and NRZ transmitters is provided by a pulsepattern generator (PPG). The optical signal is amplified by the PDFA. The datasignal from the RZ and NRZ receivers are evaluated by the BER analyser.




WSC1030/1300nm




WSC1030/1300 nm

WSC1030/1300 nm



a)

b)

Figure 5.4: Configurations of the experimental booster PDFA. a) co-propagatingpumping scheme b) bi-directional pumping scheme.

powers are combined in a 1030/1300 WSC, which is connected to the (commerciallyavailable) praseodymium doped fibre modules (NEL). Each module contains 7 m,1000 ppm Pr doped indium-based fluoride fibre between the two silica fibre pigtails(see Annex B).

Results and Discussion

The results of the BER-measurements at 1300 nm of the 10 Gbit/s NRZ and RZset-up with the PDFA in co-propagating pumping scheme are shown in Figure 5.5.The receiver sensitivity of the 10 Gbit/s NRZ and RZ receivers is -18 and -18.7 dBm,respectively. The BER-performance of the PDFA is evaluated at three different sig-nal input levels (-5 dBm, -10 dBm and -15 dBm) and for four different wavelengths(1290 nm, 1300 nm, 1310 nm and 1320 nm). The 3 dB gain bandwidth of the PDFA isover 30 nm and centred around 1300 nm. The performance of the PDFA for 10 Gbit/sNRZ and RZ is independent (less than 0.2 dB) of the wavelengths investigated. In thisco-propagating configuration, the effective fibre-to-fibre amplification (for the opticalinput powers under investigation) is in the order of 10 dB, depending on the opticalinput power, modulation format and also slightly on wavelength. In all experiments,the PDFA is used as a booster amplifier and is saturated for the investigated inputpower levels.The polarisation sensitivity of the PDFA is analysed by adjusting a polarisation con-troller in front of the PDFA and optimising the polarisation for maximum and mini-mum received optical power levels. This difference between maximum and minimumpower is less than 0.2 dB and is the cause of the observed difference in the BER forboth states of polarisation. Repeating this experiment without PDFA results in thesame polarisation sensitivity of slightly less than 0.2 dB, therefore the polarisationsensitivity of the PDFA is negligible compared to the other components in the exper-


a) b)

-2

-3

-4

-5

-6

-7

-8

-9

-10

-11-22 -21.5 -21 -20.5 -20 -19.5 -19 -18.5 -18

log(

BE

R)

P receiver [dBm]

A

B

-2

-3

-4

-5

-6

-7

-8

-9

-10

-11-21 -20 -19 -18 -17 -16 -15

log(

BE

R)

P receiver [dBm]

A

B

Figure 5.5: BER vs received power for a) 10 Gbit/s NRZ and b) 10 Gbit/s RZat 1300 nm co-propagating PDFA. (+) B2B (measured without PFDA), (X) P = -5 [dBm], (*) P = -10 [dBm] and () P = -15 [dBm]. The inset in each graph, showsthe eye diagrams of the signal before (A) and after (B) amplification by the PDFA.


imental set-up.The BER graph for the NRZ measurements (Figure 5.5a) shows that the back-to-back(B2B) curve is slightly worse (0.2 dB) than the curves with PDFA. The inset with thecorresponding eye-diagrams1 ((A) before, (B) after amplification) indicates a noisereduction of the signal after the PDFA. Apparently, the optical signal to noise ratio(OSNR) of the signal is improved by the PDFA. At a pump power of 350 mW, theco-propagating PDFA is saturated for the applied (-5, -10 and -15 dBm) input signalpower. Due to the relatively high input signal power, the power of the amplifiedspontaneous emission in the saturated amplifier is suppressed [4]. This results in abetter signal to noise ratio at the output of the saturated amplifier, compared to thesignal to noise ratio of the signal in the B2B configuration (i.e. without the PDFAinstalled between transmitter and receiver sections).Decreasing the signal input power levels of the PDFA (from -5 dBm to -10 and−15 dBm) will slightly degrade the performance, which is obvious because the ampli-fier adds relatively more noise to the signal as the signal becomes weaker. The BERgraph for the RZ measurements (Figure 5.5b) indicates a small penalty, up to 0.5 dB,for the smallest optical input power (-15 dBm).In Figure 5.6 the results of the BER-measurements for 10 Gbit/s NRZ signals, per-formed with the bi-directional pumped PDFA are shown. As the gain saturationdecreases when the optical input power is decreased from -5 to -25 dBm, the fibre-to-fibre gain increases from approximately 13 dB up to 20 dB. Due to the largeravailable total pump power in the bi-directional pumped PDFA, the gain saturationbecomes less pronounced compared with the co-propagating PDFA. The OSNR is notimproved by the amplifier and a small penalty is obtained as the input signal and thusthe OSNR decreases.In addition, the saturation behaviour of the PDFA was compared to that of an SOA,which is not optimised for booster application. The bit patterns (. . . 0 0 1 1 1 0 11 0 . . . ) and eye-diagrams are shown in Figure 5.7 for both RZ and NRZ formatsafter amplification by either PDFA or SOA. The signal input power is -5 dBm in allcases. Using a SOA, the gain of the amplifier decreases for a number of successivemark (1) bits and is (partly) recovered after a space (0) bit (see Figure 5.7c and g).This distortion (so-called pattern effect) is dependent on the bit sequence. In contrastto the large pattern effects in an SOA, no pattern effects are present in the PDFA.The pattern effects are caused by gain saturation, i.e. reduction of the optical gainas a result of depletion of the excited state by the amplification process [5]. Gainsaturation is influenced by the time constants (i.e. replenishing rate of the excitedstate, while being depleted by stimulated emission) and length of the amplifier (seeTable 1.3).The time constants in an SOA are in the same order of magnitude as the bit time,resulting in large pattern effects since the recovery of gain occurs within a few bit pe-riods. In contrast to the SOA, both length and time constants of the PDFA are muchlarger. The time constant is determined, amongst others, by the pump ground state

1Experimentally, eye patterns are generated by capturing the superposition of a sequence ofspace and mark bits on a sampling oscilloscope. The diagram provides a qualitative view of signaldegradation due to noise, timing jitter and intersymbol interference [3].


-2

-3

-4

-5

-6

-7

-8

-9

-10

-11-22 -21 -20 -19 -18 -17 -16 -15

log(

BE

R)

P receiver [dBm]

Figure 5.6: BER vs received power for 10 Gbit/s NRZ at 1300 nm for bi-directionalpumped PDFA. (+) B2B, (O) P = -5 [dBm], (×) P = -10 [dBm], (*) P = -15 [dBm],() P = -20 [dBm] and () P = -25 [dBm].


A B

C D

E F

G H

Figure 5.7: Pattern- and Eye-diagrams for PDFA (A,B,E and F) and SOA (C,D,Gand H).

absorption (the process of pumping the electrons into the excited state). A high levelof population inversion cannot be achieved over the entire active fibre. Consequently,the effective gain will be averaged over a large number of bits. The absence of patterneffect is a desired feature in booster amplifiers where input signal levels are high.

5.1.2 In-line amplifier

Optical amplifiers are often cascaded to overcome the fibre attenuation losses in along-haul communication system [2]. In such a system, the performance is affectedby accumulation of amplified spontaneous emission (ASE) noise. As the level ofASE grows, the amplifiers along the transmission line tend to saturate (due to thepower of the ASE) and the signal gain is reduced. The net result of the reduced signallevel and increased ASE level is a considerable degradation of the SNR [2]. An opticalrecirculating loop was used to estimate, in a laboratory environment, the transmissionperformance of a cascade of amplifiers over a long transmission distance.Within the optical recirculating loop set-up, the amplifiers are operated as in-lineamplifiers. The input signal power is moderately large, and hence the amplifiers are


slightly saturated. Due to the slow gain dynamics of the amplifier and the amplifiersaturation, disturbances in the average power of the signal in chains of amplifiers arelevelled out by the self regulation process. When the signal input power is belowthe equilibrium input power, the gain of the amplifier will increase. As a result, theinput signal at the next amplifier in the chain will approach the equilibrium inputpower. In a similar way, due to reduced gain, excessive input powers are reduced tothe equilibrium value.

Experimental set-up

The experimental set-up of the recirculating loop [6] is shown in Figure 5.8. Thetransmitter (Tx), which can be operated at bit rates of 622 Mbit/s up to 10 Gbit/s,resembles the NRZ transmitter used in the booster amplifier characterisation exper-iments (see Figure 5.3). The CW light (λ = 1310 nm) generated by a HP 8167Btuneable laser is amplified by an SOA (Philips CQF 882/e) and modulated by aLiNbO3 external modulator. A 231 − 1 NRZ PRBS is generated by a HP 70843 pulsepattern generator (PPG), which drives the modulator. Directly after the SOA, atuneable optical bandpass filter with a 3 dB bandwidth of 1 nm is used to reduce theASE noise from the amplifier. The power of signal injected into the recirculating loopis adjusted by a variable optical attenuator.A loop timing and control unit operates the two acousto-optical modulator switches(AOS) used for data loading and extraction. This unit also provides trigger pulses forgating of the BER-set and the sampling oscilloscope, to evaluate the data signal whichpassed a selected number of round trips in the loop, only. The optical recirculatingloop consists of a bi-directional pumped PDFA (see Figure 5.4b), which is connectedbetween 2 × 12.5 km Lucent Allwave fibre. Suppression of the ASE noise (to reducesaturation of the PDFA due to ASE) was provided by a 1 nm tuneable bandpass fil-ter. The PDFA was equipped with optical isolators in order to achieve unidirectionalsignal (and noise) propagation within the loop. A variable optical attenuator withinthe loop was used to obtain unity gain, in order to prevent the loop from saturatingand oscillating.A tap coupler is inserted at the output of the 50:50 coupler in order to monitor theevolution of power in the loop. A constant operation regime of the PDFA and con-stant average output power at the output of the 50:50 coupler can be achieved bycarefully adjusting the setting of the optical attenuator within the loop.The receiver section (Rx), used for BER-measurements, is similar to the set-up of Fig-ure 5.3. In the 622 Mbit/s NRZ experiments, a Nortel (MDCRL41-20C41) receiverwas used, while a NEL (MOS43CM) receiver was used in the 10 Gbit/s experiments.Eye diagrams can be obtained by writing the output of a photodetector (not shown)directly to the sampling oscilloscope. The recovered clock signal (taken from the re-ceiver) is used as a trigger for the oscilloscope. An optical attenuator in front of thephotodetector was used to keep optical signals sufficient small to prevent the electricalamplifier inside the photodetector from clipping, at the expense of reduction of signalrise and fall times (reduced bandwidth).


α

TxPPG BERAnalyzer

Attenuator

BPF 1 nm

Rx

Powermeter

12.5 km SMF12.5 km SMFα

Attenuator

Master timercircuit

Acousto-opticmodulator

PDFA

50:50

90:10

α

Attenuator

Figure 5.8: The optical recirculating loop set-up. The electrical data signal for theNRZ transmitter (Tx) is provided by a pulse pattern generator (PPG). Acousto-optical switches (AOS), used to admit and extract data from the loop, are driven bya master time circuit. The optical signal is amplified by the PDFA placed between 2× 12.5 km fibre. The data signal from NRZ receiver (Rx) are evaluated by the BERanalyser.


a) b)

-2

-3

-4

-5

-6

-7

-8

-9

-10

-11-21 -20 -19 -18 -17 -16 -15 -14

log(

BE

R)

P receiver [dBm]

-2

-3

-4

-5

-6

-7

-8

-9

-10

-11-36 -34 -32 -30 -28 -26 -24 -22

log(

BE

R)

P receiver [dBm]

Figure 5.9: BER as a function of received power as a function of number of roundtrips (1 round trip equals 25 km). a) 622 Mbit/s showing the curves for 0 (B2B), 1, 2,4, 6, 8, 10, 15, 20, 30, 40, 50, 80 and 89 round trips (curves from left to right) and b)10 Gbit/s showing the curves for 0 (B2B), 1, 2, 8, 10, 11 and 15 round trips (curvesfrom left to right).

Results and Discussion

The results of the BER-measurements are summarised in Figure 5.9. In all exper-iments, unity gain is maintained within the loop. The losses within the loop canbe attributed to transmission fibre (9 dB) and additional loop equipment (11 dB),the including variable attenuator. In the experiments, the signal input power of thePDFA is -14 dBm, while the gain of the PDFA (including input and output isolators)is approximately 20 dB.For measurement of the back-to-back curve the signal is injected into the 50:50 cou-pler and measured directly. The other curves are measured by using the gating optionof the error detector.The results of the BER-measurements conducted at 622 Mbit/s at 1310 nm are sum-marised in Figure 5.9a. The BER curves indicate an increasing penalty with increasingnumber of round trips (i.e. distance). Under unity gain conditions, the average out-


A B

C D

Figure 5.10: Eye-diagrams (622 Mbit/s) showing signal degradation after a) 0 (B2B),b) 1, c) 10 and d) 50 round trips (1 round trip equals 25 km).

put power of the amplified transmission span within the loop equals the average inputpower. Due to the power self regulation process, the average power remains constantwhile ASE noise component increases at the expense of signal power. The observedpenalty in the BER is related to the reduction of the signal to noise ratio caused bythe addition of ASE noise at each amplifier.At a bit rate of 622 Mbit/s, error free transmission (BER ≤ 10−9) is possible upto 10 round trips (approximately 250 km). No BER floor (i.e. deviation from thelinear relationship between log (BER) and the optical power at the receiver PReceiver

expressed in dBm) is observed for transmission over 10 round trips (approximately250 km). Due to the absence of optical pre-amplification of the optical signal at thereceiver end, the BER measurements are limited by available receiver power.For 15 to 50 round trips (375 to 1250 km), the slope of the BER curves remainssimilar to the slope of the BER curves for transmission over up to 10 round trips(approximately 250 km). Transmission over more than 2000 km (80 round trips) wasdemonstrated using this circulating loop set-up. In Figure 5.10, the eye-diagrams (at622 Mbit/s) of the transmitted (a) and received signals (b, c and d) are shown. Theobserved eye diagrams are in good agreement with the measured BER data.In Figure 5.9b the 10 Gbit/s results are summarised. Due to the lack of optical pre-amplification at the receiver, and the decreased OSNR, the BER curves can not bemeasured up to BER 10−9 for more than one round trip.In the optical recirculating loop experiments, the observed penalties are caused by


both optical signal degradation in the amplifier and fibre spans in the loop and im-pairments due to the measuring system. The loop equipment, especially the 50:50coupler, AOS and the attenuator, is the cause of significant attenuation losses withinthe loop.

5.1.3 Pre-amplifier

At the end of the transmission path, the optical signal is converted into an electricalsignal. The sensitivity of the receiver is frequently improved by pre-amplification ofthe optical signal, using a fibre amplifier, before the signal enters the detector. Anoptical pre-amplifier is used to amplify the received optical signal prior to electricalamplification and hence increases the sensitivity of the receiver. Since the detec-tor will convert all photons into electrons, spontaneous emission exiting the opticalamplifier will introduce additional noise. In order to reduce the spontaneous noisecontributions, both optical and electrical filtering is applied at the receiver. Afterpre-amplification of the optical signal, the thermal noise of the receiver becomes neg-ligible compared with shot noise [2].The performance of the pre-amplifier is characterised through its gain and noise figure,while the receiver is characterised through its sensitivity. The sensitivity of a (pre-amplified) receiver is defined as the minimum input signal power required to achievea bit-error-rate of 10−9 at a given bit rate. The performance of the pre-amplifier isdetermined by its gain and the amount of amplified spontaneous emission (aroundthe signal wavelength) added to the signal.Here, the noise analysis by Olsson [7], is applied to determine noise figure of ex-perimental pre-amplifier from the improvement of the receiver sensitivity caused bypre-amplification. The change of the signal to noise ratio (SNR) prior and after pre-amplification is, amongst others derived, from bit-error-rate measurements.An optical pseudo random bit sequence is used as a test signal. The extinction ratioζ, defined as the ratio of the optical power for a mark bit and space bit [1], is slightlywavelength dependent, due to the wavelength dependence of the output power of thetransmitter. The extinction ratio is given by

ζ =Ps1

Ps0

(5.1)

where Ps0and Ps1

are the average signal power for a space and mark bit, respectively.Usually, the average signal power for a space bit is not zero, due to stray light orthermally generated electron-hole pairs in the photodetector in the absence of anyoptical signal [2]. Using the noise analysis by Olsson [7], the noise characteristicsof the pre-amplifier are derived from the bit-error-rate characteristics and receiversensitivities. The bit-error-rate or the error probability Pe, for optimum decisionthreshold settings, is given by [2]

BER = Pe(Q) =1√2π

exp(−Q2

2 )

Q(5.2)


under the assumption that the statistics of the various types of noise (e.g. thermalnoise, shot noise) are well described by Gaussian probability distribution functions [2].The parameter Q is defined by [7]

Q =

√

S(1) −√

S(0)√

Ntot(1) +√

Ntot(0)(5.3)

Where S(1), S(0) and Ntot(1), Ntot(0) are the signal and total noise power for a mark(1) and space (0), respectively. Hence, the parameter Q is related to the signal-to-noise ratio required to achieve a specific bit-error-rate [8]. A Bit-Error-Ratio (BER)of 10−9 is obtained for Q = 6.For an on/off modulated signal (e.g. NRZ or RZ format) of average transmitted powerPs and the probability of mark and space bits is equal, the photo current equivalentsof the signal power at the receiver are given by

S(1) = (ηinGPs1ηoutαcRd)

2 (5.4)

S(0) = (ηinGPs0ηoutαcRd)

2 (5.5)

where G is the gain, Rd is the detector responsivity, αc are connection losses (e.g. ofthe optical filter) and the amplifier input and output coupling efficiencies, which areassumed to be independent of signal wavelength and power) are represented by ηin

and ηout, respectively. The average signal power for a mark bit is given by [1]

Ps1= Ps

2ζ

ζ + 1(5.6)

and the average signal power for a space bit is [1]

Ps0= Ps

2

ζ + 1(5.7)

The total noise power for a mark Ntot(1) and space bit Ntot(0) are given by

Ntot(1) = 2e(ηinGPs1+ Psp)ηoutαcRdBe

+4(ηoutαc)

2ηinGPs1PspRdBe

Bo

+2(ηoutαcPsp)

2Rd(BoBe − 12B2

e )

B2o

+4kBT

RLBe (5.8)

Ntot(0) = 2e(ηinGPs0+ Psp)ηoutαcRdBe

+4(ηoutαc)

2ηinGPs0PspRdBe

Bo

+2(ηoutαcPsp)

2Rd(BoBe − 12B2

e )

B2o

+4kBT

RLBe (5.9)


In these equations, the first term on the right hand side is shot noise, second term issignal-spontaneous beat noise, the third term is spontaneous-spontaneous beat noise(as defined by equations 4.21, 4.22 and 4.23, respectively) and the last term equals thethermal noise of the receiver. The thermal noise is given by 4kBT

RLBe, where kB is the

Boltzmann constant, T is the absolute temperature, and RL is the load resistor [2].Psp is the amplified spontaneous emission at the signal wavelength, while Be and Bo

are the electrical bandwidth and the optical bandwidth of the receiver, respectively.The noise figure of the PDFA, used as a pre-amplifier in a direct detection system,was derived in chapter 4. This noise figure, given by equation 4.24, is calculated foran input signal without the presence of spontaneous emission originating from thesource (shot noise limited).

F =

[

αcη

η2in

(

ηinGPs + Psp

G2Psηout+

2ηinPsp

GhνBo+

(Bo − 12Be)P

2sp

G2PshνB2o

)]

(4.24)

The three successive terms account for the contributions of shot noise, signal-sponta-neous beat noise and spontaneous-spontaneous beat noise, respectively.

Experimental set-up

In Figure 5.11, the set-up for the experimental assessment of the performance of aPDFA as an optical pre-amplifier is shown. The Continuous Wave (CW) light from aHP 8167B Tuneable Laser Source (TLS) is modulated by an external LiNbO3 modu-lator. The 231−1 PRBS, NRZ data pattern is generated by a HP 70843 Pulse PatternGenerator (PPG). An optical amplifier is omitted in order to obtain a shot noise lim-ited test signal (signal without the presence of spontaneous emission originating fromthe source).The PDFA was operated in a bi-directional pumping scheme. Usually, optical iso-lators are applied at both amplifier input and output, to prevent instability due toreflections of signal and ASE. An optical isolator was applied at the amplifier output.However, an input isolator, indispensable for optimal system performance, was omit-ted because of the impact of this isolator on the noise figure due to the 1.0 dB extraloss.Between the PDFA pre-amplifier and the photo detector (inside the receiver) a band-pass filter has been placed in order to reduce the spontaneous beat-noise compo-nents. In the experiments, an optical filter with a 3 dB bandwidth of either 35.5 GHz(0.2 nm), 88.7 GHz (0.5 nm) or 177 GHz (1.0 nm) was used.The optical receiver (NEL MOS43CM) has a sensitivity of approximately -15 dBmat 10 Gbit/s and provides clock and data regeneration. The (electrical) clock anddata signals are fed to a HP 70843 Bit-Error-Rate (BER) Analyser. The electricalbandwidth of the receiver Be is 7.5 GHz.


The wavelength dependent fibre-to-fibre gain and the fibre-to-fibre noise figures (asdefined equations 4.33 and 4.45, see Figure 4.6) are depicted in Figure 5.12 (derived


PDFA

α

10 Gbit/s NRZTuneable laser source HP 8167B

NEL Rx

50:50splitter

Power meter

PPG

BERAnalyser

BPF

Attenuator

Figure 5.11: Set-up for determination of the improvement of the receiver sensitivityusing a PDFA as pre-amplifier. The electrical data signal for the NRZ transmitter isprovided by a pulse pattern generator (PPG). The optical signal is amplified by thePDFA pre-amplifier. The data signals from the NRZ receiver (Rx) are evaluated bythe BER analyser.

from static gain measurements, see chapter 4). The gain bandwidth (i.e. the wave-length range where the gain of the amplifier is at least half the maximum obtainablegain) of the bi-directional pumped PDFA (with both input and output isolators) isapproximately 30 nm centred around 1305 nm. The maximum fibre-to-fibre gain ofthe experimental bi-directional pumped PDFA is approximately 22 dB, the corre-sponding noise figure is 7.5 dB.The overall small signal gain as a function of signal input power of the experimentalbi-directional pumped PDFA, with a 1.0 nm optical bandpass filter at the ampli-fier output, is shown in Figure 5.13 for the signal wavelengths 1290, 1300, 1310 and1320 nm.The receiver sensitivity, at signal wavelengths between 1290 and 1320 nm, was deter-mined for both receiver (back-to-back configuration) and pre-amplified receiver. Thesensitivity improvement (at a BER of 10−9) at 1310 nm using a bi-directional pumpedPDFA as an optical pre-amplifier is depicted in Figure 5.14.The extinction ratio of the signal varies between 9 and 19, within the wavelengthregion 1290 – 1320 nm. The penalty in receiver sensitivity caused by the differentextinction ratios is less than 0.5 dB.The results of the sensitivity measurements for three different optical filter band-widths B0 are summarised in Table 5.1. The insertion losses of the 0.2 nm and0.5 nm Fabry-Perot type filters are 5.3 dB and 4.3 dB respectively, while the loss ofthe 1.0 nm bandpass filter (Newport) is 1.8 dB. The signal at the output of the am-plifier is significantly reduced by the large insertion losses of the filters. Note, lossesat the output of the amplifier do not change the output SNR, and therefore the noisefigure is not influenced by these losses.After determination of the (nett) gain G of the pre-amplifier, equation 5.2 – 5.9 areused calculate the bit-error-rate as a function of signal power at the receiver. In theseequations, the ASE power Psp within the filter bandwidth Bo is not known a priori,


-5

0

5

10

15

20

25

30

1260 1280 1300 1320 1340

Gai

n, N

oise

fig

ure

[dB

]

Wavelength [nm]

GainNoise figure

Figure 5.12: Measured gain (G) and noise figure (F ) vs wavelength (in bi-directionalpropagating pump configuration for 2 modules (14 m)). The probe signal power is-30 dBm. The applied pump power is 2 × 290 mW.

0

5

10

15

20

25

30

35

-36 -34 -32 -30 -28 -26 -24

Ove

rall

gain

[dB

]

Signal Power [dBm]

1290130013101320

Figure 5.13: Measured overall gain for bi-directional PDFA – 1 nm filter configurationvs signal input power. The applied pump power is 2 × 290 mW.


-3

-4

-5

-6

-7

-8

-9

-10-40 -35 -30 -25 -20 -15 -10

log

(BE

R)

P receiver [dBm]

B2BPreAmp

Sensitivity

improvement

Figure 5.14: Bit-Error-Rate curves indicating the receiver sensitivity improvementusing a pre-amplified receiver at 1310 nm compared to same receiver without opticalpre-amplification (B2B). The optical filter bandwidth is 0.5 nm.

Table 5.1: Improvement of receiver sensitivity for NRZ signals at a bit rate of10 Gbit/s using a PDFA pre-amplifier and the (calculated) gain G and noise figure Fof the pre-amplifier

λ Bo Sensitivity Preamp Sens. ∆ G F[nm] [nm] [dBm] [dBm] [dB] [dB] [dB]

1290 0.2 -14.5 -28.5 14.0 20.1 11.31300 0.2 -15.0 -30.0 15.0 23.1 10.51310 0.2 -15.0 -28.5 13.5 21.3 12.01290 0.5 -14.5 -29.0 14.5 20.2 10.31300 0.5 -15.0 -30.0 15.0 23.1 9.81310 0.5 -15.0 -29.5 14.5 21.6 11.01290 1.0 -14.5 -31.0 16.5 19.3 8.21300 1.0 -15.0 -30.5 15.5 21.7 9.11310 1.0 -15.0 -30.5 15.5 20.5 9.51320 1.0 -15.0 -28.0 13 19.2 12.6


but can be determined by fitting the calculated BER (as a function of signal power)by measured BER data. Then, the signal power at BER of 10−9 (i.e. receiver sensi-tivity) and corresponding ASE power is determined from the calculated BER. Finally,the noise figure (according to equation 4.24) is calculated for this signal power whichequals the receiver sensitivity. The nett gain of the pre-amplifier (at BER of 10−9)and the noise figures (according to equation 4.24) are listed in Table 5.1.The noise figure is calculated using the nett gain of the amplifier (the large differencesin the insertion losses of the used optical bandpass filters do not alter the output SNR,hence these losses do not affect the calculated noise figure). The lowest noise figuresare obtained at 1300 nm, due to the highest gain obtained at this wavelength. Asthe filter bandwidth decreases, the ASE power within the optical filter bandwidthdecreases, while the required signal input power, to obtain the same BER, slightlyincreases. The noise figure is dominated by the signal-spontaneous beat noise, whichincreases as the filter bandwidth decreases.The sensitivity (at BER = 10−9) of the system with PDFA pre-amplifier (withoutinput isolator) is approximately -30 dBm, which means a 15 dB improvement. Thegain of the pre-amplifier was approximately 19–23 dB. A noise figure (according toequation 4.24) of 9 dB was directly derived from these system experiments using a1 nm optical bandpass filter. This noise figure includes signal/pump WSC and cou-pling losses at the amplifier input.The observed noise figures are relatively high for the application of the amplifier as apre-amplifier. Based on the requirements for the pre-amplifier as listed in Table 1.2,the small signal gain and the noise figure should be preferably at least 30 dB andless than 4 dB, respectively. It is expected that the performance of the experimentalpre-amplifier can be improved by increasing the gain of the amplifier, reducing thecoupling losses at the amplifier input and application of the co-propagating pumpscheme. The gain of the pre-amplifier is increased when the pump power is increased.Here, a bi-directional pump scheme was applied instead of a co-propagating pumpscheme, because of the higher total available pump power. However, the gain wasstill limited by maximum applicable pump power in this configuration.

5.2 Optical properties of the germanium gallium

sulphide glass fibre

In this section, the optical properties of praseodymium doped germanium galliumsulphide glass fibre, prepared for this study, are described. In the first paragraph, theattenuation at both pump and signal wavelengths is given. The determination of the(amplified) spontaneous emission spectrum is discussed in the next paragraph.

5.2.1 Attenuation at signal and pump wavelengths

The optical attenuation of several (13 – 137 cm long) pieces of 370 ppm praseodymiumdoped germanium gallium sulphide glass fibre with composition Ge28.8Ga1.2S70.0 at1300 nm was evaluated using the set-up shown in Figure 5.15. The measurement


GeGaS fibreSMF

ANDO FP Laser1300 nm

PowermeterNewport 2832C

Figure 5.15: Set-up used for measurement of signal absorption and scattering atten-uation of germanium gallium sulphide fibre. The light originating from a 1300 nmlaser (Ando) is launched into the sulphide fibre using a s-SMF. The residual light ismeasured using an optical powermeter (Newport) fitted with spherical detector head.

Table 5.2: Attenuation and scattering losses (at 1300 nm) of praseodymium dopedgermanium gallium sulphide glass fibre of length L and diameter Din and Dout (atthe fibre input and output, respectively).

Fibre length Input diameter Output diameter Attenuation LossL [cm] Din [µm] Dout [µm] α [dB/cm]

12.8 230 230 0.2241 263 306 0.6978 284 330 0.18113 230 230 0.24137 243 245 0.17

set-up consists of a Fabry-Perot type laser (Ando) operating at 1300 nm. The laserlight is coupled into a single mode fibre (s-SMF). First, the optical power at theoutput of the s-SMF fibre was determined by a Newport type 2832C powermeter,equipped with a Newport 818-IS-1 detector head with integrating sphere. Then, thes-SMF fibre is used to couple the laser light into the germanium gallium sulphidefibre. The surfaces of the s-SMF and the test fibre are separated by a small airgap. The power of the light at the output of the chalcogenide fibre was measured bythe Newport powermeter. The attenuation of the optical power is caused by reflec-tion, absorption and scattering. The absorption and scattering losses in the fibre arelisted in Table 5.2. The reflection losses, at both interfaces of the germanium gal-lium sulphide fibre, of approximately 1 dB were taken into account. The absorptionby praseodymium (signal ground state absorption) at wavelengths around 1300 nm isnegligible. Although neither all modi nor the complete numerical aperture (NA=0.28)of the germanium gallium sulphide fibre are irradiated using s-SMF, similar resultsare obtained when the s-SMF fibre (NA=0.13) is replaced by an 50 µm multi modefibre (MMF, NA=0.20). The dimensions of the germanium gallium sulphide fibres,originating from a single fibre drawing test, are also summarised in Table 5.2.The attenuation of the germanium gallium sulphide glasses is measured at the pumpwavelength (1030 nm), also. The set-up used for this measurement is shown in Fig-




WSC1030/1300nm

GeGaS fibre9 mm SMF

PowermeterANDO AQ2105

Figure 5.16: Set-up used for measurement of the attenuation of pump light by thegermanium gallium sulphide fibre. The pump light (1030 nm) is coupled into thesulphide fibre using a single mode fibre with core diameter of 9 µm. A lens is usedto project the residual pump light at the output of the germanium gallium sulphidefibre on the powermeter.

ure 5.16. The pump light (1030 nm) is coupled into the sulphide fibre using a singlemode fibre with core diameter of 9 µm. A lens (f=16 mm, ∅=21 mm) is used toproject the residual pump light on the surface of the detector (∅=330 µm) of thepowermeter (Ando). The measured attenuation is 32 dB, which equals 0.41 dB/cmfor the 0.78 m long fibre. The signal absorption and scattering loss at the signalwavelength of this fibre is 0.18 dB/cm (see Table 5.2). This loss at 1030 nm can bepartly contributed to pump ground state absorption at this wavelength.When the fibre is pumped at 1030 nm, no (visible) red luminescence, due to radiativedecay from the 1D2 level, is observed. The glasses used in these experiments werenot polished or etched before drawing. No (surface) crystallisation was observed,however using an infrared viewer, some scattering points within the fibre are visible.Crystallisation or soot deposition due to volatilisation of sulphur during fibre drawingof the sulphur rich glasses may be the source of these defects. The removal of thedominant scattering points (shortening the fibre) did not result in large improvementof the absorption and scattering losses.

5.2.2 Spontaneous emission

The spontaneous emission spectra were measured using Ando AQ6310B optical spec-trum analyser (OSA). The pump light (1030 nm) is coupled into the sulphide fibre,using a single mode fibre with core diameter of 9 µm for the connection. A lens isused to couple the (amplified) spontaneous emission (ASE) light into the OSA using a800 µm MMF fibre. A Schott type BG39 high-pass filter, was placed between the lensand the MMF, in order to decrease the intensity of the residual pump light coupledinto the OSA.In Figure 5.18, the spontaneous emission spectra are shown for pump power levelsbetween 13 and 25 dBm. The length of the investigated sulphide fibre is 43 cm. Addi-tional measurements do not indicate the presence of (visible) red luminescence. Theamplified spontaneous emission spectrum, for a pump power of 24 dBm, is depicted


HPFBG39

OSAANDO AQ6310B



WSC1030/1300nm

GeGaS fibre9 mm SMF 800 mm MMF

Figure 5.17: Schematic diagram of set-up used for assessment of ASE spectra of ger-manium gallium sulphide fibre. The set-up is comparable to the set-up in Figure 5.16.A high-pass filter is placed between the lens and a 800 µm MMF. The MMF is usedto couple the spontaneous emission into the OSA.

in Figure 5.19. This measured spectrum is corrected for the wavelength response ofthe high pass filter, which is slightly wavelength dependent around 1300 nm. Thepeak wavelength of the spontaneous emission is 1335 nm, the 3 dB bandwidth is ap-proximately 70 nm.The amplification of signals at a wavelength of 1312 nm was studied using the set-upshown in Figure 5.20. The signal (1312 nm) is generated by a tuneable laser. The sig-nal power is varied using a variable attenuator. Both signal and pump light (1030 nm)are coupled into the sulphide fibre using a single mode fibre with core diameter of9 µm. A lens is used to project the light at the output of the germanium galliumsulphide fibre on the powermeter (Ando). A 10 nm band-pass filter (Edmund optics1310 nm, ∅=25 mm) is placed between the lens and the powermeter in order to blockresidual pump light.The signal input power was varied in 10 dB steps between -5.3 and -55 dBm. Theapplied pump power was 17, 20, 23, 24, and 25 dBm. However, no signal amplifica-tion could be observed. This is probably caused by a combination of too low dopantconcentration, short fibre length and poor overlap between the modi of signal andpump. In addition, the (average) power density of the pump light is very low.

5.3 Design of an efficient PDFA

In this section, the layout of the praseodymium doped fibre amplifier for the differentapplications (e.g. booster, in-line amplifier or pre-amplifier) is discussed. Differentapplications put different demands on the design of the fibre (e.g. fibre length, coreradius, etc) and configuration of the praseodymium doped fibre amplifier. The fibreparameters involved in the optimisation of the fibre are length, core radius, numericalaperture, cut-off wavelength, praseodymium concentration and distribution. For eachapplication, the amplifier design is optimised with the aid of the fibre amplifier modelas described in chapter 4.Based on the requirements for the amplifier applications as listed in Table 1.2, designcriteria for the praseodymium doped fibre amplifier are established, see Table 5.3.


1000 150012501050 1100 1150 1200 1300 1350 1400 1450

Wavelength [nm]

Rel

. sig

nal p

ower

(re

f le

vel =

-49

dB

)10

-5

0

5

-10

-15

-20

-25

-30

Figure 5.18: Measured spectra showing the spontaneous emission of a praseodymiumdoped germanium gallium sulphide glass at different pump power levels. The appliedpump power is 13, 17, 20, 23, 24, and 25 dBm. The peak around 1030 nm is causedby residual pump power. The reference level of the OSA is -49 dB, the resolutionbandwidth is 10 nm.

Table 5.3: Design criteria for the praseodymium doped fibre amplifier as booster,in-line amplifier and pre-amplifier.

Parameter Booster In-line amplifier Pre-amplifier

Gain G [dB] 13 20 303 dB Saturation output 30 20 15power [dBm]Noise figure F [dB] 6–7 5 4


1250 145013501270 1290 1310 1330 1370 1390 1410 1430

Wavelength [nm]

Rel

. sig

nal p

ower

(re

f le

vel =

0 d

B)

20

5

10

15

0

-5

-10

-15

-20

Figure 5.19: Spontaneous emission spectrum of a praseodymium doped germaniumgallium sulphide glass after correction for the wavelength response of the high passfilter. The applied pump power is 24 dBm. The OSA resolution bandwidth is 2 nm.

BPFEdmundOptics



WSC1030/1300nm

GeGaS fibre9 mm SMFα

AttenuatorTuneable laser

HP 8167BPowermeter

ANDO AQ2105

Figure 5.20: Set-up used for determination of gain in praseodymium doped germaniumgallium sulphide fibre. The signal (1312 nm) is generated by a tuneable laser. Bothsignal and pump light (1030 nm) are coupled into the sulphide fibre using a 9 µmcore SMF. A lens is used to project the light at the output of the sulphide fibre onthe powermeter. A band-pass filter is placed between the lens and the powermeter inorder to block residual pump light.


In the first section, general design issues of the praseodymium doped fibre are de-scribed. In the next sections, the design of large signal amplifiers (e.g. booster)and small signal amplifiers (e.g. in-line amplifier and pre-amplifier) based on germa-nium gallium sulphide host glasses are presented, using the design criteria listed inTable 5.3. In the final section, the performance of the praseodymium doped fibreamplifier (based on the germanium gallium sulphide glass is compared with the per-formance a PDFA based fluoride host glass by modelling.

5.3.1 Design of the praseodymium doped fibre

The light guiding properties of the praseodymium doped fibre are mainly determinedby its core radius a and the refractive indices of core n1 and cladding n2 (see sec-tion 4.1.3). The refractive indices are determined by the core and cladding glasscomposition, while the core radius is determined by the fibre drawing conditions.In the design of the praseodymium doped fibre, the coupling efficiency to the appro-priate passive fibre and its resistivity against bending losses must be considered [3].To obtain low coupling loss, the numerical aperture NA =

√

n21 − n2

2 and core diame-ter a of the praseodymium doped fibre must be compatible to the passive silica fibresto which it is connected.Usually, standard Single Mode Fibre (s-SMF) is used for the signal, while specialfibres with lower cut-off wavelength λc (as defined by equation 4.14) are appliedfor the pump light. A wavelength selective coupler is used to combine both signaland pump light at the input and output of the amplifier. The techniques for effi-cient coupling of the different fibre types are discussed elsewhere (see e.g. Sudo [9]).Typically, the praseodymium doped fibre is mounted between silica fibres with highernumerical aperture and lower cut-off wavelength (≤ 1000 nm) than s-SMF (NA=0.13,λc=1280 nm). The cut-off wavelength of the fibre has to be smaller than the pumpwavelength in order to be single mode at the pump wavelength2. Depending on thefibre drawing conditions, the minimum core radius of a praseodymium doped fibre isapproximately 2 µm, which corresponds to a NA of 0.182 at a cut-off wavelength lessthan 950 nm.The optimum design of the amplifier is a compromise between the compatibility ofthe doped fibre with the passive fibres to which it is connected and a highly efficientpraseodymium doped fibre. The efficiency of the praseodymium doped fibre is relatedto the confinement of the signal, amplified spontaneous emission (ASE) and pumplight within the doped fibre core, which in turn is determined by the core diameterand the numerical aperture of the praseodymium doped fibre. Two approaches tooptimise the gain provided by the fibre are 1) to increase the numerical aperture anddecrease the core radius without changing the cut-off wavelength and 2) to decreaseboth core radius and cut-off wavelength while the numerical aperture remains un-changed.Increment of the numerical aperture accompanied with reduction of the core radius a,

2The fibre amplifier model (see chapter 4), used to design an efficient amplifier, only takes thefundamental mode into account.


101

102

103

104

1022 1023 1024 1025

Len

gth

[m]

Pr Concentration [ions/m3]

Figure 5.21: Example of the optimal length of an praseodymium doped fibre as afunction of Pr3+ concentration as calculated by the amplifier model.

while the cut-off wavelength λc and the normalised frequency V (as defined by equa-tion 4.13) remain the same, results in increment of the optical intensity in the fibrecore. The optical power is confined into the smaller core, while the shape of the modeprofiles (i.e. spatial distribution of the optical intensity) remains unchanged. Dueto the better (spatial) overlap between the doped fibre core, pump and signal power,the efficiency of the amplifier is improved. Hence, for a given cut-off wavelength, thenumerical aperture must be chosen as large as possible.To maintain the same NA value, the core radius a has to decrease as the cut-off wave-length λc decreases, while the normalised frequency V remains the same (see equation4.13). The fraction of power contained in the core is determined by equation 4.15.As the core radius decreases, the confinement of power in the core is reduced due toincrement of the spot size (field radius) of the pump and signal light. This effect ismore pronounced for the signal light than for the pump light. As a result, the effi-ciency of the amplifier increases due to increased intensity of the pump power insidethe fibre core and the better overlap between the doped fibre core and the pumppower. The intensity of the signal power inside the fibre core also increases whenthe core radius decreases, but eventually the intensity decreases when the core radiusbecomes too small. For small core radii, the efficiency of the amplifier is degradedbecause a considerable part of the optical power can not contribute to amplification,as the power propagates through the undoped cladding [10].For each design of the praseodymium doped fibre, the length of the fibre is optimisedwith respect to maximum signal gain (or equivalently maximum signal output power).The signal gain (in decibels), which is obtained by solution of equations 4.8 and 4.10-4.12, is proportional to the number of praseodymium ions in the fibre core. Hence, theoptimum gain fibre length is inversely proportional to the dopant concentration (seeFigure 5.21). Low dopant concentrations or small core radii require the applicationof longer fibres, which is unfavourable in the presence of high attenuation losses.In this analysis, the praseodymium dopant concentration is taken 500 ppm wt (ap-proximately 4 1024 ions/m3), while the dopant is distributed uniformly over the fibre


0.00

0.04

0.08

0.12

0.16

0.20

900 1000 1100 1200 1300 14000.00

0.20

0.40

0.60

0.80

1.00

Abs

orpt

ion

cros

s se

ctio

n x

1024

[m

2 ]

Em

issi

on c

ross

sec

tion

x 10

24 [

m2 ]

wavelength [nm]

Pump GSASignal GSA

Signal emission

Figure 5.22: Cross sections for pump ground state absorption, signal ground stateabsorption and stimulated emission used for the PDFA based on germanium galliumsulphide host glass

core. It is assumed that this praseodymium concentration is low enough to avoidfluorescence quenching. Dopant confinement (into a small section of the fibre core)improves the efficiency of the fibre amplifier [11]. This dopant confinement is nottaken into account in this analysis, because such fibres are more difficult to producedue to their complex fibre core structure.The material properties of the germanium gallium sulphide glasses were determinedin chapter 2. The emission and absorption cross sections for the germanium galliumsulphide host glass are depicted in Figure 5.22. The emission lifetime is 414 µs. Theattenuation loss, within the wavelength range 1000–1350 nm, is 0.1 dB/m.

5.3.2 Large signal amplifier

At the transmitter, a booster amplifier is used to improve the signal power of themodulated data signals. The amplifier is operating in the so-called saturation regime(i.e. the signal input power of the amplifier is typically between -10 and 10 dBm).For the booster amplifier, the design criterium is to maximise the output power.Typically, the output power of a booster amplifier is at least 20 dBm, while higheroutput power (up to 30 dBm) is desirable for some applications (e.g. for distributionof common antenna television (CATV) signals to a group of subscribers).At relatively high signal input powers, the gain of the amplifier decreases due tosaturation. This reduction of gain is caused by depletion of the excited state due tostimulated emission and a limited replenishing rate. The saturation output power isdefined as the level at which the amplifier gain is decreased by a factor of two withrespect to the small signal gain (i.e. gain at low input power).The maximum gain, based on the available pump power Pp, is given by

Gmax = 10 log

(

Ppλp

Psλs

)

(5.10)


where Ps is the signal input power at wavelength λs and λp is the pump wavelength.In practise, the amplifier gain is limited due to the presence of noise (e.g. ampli-fied spontaneous emission). A figure of merit for booster amplifiers is the QuantumConversion Efficiency (QCE). QCE is defined as the increase in the number of sig-nal photons as a result of amplification divided by the number of launched pumpphotons [3]3.

QCE =λs

λp

(Ps,out − Ps,in)

Pp=

λs

λp

Ps,in(G − 1)

Pp(5.11)

First, the effect of optimisation of the praseodymium doped fibre parameters (e.g.length, numerical aperture, cut-off wavelength), as discussed in section 5.3.1, on thedesign of the amplifier will be addressed. Next, the design of a booster amplifier,using the design criteria listed in Table 5.3, is presented.

Optimisation of fibre parameters

The calculated signal gain and the corresponding optimum fibre length as a functionof pump power for a booster amplifier are shown in Figure 5.23a. The input signalpower, used here, is 0 dBm at a wavelength of 1342 nm. The signal wavelength is lo-cated near the peak of the emission spectrum, while the pump wavelength is 1023 nm,which corresponds with the maximum absorption wavelength. A counter-propagatingpump scheme is applied. The optimum length of the praseodymium doped fibre is afunction of the overlap between the doping profile and the mode profiles of signal andpump light. Longer optimum fibre lengths are needed to achieve maximum gain atincreased pump power, since high pump power causes inversion of the praseodymiumdopant over longer lengths of fibre [13]. The gain (or equivalently output power) ismainly determined by the available pump power. Note that physical damage mayoccur if the optical intensities inside the amplifier become too high. The calculatedQCE is shown in Figure 5.23b. As the QCE levels off at high pump powers, the perfor-mance of the booster amplifier will be optimised by maximising QCE (i.e. maximisingthe signal output power / signal gain) for a given pump power.In Figure 5.24, the calculated signal gain and corresponding optimum fibre length areshown as a function of cut-off wavelength, with the numerical aperture as parameter.The gain and fibre length are shown for NA between 0.15 and 0.25. The input signalpower is 0 dBm at a wavelength of 1342 nm. The pump power is 275 mW at 1023 nm.The optimum fibre length, defined as the fibre length at which maximum signal gainoccurs, increases as the numerical aperture increases or the cut-off wavelength de-creases. For a given NA, the gain has a maximum with regard to cut-off wavelength,the optimum cut-off wavelength is situated between 800 and 850 nm and is almost in-dependent of NA. The gain increases with increasing NA due to an improving overlapbetween the core, pump and signal power. For a core diameter of 4 µm, the highestQCE and gain is obtained for NA of 0.182 and a cut-off wavelength of 950 nm. In theremainder of this section, those values for NA and cut-off wavelength will be used to

3The energy of a photon at wavelength λ equals hc/λ [12].


a)

0

10

20

30

0 100 200 300 400 5000

5

10

15

Lar

ge s

igna

l gai

n [d

B]

Opt

. fib

re le

ngth

[m

]Pump power [mW]

GainLength

b)

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500

Con

vers

ion

effi

cien

cy [

mW

/mW

]

Pump power [mW]

QCE

Figure 5.23: a) Calculated large signal gain and corresponding optimum fibre lengthand b) quantum conversion efficiency versus pump power for a booster amplifier. Thenumerical aperture is 0.182. The input signal power is 0 dBm at a wavelength of1342 nm. The pump wavelength is 1023 nm. A counter-propagating pump scheme isapplied.


a)

18

19

20

21

22

600 650 700 750 800 850 900 950 1000

Gai

n [d

B]

Cut-off wavelength [nm]

NA=0.15

NA=0.25

b)

5

10

15

20

25

600 650 700 750 800 850 900 950 1000

Opt

Len

gth

[m]


NA=0.15

NA=0.25

Figure 5.24: a) Calculated large signal gain and b) corresponding optimum fibrelength versus cut-off wavelength for a booster amplifier. The numerical aperture isincreased in steps of 0.01 between 0.15 and 0.25. The input signal power is 0 dBmat a wavelength of 1342 nm. The pump power is 275 mW at 1023 nm. A counter-propagating pump scheme is applied.

show the properties of a booster amplifier based on the germanium gallium sulphidehost glass.

Design of a booster amplifier

For a booster amplifier, based on the germanium gallium sulphide host glass, approx-imately 1700 mW of pump power is required to obtain a gain of 13 dB for input powerof 17 dBm. The main characteristics of the booster amplifier, are listed in Table 5.4.For the booster amplifier, a counter-propagating pump scheme is applied. The satu-ration behaviour of such amplifier is shown in Figure 5.25. The main design criteriumfor the booster amplifier is the 3 dB saturation output power, which is defined asthe level at which the amplifier gain is decreased by a factor of two with respect tothe small signal gain (i.e. gain at low input power). Saturation in praseodymiumdoped fibre amplifiers, based on germanium gallium sulphide host glasses, is rather


Table 5.4: Proposed design for the praseodymium doped fibre amplifier used asbooster amplifier.

Parameter Design criteria Proposed design

Length [m] – 9.70Cut-off wavelength [nm] – 950Numerical aperture [-] – 0.182Pump power [mW] at 1023 nm – 1700(counter-propagating pump scheme)Large signal gain [dB] at 1342 nm 13 133 dB saturation output power [dBm] 30 25.2Noise figure F [dB] 6–7 3.2

0

10

20

30

40

50

60

14 16 18 20 22 24 26 28 30 320

0.2

0.4

0.6

0.8

1.0

1.2

Sign

al g

ain

[dB

]

QC

E [

mW

/mW

]

Signal output power [dBm]

Gain 1700 mWQCE 1700 mW

Figure 5.25: Calculated signal gain and conversion efficiency vs signal output powerfor a booster amplifier at 1700 mW pump power. The numerical aperture is 0.182.The wavelength of the input signal is 1342 nm. The pump wavelength is 1023 nm. Acounter-propagating pump scheme is applied.


0

5

10

15

20

25

30

1250 1275 1300 1325 13500

5

10

15

20

25

30

Gai

n [d

B]

Noi

se f

igur

e [d

B]

Wavelength [nm]

GNF

Figure 5.26: Calculated large signal gain and noise figure of a booster amplifier at1700 mW pump power. The numerical aperture is 0.182. The input signal power is0 dBm. The pump wavelength is 1023 nm. A counter-propagating pump scheme isapplied.

strong. For the proposed booster amplifier, the 3 dB saturation output power isapproximately 25 dBm. This is lower than the design criterium for the 3 dB satura-tion output power, which is 30 dBm (see Table 5.3). However, the saturated outputpower of this amplifier is approximately 30 dBm. To obtain a 3 dB saturation outputpower of 30 dBm for the booster amplifier, a pump power considerably larger than1700 mW is required. The highest QCE is obtained for signal input power of approx-imately 10 dBm.The wavelength dependency of the gain and noise figure of the germanium galliumsulphide booster amplifier is depicted in Figure 5.26. The input signal power is 0 dBm.The maximum gain is obtained at a wavelength of 1342 nm. The applied pump poweris 1700 mW at 1023 nm, corresponding with QCE of 0.68. Due to the absence of signalground state absorption in germanium gallium sulphide host glasses for wavelengthsshorter dan 1350 nm, the noise figure remains constant in a broad wavelength range.The noise figure, around the optimum gain wavelength, is approximately 3.2 dB. Inthe calculations of the amplifier noise figure, it is assumed that an optical filter witha bandwidth of 1 nm is applied at the output of the booster amplifier. In boosteramplifiers, the high signal power causes the noise figure to be dominated by the signal-spontaneous emission beat noise. In saturated amplifiers (e.g. a booster amplifier),the power of amplified spontaneous emission is much smaller than the signal power,hence optical filtering is less important [10].In general, the amplifier generates ASE noise, and hence the noise figure of the ampli-fier is greater than unity (0 dB) [13], i.e. degradation of the SNR occurs. In the highgain regime, the minimum noise figure of a PDFA is 3 dB. This minimum, which onlyapplies to the spectral region where high gains are achieved, is commonly refereed toas the signal spontaneous beat noise or quantum limit [13]. If the gain of the satu-rated amplifier is high (i.e. G >> 1), the calculated NF (according to equation 4.24)represents a good approximation of the amplifier noise figure. However, when the am-


0

10

20

30

40

50

60

-40 -30 -20 -10 0 10 20 30

Sign

al g

ain

[dB

]


Gain 1700 mW

Figure 5.27: Calculated signal gain for a booster amplifier at 1700 mW pump power.The wavelength of the input signal is 1342 nm. The pump wavelength is 1023 nm. Acounter-propagating pump scheme is applied. the slope of the gain curve is approxi-mately -1 dB/dBm for signal input power > -20 dBm).

plifier operates in the saturated gain regime, the net gain (in a particular wavelengthrange) can be small (e.g. < 10 dB). In this case, the amount of ASE noise generatedby the saturated amplifier is negligible and the magnitude of signal amplification bystimulated emission is comparable to the magnitude of signal attenuation due to fi-bre losses and signal ground state absorption. Hence, the effect of gain saturationis to increase the SNR and consequently the NF of the saturated amplifier tends toapproach unity [13].When the praseodymium doped fibre amplifier is in saturation, the slope of the gaincurve is approximately -1 dB/dBm (see Figure 5.27 for signal input power > -20 dBm).In this case, the output power is nearly independent of input power and (slow) powerfluctuations are levelled out by the saturated amplifier. Intensity-modulated signalsare not distorted for high modulation frequencies [14], as the dynamics of the pop-ulation inversion are slow in comparison to the transit time of the pump and signalthrough the amplifier [15] (see section 4.1.1). Consequently, the effective gain forintensity-modulated signals will be averaged over a large number of bits.

5.3.3 In-line amplifier

Cascaded amplifiers provide amplification of the signals along the transmission link.The gain of each in-line amplifier compensates for the attenuation of the signal powerbetween two amplifiers. Besides providing signal gain, each in-line amplifier addsnoise due to amplified spontaneous emission. The noise accumulates over the cascadeof amplifiers. The signal gain of the amplifier decreases, as the ASE level increasesand the amplifiers becomes saturated. The total power of both signal and ASE atthe amplifier output remains almost constant. The signal-to-noise ratio (SNR) grad-ually degrades along the transmission link, because the average signal level drops and


the ASE level increases [1, 2]. In long transmission spans, short amplifier spacingis required to obtain good SNR [16]. However, due to the increased number of am-plifiers needed to cover the entire length of the transmission span, the system costincreases [1].In Table 5.3, the requirements for the in-line amplifier are given. The application asin-line amplifier requires a relatively high saturation output power, low SNR degra-dation (i.e. low noise figure) and polarisation independency. The optimum design ofan in-line amplifier is dependent on many factors, including amplifier spacing and thecharacteristics of the transmission fibre (e.g. signal attenuation losses and dispersion).The in-line amplifier is essentially a small-signal amplifier, like the pre-amplifier. Thedesign of the in-line amplifier is comparable to the design of a pre-amplifier, which isdiscussed in the next section.

5.3.4 Pre-amplifier

The optical pre-amplifier is used to improve the signal prior to detection and electricalamplification at the receiver. The pre-amplifier operates in the so-called small signalgain regime. Due to the low input power (in the order of -30 dBm), low loss betweenthe fibre and the amplifier (insertion loss) is required. Furthermore, a relatively highgain and low noise contribution by the pre-amplifier are important. The requirements(typical values) for the pre-amplifier are given in Table 5.3. For the pre-amplifier,the design criterium is to minimise the noise generated by the amplifier, in order tominimise the signal input power needed to obtain error free transmission (i.e. increasereceiver sensitivity). For this application, the co-propagating pump configurationprovides the lowest noise caused by amplified spontaneous emission (See section 4.3.2).

Optimisation of fibre parameters

Generally, the Quantum Conversion Efficiency (QCE), as defined in equation 5.11,of a pre-amplifier is low (≤ 0.05). For the purpose of design optimisation of thepre-amplifier, the gain efficiency is used as a figure of merit. The gain efficiency isdefined as the ratio between small signal gain (expressed in units of decibels) and thelaunched pump power (in milliwatts) [3]. The aim is to maximise the gain efficiency(for small signal power) and simultaneously minimise noise figure of the pre-amplifier.To obtain the maximum gain for a given input signal, the fibre length is optimisedfor each pump power. The optimum pump power is obtained at the maximum of thegain to pump power ratio.The calculated small signal gain and corresponding optimum fibre length as a func-tion of launched pump power for a pre-amplifier are shown in Figure 5.28a. Theinput signal power is -30 dBm at a wavelength of 1342 nm. This signal wavelength islocated at the peak of the emission spectrum, while the pump wavelength is 1023 nm,which corresponds with the maximum absorption wavelength of praseodymium in thegermanium gallium sulphide glass. A co-propagating pump scheme is applied. Longeroptimum fibre lengths are needed to achieve maximum gain at increased pump pow-


a)

0

10

20

30

40

50

0 50 100 150 200 250 3000

5

10

15

20

25

Smal

l sig

nal g

ain

[dB

]

Opt

. fib

re le

ngth

[m

]

Pump power [mW]

GainLength

b)

0.00

0.05

0.10

0.15

0.20

0.25

0 50 100 150 200 250 300

Gai

n ef

fici

ency

[dB

/mW

]

Pump power [mW]

Gain efficiency

Figure 5.28: a) Calculated small signal gain and optimum fibre length and b) gainefficiency versus pump power for a pre-amplifier. The numerical aperture is 0.182.The input signal power is -30 dBm at a wavelength of 1342 nm. The pump wavelengthis 1023 nm. A co-propagating pump scheme is applied.

ers. The gain efficiency is shown in Figure 5.28b as a function of pump power. Thehighest gain efficiency (i.e. the highest gain per unit pump power) is obtained at apump power of 112.5 mW.The small signal gain (at a signal wavelength of 1342 nm) is shown in Figure 5.30, asa function of the cut-off wavelength and with the NA as parameter. The NA is variedbetween 0.15 and 0.25. The input signal power is -30 dBm and the pump power is112.5 mW at 1023 nm. At small signal power levels (-40 – -20 dBm), the gain isnearly independent of the input signal power (see Figure 5.29).The optimum fibre length, defined as the fibre length at which maximum signal gainoccurs, increases as the numerical aperture increases or the cut-off wavelength de-creases. For a given NA, the gain has a maximum with respect to cut-off wavelength,the optimum cut-off wavelength is situated between 800 and 850 nm and the optimumcut-off wavelength is almost independent of NA. The small signal gain increases withincreasing NA, due to reduction of mode field diameters (i.e. spatial distribution of


0

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-40 -30 -20 -10 0 10

Gai

n [d

B]


Figure 5.29: Calculated small signal gain as a function of signal input power. Thesignal wavelength is 1342 nm. The pump power is 112.5 mW at a wavelength of1023 nm. A co-propagating pump scheme is applied.

Table 5.5: Proposed design for the praseodymium doped fibre amplifier used as pre-amplifier.

Parameter Design criteria Proposed design

Length [m] – 12.48Cut-off wavelength [nm] – 950Numerical aperture [-] – 0.182Pump power [mW] at 1023 nm – 165(co-propagating pump scheme)Small signal gain [dB] at 1342 nm 30 303 dB saturation output power [dBm] 15 9.1Noise figure F [dB] 5 3.2 – 3.5Signal power required for Q=6 [dBm] – -38.5

the optical intensity) of the optical pump and signal beams, which results in higheroptical intensities in the doped core. For a core diameter of 4 µm, the highest gainand gain efficiency is obtained for NA of 0.182 and a cut-off wavelength of 950 nm(see Figure 5.30). In the remainder of this section, those values for NA and cut-offwavelength will be used to evaluate the properties of a pre-amplifier based on thegermanium gallium sulphide host glass.

Design of a pre-amplifier

In Figure 5.31, the wavelength dependence of the gain and noise figure of a ger-manium gallium sulphide pre-amplifier is depicted. The main characteristics of thispre-amplifier, are listed in Table 5.5. The input signal power is -30 dBm. The max-imum gain is obtained at a wavelength of 1342 nm. The pump power is 165 mW at


a)

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600 650 700 750 800 850 900 950 1000

Gai

n [d

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NA=0.15

NA=0.25

b)

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600 650 700 750 800 850 900 950 1000

Opt

Len

gth

[m]


NA=0.15

NA=0.25

Figure 5.30: a) Calculated small signal gain and b) optimum fibre length versus cut-off wavelength for a pre-amplifier. The numerical aperture is increased in steps of0.01 between 0.15 and 0.25. The input signal power is -30 dBm at a wavelength of1342 nm. The pump power is 112.5 mW at 1023 nm. A co- propagating pump schemeis applied.


-5

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1250 1275 1300 1325 13500

5

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20

Gai

n [d

B]

Noi

se f

igur

e [d

B]

Wavelength [nm]

GNF

Figure 5.31: Calculated small signal gain and noise figure of a pre-amplifier at 165 mWpump power. The numerical aperture is 0.182. The input signal power is -30 dBm.The pump wavelength is 1023 nm. A co-propagating pump scheme is applied.

1023 nm, corresponding with a gain efficiency of 0.18 dB/mW.The signal gain is approximately 30 dB around 1342 nm. The 3 dB saturation out-put power is approximately 9 dB, which is less than the design criterium listed inTable 5.3 (15 dBm). The noise figure (see Figure 5.31) is approximately 3.2–3.5 dBin the wavelength range where the gain of the amplifier exceeds 10 dB. For an idealtransmitter and receiver (i.e. infinite extinction ratio ζ = Ps1

/Ps0, unity receiver

responsivity Rd and in the absence of thermal noise at the receiver), the minimumsignal input power to obtain Q = 6 equals -38.5 dBm.In the calculations of the noise figure, it is assumed that an optical filter with abandwidth of 1 nm is applied at the output of the pre-amplifier. The noise figure ofthe pre-amplifiers, is dominated by shot noise and spontaneous-spontaneous emissionbeat noise. The use of optical filtering is necessary to obtain low noise figures [10].

5.3.5 Performance of PDFA, based on different host glass types

In this section, the optimised designs for the praseodymium doped fibre amplifierbased on germanium gallium sulphide host glasses are compared with amplifiers basedon fluoride glasses fibre. The performance of both amplifiers, based on calculations forboth host glass types, are compared for similar signal gain in both booster and pre-amplifier applications. For the purpose of this analysis, both amplifiers are pumped atthe optimum pump wavelength (i.e. 1023 nm for the sulphide amplifier and 1011 nmfor the fluoride amplifier), which corresponds with the maximum absorption wave-length.The fluoride amplifier is based on the optical properties of a 1000 ppm wt praseody-mium doped fluoride fibre with a cut-off wavelength of 950 nm and a numericalaperture of 0.182. Maximum signal gain is obtained around 1310 nm. The opticalproperties are equal to those presented in Annex A.1. The length of the praseodymium


Table 5.6: Comparison of the design and performance of the praseodymium dopedfibre amplifier, based on sulphide and fluoride host glasses and used as a boosteramplifier.

Parameter Sulphide Fluoride

Length [m] 11.91 5.66Cut-off wavelength [nm] 950 950Numerical aperture [-] 0.182 0.182Dopant concentration [ppm] 500 1000Pump wavelength (optimum) [nm] 1023 1011Pump power [mW] 275 550(counter-propagating pump scheme)Large signal gain (max.) [dB] 20 20Quantum Conversion Efficiency [mW/mW] 0.502 0.2663 dB saturation output power [dBm] 14.7 15.9Max. signal gain wavelength [nm] 1342 1310Noise figure F [dB] 4.1 – 4.3 3.4 – 7.3

doped fluoride fibre is optimised with respect to maximum gain.The praseodymium dopant concentration for the germanium gallium sulphide basedPDFA is 500 ppm wt. The absorption and emission cross sections are shown in Fig-ure 5.22. The emission life time of the 1G4 level is 414 µs. The cut-off wavelengthof this fibre is 950 nm and the numerical aperture is 0.182. The background loss isassumed to be 0.1 dB/m.

Booster amplifier

The large signal gain and optimum fibre length as a function of applied pump powerare depicted in Figure 5.32. A counter-propagating pump scheme is applied. Theinput signal power is 0 dBm. For both amplifiers, the selected signal wavelength islocated at the peak of the emission spectrum (i.e. 1342 and 1310 nm, respectively).Theoretically, the sulphide amplifier provides higher gain than the fluoride amplifierfor equal pump power (i.e. the sulphide amplifier has much higher efficiency), evenat small pump power levels (see Figure 5.32).The key figures related to the design and performance of the booster amplifier (basedon different sulphide and fluoride host glasses) are listed in Table 5.6. The design (inparticular the applied pump power and fibre length) of the sulphide and fluoride basedamplifiers was optimised to obtain 20 dB signal gain for 0 dBm input signal power (i.e.20 dBm signal output power) for both amplifiers. For the fluoride booster amplifier,optimisation of fibre length (instead of using modules containing 7 or 14 m of fibre) foreach pump power results in higher gain compared to the results presented in chapter4. The optimum length of the fluoride amplifier is much shorter compared to theoptimum length of the sulphide amplifier, due to the higher dopant concentration. As


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igna

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e le

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[m

]

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G SulphideG FluorideL SulphideL Fluoride

Figure 5.32: Comparison of the calculated large signal gain and associated optimumfibre length for booster amplifiers based on sulphide and fluoride host glass. Thepump wavelength is 1023 nm and 1011 nm for the sulphide amplifier and fluorideamplifier, respectively. The input signal power is 0 dBm at a wavelength of 1342 and1310 nm, respectively. A counter-propagating pump scheme is applied.

discussed in section 5.3.1, the optimum length of the amplifier is almost proportionalto the dopant concentration.The wavelength dependency of the large signal gain and noise figure is shown inFigure 5.33. The optimum gain wavelength of the sulphide amplifier is shifted 30 nmto longer wavelengths compared to the fluoride amplifier. The applied pump powerfor the sulphide amplifier is 275 mW which corresponds to a quantum conversionefficiency of 0.5. Due to the lower efficiency of the fluoride amplifier, 550 mW ofpump power is required in order to obtain a similar maximum gain of approximately20 dB.The calculated noise figure (at signal input power of 0 dBm) of both types of boosteramplifier is approximately 4 dB at a wavelength of 1310 nm (see Figure 5.33). Inthe wavelength range between 1275 and 1300 nm, the noise figure of the sulphideamplifier is slightly higher than that of the fluoride amplifier, due to the lower gain ofthe sulphide amplifier in this wavelength range. The increase of the noise figure of thefluoride amplifier at long wavelengths is due to the signal ground state absorption.It is expected that the noise figure of the sulphide amplifier will increase also forwavelengths larger than 1350 nm, due to signal ground state absorption. The noisecharacteristics for the praseodymium doped fluoride fibre amplifier were reported bySugawa et al. [17]. The lowest noise figures are obtained for amplified signal outputpower between -20 and 0 dBm. Outside this interval, the noise figure increases.The gain saturation is shown in Figure 5.34. The required pump power for the sulphideamplifier is 275 mW and 550 mW for the fluoride amplifier in order to obtain a gain of20 dB for input signals of 0 dBm. The 3 dB saturation output power of the sulphidefibre is 14.7 dBm, while the 3 dB saturation output power of the fluoride amplifieris 15.9 dBm. For input signal power levels less than 0 dBm, the gain of the sulphideamplifier is larger than the gain of the fluoride amplifier. When the sulphide based


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G SulphideG Fluoride

NF SulphideNF Fluoride

Figure 5.33: Comparison of large signal gain and noise figure of booster amplifiersbased on sulphide and fluoride host glass. The applied pump power for the sulphideamplifier is 275 mW at 1023 nm, while the pump power of the fluoride amplifier is550 mW at 1011 nm. The input signal power is 0 dBm. A counter-propagating pumpscheme is applied.

praseodymium doped fibre amplifier is in saturation, the slope of the gain curve isclose to -1 dB/dBm. Hence, the output power of the sulphide amplifier in saturation isnearly independent of input power. The output power of the fluoride amplifier slightlyincreases for signal input powers between 0 and 20 dBm. In general, the calculatedquantum conversion efficiency (QCE) of the sulphide amplifier is much higher thanthat of the fluoride amplifier.

Pre-amplifier

In Figure 5.35, the small signal gain and the corresponding optimum fibre lengthas a function of applied pump power are shown. A co-propagating pump scheme isapplied, which provides the lowest noise caused by amplified spontaneous emission(See section 4.3.2). For both amplifiers, the signal wavelength is located at the peakof the emission spectrum (i.e. 1342 and 1310 nm, respectively), while the appliedsignal input power is -30 dBm. Optimisation of fibre length for the fluoride basedpre-amplifier (instead of using modules containing 7 or 14 m of fibre) for each pumppower results in higher gain efficiency compared to the results presented in chapter4. The calculated gain-efficiency of a pre-amplifier, based on a sulphide host glass, ismuch higher than the efficiency of a fluoride amplifier. Again, to a large extend thedifferences in the optimum length of the fibre are caused by the difference in dopantconcentration (500 vs. 1000 ppm).The key figures related to the design and performance of the pre-amplifier (basedon different sulphide and fluoride host glasses) are listed in Table 5.7. The design(in particular the applied pump power and fibre length) of the sulphide and fluoridebased amplifiers was optimised to obtain approximately 21 dB signal gain for -30 dBminput signal power for both amplifiers.


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]

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QCE S.QCE F.

Figure 5.34: Comparison of signal gain and quantum conversion efficiency of boosteramplifiers based on sulphide and fluoride host glass as a function of the signal outputpower. The applied pump power for the sulphide amplifier is 275 mW at 1023 nm,while the pump power of the fluoride amplifier is 550 mW at 1011 nm. A counter-propagating pump scheme is applied.

Table 5.7: Comparison of the design and performance of the praseodymium dopedfibre amplifier, based on sulphide and fluoride host glasses and used as a pre-amplifier.


Length [m] 10.63 5.31Cut-off wavelength [nm] 950 950Numerical aperture [-] 0.182 0.182Dopant concentration [ppm] 500 1000Pump wavelength (optimum) [nm] 1023 1011Pump power [mW] 112.5 400(co-propagating pump scheme)Small signal gain (max.) [dB] 21 213 dB saturation output power [dBm] 8.1 14.2Max. signal gain wavelength [nm] 1342 1310Noise figure F [dB] 3.3 – 3.5 3.1 – 4.0Signal power required for Q=6 [dBm] -38.7 -38.6


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]

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]

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G SulphideG FluorideL SulphideL Fluoride

Figure 5.35: Comparison of the small signal gain and optimum fibre length for pre-amplifiers based on sulphide and fluoride host glass. The pump wavelength for thesulphide amplifier is 1023 nm, while the fluoride amplifier is pumped at 1011 nm. Theinput signal power is -30 dBm at a wavelength of 1342 and 1310 nm, respectively. Aco-propagating pump scheme is applied.

The small signal gain as a function of signal wavelength is depicted in Figure 5.36.Due to the difference in gain efficiency, a pump power of 112.5 mW for the sulphideamplifier is sufficient to obtain a maximum signal gain of approximately 21 dB forinput signals of -30 dBm, while the pump power requirement for the fluoride amplifierequals 400 mW in order to achieve similar gain. The optimum gain wavelength of thesulphide amplifier is shifted 30 nm to longer wavelengths compared to the fluorideamplifier.The calculated noise figure as a function of signal wavelength is also shown in Fig-ure 5.36. Over a broad wavelength range the noise figure for both amplifiers is around3.4 dB. At the long wavelength side of the gain spectrum, the noise figure increasesdue to signal ground state absorption. The noise figure of the fluoride amplifier, cal-culated here, is comparable to the noise figures for the praseodymium doped fluoridefibre amplifier reported by Sugawa et al. [17]. A noise figure between 3 and 4 dB canbe obtained for a fluoride amplifier providing 20 dB of gain using a 200 mW pump forsignal input power between -40 and -20 dBm. Outside this interval, the noise figureincreases.The minimum signal input power to obtain Q = 6 is comparable for the pre-amplifiersbased on sulphide and fluoride host glasses (-38.7 and -38.6 dBm, respectively) foran ideal transmitter-receiver pair (i.e. infinite extinction ratio ζ = Ps1

/Ps0, unity

receiver responsivity Rd and in the absence of thermal noise).

From the examples shown in this section, it is evident that the overall amplifierperformance of the fluoride type amplifier is limited by its low quantum efficiency.Due to the longer emission lifetime of praseodymium in the sulphide glass host (i.e.400 versus 130 µs), the efficiency of amplifiers based on these host glass types is muchhigher compared to fluoride based amplifiers, leading to advantageous reduction of


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NF SulphideNF Fluoride

Figure 5.36: Comparison of small signal gain and noise figure of pre-amplifiers basedon sulphide and fluoride host glass. The applied pump power for the sulphide amplifieris 112.5 mW at 1023 nm, while the pump power of the fluoride amplifier is 400 mWat 1011 nm. The input signal power is -30 dBm. A co-propagating pump scheme isapplied.

required pump power. However, the shift of the maximum gain to longer wavelengthsis considered as a drawback for the use of sulphide host glass for the praseodymiumdoped fibre amplifier in telecommunication systems operating in the O-band (1290–1340 nm).

5.4 Conclusions

When the experimental PDFA (based on commercially available fluoride glass fibre)is used in a booster application, the amplifier is saturated due to the high signal inputpowers. The power of the amplified spontaneous emission in the saturated amplifieris suppressed. This can result in a better signal to noise ratio at the output of thesaturated amplifier. Compared to to the pattern dependent behaviour observed forsaturated semiconductor optical amplifiers, saturation of the PDFA does not result inpattern dependent behaviour. Furthermore, the polarisation sensitivity of the PDFAis negligible.Within the optical recirculating loop set-up, the experimental PDFA, based on fluo-ride fibre, is operated as an in-line amplifier. The input signal power is moderatelylarge, and hence the amplifier is slightly saturated. Due to the slow gain dynamics ofthe amplifier and the amplifier saturation, disturbances in the average power of thesignal in chains of amplifiers are levelled out by the self regulation process. In the op-tical recirculating loop experiments, the observed penalties in receiver sensitivity arecaused by both optical signal degradation in the amplifier (i.e. accumulation of ASEnoise) and fibre spans in the loop and impairments due to the measuring system.The sensitivity of the receiver with fluoride fibre based PDFA pre-amplifier is ap-proximately -30 dBm, which equals a 15 dB improvement compared to the receiverwithout pre-amplifier. The small signal gain is approximately 20 dB, while the noise


figure, derived from these experiments, is 9.5 dB at 1.31 µm. It is expected that theperformance of the experimental pre-amplifier can be improved by increasing the gainof the amplifier, reducing the coupling losses at the amplifier input and applicationof a co-propagating pump scheme.The fibre amplifier model, as derived in chapter 4, can be used to design praseodymiumdoped fibre amplifiers, based on germanium gallium sulphide glasses. The calculatedsaturated output power of a booster amplifier is 30 dBm using 1700 mW pump power.The output power of the saturated PDFA, based on sulphide fibre, is nearly indepen-dent of input power, i.e. the slope of the gain curve is approximately -1 dB/dBm forinput power between -20 and +20 dBm. The calculated small signal gain (-30 dBm)obtained by a sulphide based pre-amplifier is 30 dB for 165 mW pump power. The cal-culated maximum gain is obtained at a signal wavelength of 1342 nm, which matchesthe peak of the emission spectrum.The calculated quantum conversion efficiency and gain efficiency of the sulphide am-plifier are much higher than that of the fluoride amplifier. The sulphide amplifierprovides higher gain than the fluoride amplifier for equal pump power, even at smallpump power. It is evident that the overall amplifier performance of the fluoride typeamplifier is hampered by its low quantum efficiency. Due to the longer emission life-time of praseodymium in the sulphide glass host compared to fluoride host glasses (i.e.about 400 versus 130 µs), the efficiency of amplifiers based on sulphide host glassesis much higher, leading to advantageous reduction of the required pump power. Themaximum gain wavelength of the sulphide amplifier is approximately 1340 nm, andis shifted to longer wavelengths compared to the maximum gain wavelength of thefluoride amplifier, which is approximately 1310 nm. This shift of the maximum gainto longer wavelengths is considered as a drawback for the use of sulphide host glassfor the PDFA in telecommunication systems operating around 1.31 µm.The signal attenuation loss at the signal wavelength of a 370 ppm praseodymiumdoped germanium gallium sulphide glass fibre with composition Ge28.8Ga1.2S70.0 is0.2 dB/cm. The attenuation at 1030 nm equals 0.43 dB/cm, which can be partlycontributed to pump ground state absorption at this wavelength. Ideally, the atten-uation losses of a praseodymium doped fibre should be less than 0.1 dB/m to obtainan efficient amplifier. The peak wavelength of the spontaneous emission spectra islocated at 1335 nm, the 3 dB bandwidth is approximately 70 nm. Additional mea-surements do not indicate the presence of (visible) red luminescence.Based on the observed performance of the experimental PDFA based on fluoride hostglass and the high, calculated efficiency of the PDFA based on sulphide glass, it is ex-pected that the PDFA based on germanium gallium sulphide glass will be a promisingcandidate as fibre amplifier for the O-band (1290 –1340 nm). However, experimen-tal techniques should be improved to allow production of single mode praseodymiumdoped fibre based on germanium gallium sulphide glasses with a core diameter of≤ 4 µm and attenuation loss of ≤ 0.1 dB/m.


5.5 Nomenclature

a core radius mBe electrical bandwidth HzBo optical bandwidth HzDin fibre diameter at input side mDout fibre diameter at output side me elementary charge = 1.602 · 10−19 CF noise figure -G gain -h Plank’s constant = 6.62559 · 10−34 JskB Boltzmann’s constant =1.38066 10−23 JK−1

N electrical noise power at receiver A2

Ntot(1) electrical noise power for ”mark” A2

Ntot(0) electrical noise power for ”space” A2

P optical power WPe error probability -Pdark ”dark” power originating from the photodetector WPs,in signal input power WPs,out signal output power WPp pump power WP−

p counter-directional propagating pump power WPreceiver optical power at the receiver WPs signal power WPs1

signal power for ”mark” WPs0

signal power for ”space” WPsp noise power WQ Quality factor related to SNR -Rd detector responsivity A W−1

RL load resistance ΩS electrical signal power at receiver A2

S(0) electrical signal power for ”space” A2

S(1) electrical signal power for ”mark” A2

T temperature KV normalised frequency -


αc connection losses -ζ extinction ratio -η photodiode quantum efficiency -ηin input coupling loss -ηout output coupling loss -λ wavelength mλc cut-off wavelength mλp pump wavelength bound m


λs signal wavelength bound mν frequency of light wave Hzρ praseodymium concentration m−3

τ spontaneous emission lifetime s

5.6 Bibliography


[2] G. Agrawal, Fiber-optic communication systems. Microwave and Optical Engi-neering, New York: John Wiley, 2nd ed., 1997. ISBN 0-471-17540-4.

[3] P. Becker, N. Olsson, and J. Simpson, Erbium-doped fiber amplifiers. Fundamen-tals and Technology. Optics and photonics, San Diego, CA: Academic Press,1999. ISBN 0-1208-4590-3.

[4] A. Bjarklev, Optical Fiber Amplifiers, Design and system applications. Norwood:Artech House, 1993. ISBN 0-89006-659-0.

[5] J. Jennen, Noise and saturation effects in high-speed transmission systems withsemiconductor optical amplifiers. PhD thesis, Eindhoven University of Technol-ogy, 2000. ISBN 90-386-1760-7.

[6] N. Bergano and C. Davidson, “Circulating loop transmission experiments for thestudy of long-haul transmission systems using erbium-doped fiber amplifiers,” J.Lightwave Technol., vol. 13, pp. 897–888, May 1995.


[8] G. Keiser, Optical Fiber Communications. McGraw–Hill, 3rd ed., 2000. ISBN0-07-116468-5.


[10] M. Artiglia, P. d. Vita, and M. Potenza, “Optical fibre amplifiers: physical modeland design issues,” Optical and Quantum Electronics, vol. 26, pp. 585–608, 1994.

[11] A. Ankiewicz and F. Ruhl, “Effect of dopant distribution on optimisation of Pr-doped fibre amplifiers,” Optical and Quantum Electronics, vol. 26, pp. 987–993,1994.




[14] A. v. Osch, “Modelling of praseodymium-doped fluoride and sulfide doped fibreamplifiers for the 1.3µm wavelength region,” EUT Report 95-E-294, EindhovenUniversity of Technology, October 1995.

[15] J. Valles, M. Hotoleanu, and E. Voiculescu, “Modelling of the temporal responseof Pr3+-doped fluoride fibre amplifiers,” Pure Appl. Opt., vol. 6, pp. 779–792,1997.

[16] S. Wannenmacher, “Praseodymium doped fibre amplifier for optical amplificationat 1300 nm,” in Global telecommunications conference, vol. 3, pp. 1618–1623,IEEE, 1996.

[17] T. Sugawa and Y. Miyajima, “Noise characteristics of Pr3+-doped fluoride fibreamplifier,” Electron. Lett., vol. 28, no. 3, pp. 246–247, 1992.

Chapter 6

Conclusions and

recommendations

Due to their potentially high gain efficiency (i.e. high signal gain per unit pumppower), rare earth doped amplifiers are considered as suitable travelling-wave am-plifiers for optical communication systems. In order to fully exploit the transparentwindows of the installed fibre, and particularly the 1.31 µm wavelength region, apowerful amplifier technique for these wavelengths is needed in the near future.In the 1290–1340 nm wavelength range, praseodymium doped fibre amplifiers are com-mercially available since the late 1990s, however the efficiency of these (fluoride based)amplifiers is low. In this study, the objective is to develop a praseodymium dopedfibre amplifier with improved efficiency based on sulphide host glasses for telecom-munication systems, deploying the O-band (the wavelength range between 1290 and1340 nm). Furthermore, the objective is to assess the performance (i.e. gain, satura-tion and noise characteristics) of praseodymium doped fibre amplifiers in telecommu-nication systems by means of modelling and measurements.For the development of such amplifier, the thermo-physical properties of the hostglasses are of major importance for the production process of the glass fibre. In ad-dition, the optical properties of the (praseody-mium doped) host glasses determinethe efficiency of the amplifier. Here, the processing (e.g. melting and fibre drawing)and the determination of the optical and thermo-physical properties of candidate(praseodymium doped) germanium gallium sulphide host glasses have been investi-gated. Furthermore, modelling and experimental studies were performed to determinethe performance of praseodymium doped fibre amplifiers in telecommunication sys-tems.

213


6.1 Conclusions

6.1.1 Main results of this study

Praseodymium doped germanium gallium sulphide host materials

The suitability to use germanium gallium sulphide glass as a host material for thePDFA is confirmed by its measured optical properties. The germanium gallium sul-phide glasses are highly transparent around the amplifiers’ pump and signal wave-lengths (i.e. 1010–1040 nm and 1290–1340 nm, respectively). The difference in therefractive index of core and cladding glass, needed to construct an optical fibre, canbe achieved by a small difference in the sulphur content between core and claddingglasses.For example, a single-mode fibre can be constructed using Ge27.7Ga1.1S71.1 andGe27.0Ga1.1S71.9 as core and cladding glasses, respectively. The refractive index dif-ference (near 1000 nm) is approximately 0.35%, i.e. the numerical aperture1 equals0.17. A cut-off wavelength2 of 950 nm is obtained at a core radius of circa 2.1 µm,which is considered to be possible using (pilot scale) fibre drawing equipment.One of the main requirements for the host glass is a low effective phonon energy, whichdetermines the rate of non-radiative energy transfer from, in case of praseodymiumdoping, the 1G4 excited state to the next lower energy level 3F4 by lattice vibrationsof the glass host. The effective phonon energy of the germanium gallium sulphideglasses is approximately 490 cm−1 and is comparable to that of fluoride glasses. Dueto the (up to four times) longer emission lifetime of praseodymium in the sulphidehost glass compared to fluoride host glasses, the luminescence quantum efficiency ofthe praseodymium doped germanium gallium sulphide glasses prepared in this studyis higher than the efficiency of fluoride glasses. The higher efficiency of amplifiers,based on sulphide host glasses, will result in an advantageous reduction of the requiredpump power for the PDFA based on sulphide host glasses compared to PDFAs basedon fluoride host glasses.In the germanium gallium sulphide glasses, maximum pump ground state absorptionof praseodymium is located at a pump wavelength of approximately 1030 nm and thepeak wavelength of the stimulated emission cross section is approximately 1.34 µm.The signal ground state absorption below 1.3 µm is negligible.Using the pure chemical elements as a starting material, germanium gallium sulphideglasses were prepared successfully by melting in vitreous silica ampoules. Purificationof the raw materials, especially sulphur, is essential to obtain highly transparent hostglasses, especially near the amplifiers’ pump and signal wavelengths. Note that thehigh vapour pressure of the germanium gallium sulphide glasses is considered as adisadvantage during preparation of glass fibres from this material. However, suitabletechniques to deal with the high vapour pressure of the glasses during melting areavailable (e.g. melting in sealed vitreous silica ampoules).The suitability of the germanium gallium sulphide glasses for fibre drawing is mainly

1This number expresses the light gathering ability of a fiber and is given by the square root ofthe squared refractive index of the core minus the squared refractive index of the cladding.

2The fibre is single-mode for wavelengths longer than the cut-off wavelength of the fibre.

Conclusions and recommendations 215

determined by the thermo-physical properties of the material (such as mechanicalstrength, heat conductivity, viscosity, glass transition, crystallisation and meltingtemperatures). The stability of the germanium gallium sulphide glasses, as describedby the difference between the glass transition temperature and the crystallisation tem-perature, is sufficiently high (185 C) for fibre drawing. In addition, it is concludedfrom the measured viscosity – temperature relation that the viscosity of the glass issufficiently low to draw fibres well below the crystallisation temperature.

Fibre drawing of chalcogenide glasses

Germanium gallium sulphide glass fibres can be prepared from solid preforms withcore-cladding structure. In the rod-in-tube process, the fibre preform is constructedby inserting a (thin) rod of core material into the cladding tube. Thin core glass rodscould be prepared by stretching of (initially thick) core glass rods (as melted) to thedesired diameter in the fibre drawing tower. Cladding glass tubes can be prepared bya hot deformation process, developed in this study. The assembly of germanium gal-lium sulphide preforms (with core-cladding structure) and the fibre drawing of thesepreforms is rather complicated and could not be realised in the course of this study,due to the limited availability of suitable glass samples of the required dimensions.However, thin core glass rods and cladding glass tubes could be prepared.To improve the surface quality of the core and cladding materials, prior to preformassembly and subsequent fibre drawing, diluted aqueous solutions of e.g. caustic sodacould be used to etch the surface. If necessary, acids can be used to clean contami-nated glass surfaces, without causing impairments to the glass surface.The working range (i.e. the applicable fibre drawing rate as a function of furnacetemperature) for fibre drawing of germanium gallium sulphide glass rods or preformsinto fibre is derived using a mathematical fibre drawing model. The model incorpo-rates mass and heat transfer in the neckdown and can be easily adapted to simulatethe fibre drawing of materials with different physical properties. The maximum ap-plicable furnace temperature is bound by the local temperatures inside the neckdown,which may not exceed either the temperature at which the viscosity is too low for fibredrawing or the on-set crystallisation temperature. The local stresses occurring withinthe neckdown are computed by the model. The model can be used to determine theworking conditions at which the stresses (which are in turn related to the appliedfibre drawing force) do not exceed the tensile strength of the glass.Modelling results show that precise control of the furnace temperature becomes morecritical as the fibre drawing speed increases. The fibre drawing of germanium galliumsulphide glass rods, into fibres with an outer diameter of approximately 300 µm, wasdemonstrated on a pilot scale fibre drawing machine. Based on the modelling results,it is expected that germanium gallium sulphide fibres with diameters of approximately125 µm can be drawn using this equipment when improved process control (i.e. au-tomatic control of the fibre drawing velocity and measurement of the drawing force)is applied.


Modelling light amplification in praseodymium doped single-mode fibres

A spatially and spectrally resolved praseodymium doped fibre amplifier model is usedto study the amplifier characteristics of praseodymium doped fibres using the opti-cal properties of the praseodymium dopant and the host glasses. The (steady state)amplifier model describes the evolution of signal, ASE, and pump power within thepraseodymium doped fibre. The model can be used to calculate the amplification ofboth continuous wave signals and signals which are (amplitude) modulated at highfrequencies (i.e. higher than approximately 10–100 kHz).In this study, the optical properties of praseodymium doped glasses were used asinput data for the existing, steady state amplifier model. The model outcome is vali-dated for fluoride host glasses using the results of measurements on an experimentalpraseodymium doped fibre amplifier. The model is considered to be suitable for thedesign and development of new types of PDFAs based on other glass compositions orgeometrical configurations.Although the amplifier model is derived for praseodymium doped fibre amplifiers, themodel can be easily adapted to calculate the gain and noise figures for other rare-earth doped fibre amplifiers based on four level operation (e.g. neodymium dopedfibre amplifier).

Performance and design of PDFAs for telecommunication systems

In principle, the PDFA can be easily optimised for dedicated usage as booster, in-lineor pre-amplifier. The signal output power of a saturated PDFA is nearly indepen-dent of signal input power. As saturation of the PDFA does not result in bit patterndependent fluctuations of the signal gain, PDFAs are well suited for large signal am-plification (e.g. booster application). Furthermore, the PDFA can be applied aspre-amplifier, due to its high small-signal gain and low noise figure. In general, thedependence of the signal gain of the PDFA on the state of polarisation of the signal(i.e. the polarisation sensitivity) is negligible.The fibre amplifier model is a suitable tool for optimisation of the design of thepraseodymium doped fibre amplifier devices. In fibre amplifiers, the propagation di-rection of the pump light compared to the signal light direction are important param-eters that influence gain and noise properties. The main parameters involved in theoptimisation of the praseodymium doped fibre itself are length, core radius, numericalaperture, cut-off wavelength, praseodymium dopant concentration and praseodymiumdopant distribution.The gain efficiency of the praseodymium doped fibre is related to the confinementof the signal, amplified spontaneous emission and pump light within the doped fibrecore, which in turn is determined by the core diameter and the numerical apertureof the praseodymium doped fibre. The numerical aperture is determined by the re-fractive indices of the core and cladding glass, which in turn are related to the glasscomposition. The proper core diameter is established in the fibre drawing process.For example, the required core diameter is between 3 and 4 µm, for a fibre with acut-off wavelength of 950 nm. In this case, the numerical aperture is between 0.182and 0.242, respectively.


Table 6.1: Comparison of the design and performance of a praseodymium doped fibreamplifier, based on sulphide and fluoride host glasses and used as a booster amplifieror as a pre-amplifier.

Parameter Booster Booster Pre-amp Pre-amp

Host material Sulphide Fluoride Sulphide FluorideLength [m] 11.91 5.66 10.63 5.31Cut-off wavelength [nm] 950 950 950 950Numerical aperture [-] 0.182 0.182 0.182 0.182Dopant concentration [ppm] 500 1000 500 1000Pump wavelength (optimum) [nm] 1023 1011 1023 1011Pump power [mW] 275 550 112.5 400(counter-/co-prop. pump scheme) counter counter co coLarge signal gain (max.) [dB] 20 20Small signal gain (max.) [dB] 21 21Quantum Conv. Eff. [mW/mW] 0.502 0.266Gain efficiency [dB/mW] 0.187 0.0533 dB sat. output power [dBm] 14.7 15.9 8.1 14.2Max. signal gain wavelength [nm] 1342 1310 1342 1310Noise figure F [dB] 4.1 – 4.3 3.4 – 7.3 3.3 – 3.5 3.1 – 4.0

The amplifier model is used to compare the performance (i.e. gain, saturation andnoise characteristics) of the praseodymium doped amplifier, based on sulphide hostglasses on one side and fluoride host glasses on the other side. The maximum gainwavelength of the sulphide amplifier is approximately 1340 nm (see Table 6.1) andis shifted to longer wavelengths compared to the maximum gain wavelength of thefluoride amplifier, which is approximately 1310 nm. This shift of the maximum gainto longer wavelengths is considered as a drawback for the use of sulphide host glassfor the PDFA in telecommunication systems operating around 1.31 µm.In general, the calculated quantum conversion efficiency and gain efficiency of thesulphide amplifiers are much higher than that of the fluoride amplifier. For exam-ple, the calculated quantum conversion efficiency3 of a booster amplifier (signal inputpower 0 dBm, signal output power 20 dBm) based on sulphide host glasses is twiceas large as that of a fluoride based booster amplifier (see Table 6.1). The calculatedgain efficiency of a pre-amplifier (signal input power -30 dBm, gain 20 dB) based onsulphide host glasses is 0.134 dB/mW higher than that of a fluoride based amplifier(see Table 6.1).Due to the higher efficiency, less pump power is needed to obtain high gain. Fur-thermore sulphide fibres can be shorter than fluoride fibres, when the same dopantconcentration is applied. The noise figures (near the maximum gain wavelength) of

3The quantum conversion efficiency is defined as the increase in the number of signal photons asa result of amplification divided by the number of launched pump photons.


Table 6.2: Comparison of the properties of praseodymium doped germanium galliumsulphide host glasses (prepared in this study) and praseodymium doped fluoride hostglasses (as incorporated in the experimental PDFA).


Emission lifetime [s] 410 10−6 130 10−6

Stimulated emission cross section [m2] 0.45 10−24 0.4 10−24

Corresponding peak wavelength [m] 1342 10−9 1310 10−9

Pump ground state cross section [m2] 0.16 10−24 0.04 10−24

Corresponding peak wavelength [m] 1023 10−9 1011 10−9

Signal ground state absorptionnegligible for wavelengths less than [m] 1350 10−9 1300 10−9

the chalcogenide and fluoride based praseodymium doped amplifiers are comparable.The 3 dB saturation output power of the amplifier based on sulphide host glasses islower than that of an amplifier based on fluoride host glasses. The calculated signaloutput power of the saturated PDFA, based on a sulphide fibre, is nearly independentof signal input power, i.e. the slope of the gain curve is approximately -1 dB/dBm.This phenomenon allows for stabilisation of the signal power within a transmissionlink containing several in-line amplifiers.

6.1.2 Prospects for a PDFA based on germanium gallium sul-

phide glasses

In Table 6.2, a comparison of the properties of praseodymium doped germanium gal-lium sulphide host glasses (prepared in this study) and praseodymium doped fluoridehost glasses (as incorporated in the experimental PDFA) is given. The (maximum)stimulated emission cross sections of both host glass types are comparable, althoughthe peak wavelength is 1340 nm and 1310 nm in the sulphide and fluoride host glass,respectively. As a result of the mentioned difference in the peak wavelength of thestimulated emission cross section and signal ground state absorption, the maximumgain wavelength of the sulphide amplifier is shifted to longer wavelengths comparedto the maximum gain wavelength of the fluoride amplifier. This is considered as adrawback for the use of sulphide host glass for the PDFA in telecommunication sys-tems operating around 1.31 µm.In Table 6.1, as an example, a comparison of the design and performance of praseody-mium doped fibre amplifiers based on sulphide and fluoride host glasses is shown.The calculated quantum conversion efficiency and gain efficiency of the sulphide am-plifiers is higher than to those of the fluoride amplifier. The higher efficiency leads toan advantageous reduction of the pump power, needed to obtain large signal outputpower, which is especially important for booster amplifiers. The better efficiency ofthe PDFA based on sulphide host glass compared to the fluoride host glass is ex-


plained by the four times higher pump ground state absorption cross section and thehigher emission lifetime (see Table 6.2).Based on the observed performance of the experimental PDFA based on fluoride hostglass and the high (calculated) efficiency of PDFAs based on sulphide host glass, it isexpected that the PDFA based on germanium gallium sulphide glass will be a promis-ing candidate as fibre amplifier for the O-band (1290–1340 nm). The PDFA basedon fluoride host glasses is already commercially available. When the PDFA based onsulphide host glasses becomes available, the choice whether to apply a PDFA basedon sulphide host glasses or based on fluoride host glasses is strongly dependent on theintended application.As powerful pump lasers have become available, the development of PDFA with highgain and high saturation output power is feasible. Due to the high quantum conver-sion efficiency, the PDFA based on sulphide host glasses offers a potentially betterperformance in booster applications (e.g. amplification of (analogue) CATV signals)than the PDFA based on fluoride host glasses. In contrast to semi-conductor ampli-fiers and Raman amplifiers, the PDFA is well suited for the amplification of amplitudemodulated signals, because signal distortion by the saturated amplifier (e.g. patterneffect) is negligible.The signal output power of the saturated PDFA, based on a sulphide fibre, will benearly independent of signal input power, which is a favourable phenomenon whenused as an in-line amplifier. The ability of stabilisation of the signal power within atransmission link containing several in-line amplifiers is more pronounced for PDFAsbased on sulphide host glasses compared to PDFAs based on fluoride host glasses.Due to its high small signal gain and low noise figure, the PDFA can also be used asa pre-amplifier to enhance receiver sensitivity. In this application, the performanceof the PDFA based on either sulphide or fluoride host glasses will be similar and thedifference in gain efficiency is less decisive.

6.2 Recommendations

In conclusion to this thesis, the following recommendations are made for future work.In this study, praseodymium doped germanium gallium sulphide fibres with a di-ameter of approximately 300 µm were prepared. These fibres did not comprise acore-cladding structure. In order to reduce the diameter of the fibre to circa 125 µm,it is recommended to monitor the force during fibre drawing and to apply a ratiocontroller for the preform feeding velocity and the fibre drawing velocity of the pilotscale fibre drawing tower.The requirements for rare earth doped fibres, used in fibre amplifiers (e.g. dispersion,absorption and scattering losses of the fibre), are less stringent compared to thoseused for long-haul transmission. However, experimental techniques should still beimproved to enable production of single mode praseodymium doped fibres, based ongermanium gallium sulphide glasses with a core diameter of ≤ 4 µm and attenuationloss of ≤ 0.1 dB/m. Currently, the measured losses by attenuation at the pump and


signal wavelengths are ≥ 0.2 dB/cm. These losses can probably be minimised byusing extremely pure base materials.The fibre drawing model, presented here, can be used to determine the working con-ditions (e.g. fibre drawing velocity and furnace temperature) for fibre drawing. Theaccuracy of the model results possibly can be improved by detailed modelling of bothradiative heat transfer within the glass and radiative heat transfer between the glassand the furnace.The modular test set-up for the praseodymium doped fibre amplifier can be used forcharacterisation of gain and noise properties of praseodymium doped fibres. In fu-ture work, the performance of PDFAs based on new developed praseodymium dopedgermanium gallium sulphide fibres could be tested using this set-up.The optimum design of the amplifier is a compromise between the compatibility ofthe doped fibre with the passive fibres to which it is connected and the efficiency ofthe praseodymium doped fibre. When high optical powers are applied, reduction ofthe insertion losses, due to the coupling of the praseodymium doped fibre and thepassive fibre become of major importance. To obtain low coupling loss, the numericalaperture and core diameter of the praseodymium doped fibre must be compatible tothe passive silica fibres to which it is connected. Lowering the insertion losses willresult in reduction of the noise figure, too. This is especially important if the PDFAis used as a pre-amplifier.Currently, it is assumed that the input signals for the amplifier model do not containspontaneous emission originating from the light source (e.g. laser). In practice, thesignal is accompanied by some spontaneous emission noise (e.g. originating from thelaser). To address the effects of amplified spontaneous emission noise on the per-formance of e.g. in-line and pre-amplifiers, this spontaneous emission noise may beincorporated into the model by adaptation of the boundary conditions at the amplifierinput.The recirculating loop test-set up is a powerful tool to evaluate the performance ofthe PDFA as an in-line amplifier. Prior to detection in the receiver section, signifi-cant attenuation of the signal power occurs due to attenuation losses caused by thetransmission fibre and the loop equipment. As the signal power at the receiver maybe insufficient to determine bit error rate properly, it is recommended to apply pre-amplification in the receiver section of the recirculating loop.In this work, the analysis of amplifier performance was restricted to signals at a singlewavelength. The large gain bandwidth of the PDFA allows application of wavelengthdivision multiplexing techniques to increase capacity of the telecommunication link.It is recommended to evaluate the performance of the PDFA in these systems exper-imentally, too. In addition, the amplifier model could be adapted to calculate thesignal gain at multiple wavelengths simultaneously.

Appendix A

Summary of differential

operations in cylindrical

coordinates

The Laplacian of a vector field (in cylindrical coordinates) is defined [1] as

∇2u = ∇(∇ · u) − [∇× [∇× u]] (A.1)

Differential operations involving the velocity u [1] in the r, z and θ directions.

[

∇2u]

r=

∂

∂r

(

1

r

∂

∂r(rvr)

)

+1

r2

∂2vr

∂θ2− 2

r2

∂vθ

∂θ+

∂2vr

∂z2(A.2)

[

∇2u]

z=

1

r

∂

∂r

(

r∂vz

∂r

)

+1

r2

∂2vz

∂θ2+

∂2vz

∂z2(A.3)

[

∇2u]

θ=

∂

∂r

(

1

r

∂

∂r(rvθ)

)

+1

r2

∂2vθ

∂θ2+

2

r2

∂vr

∂θ+

∂2vθ

∂z2(A.4)

Differential operations involving the stress tensor τ in the r, z and θ directions, whereτ is symmetrical [1].

[∇ · τ ]r =1

r

∂

∂r(rτrr) +

1

r

∂

∂θτrθ −

1

rτθθ +

∂τrz

∂z(A.5)

[∇ · τ ]z =1

r

∂

∂r(rτrz) +

1

r

∂τθz

∂θ+

∂τzz

∂z(A.6)

[∇ · τ ]θ =1

r

∂

∂θ(rτθθ) +

∂τrθ

∂r+

2

rτrθ +

∂τθz

∂z(A.7)

A.1 Bibliography

[1] R. B. Bird, W. Steward, and E. Lightfoot, Transport Phenomena. New York: J.Wiley & Sons, 1960. ISBN 0 471 07392 X.

221

Appendix B

Specifications of optical

components

B.1 Praseodymium doped fluoride fibre modules

Table B.1: Specifications of the praseodymium doped fluoride fibremodules type NEL FFM–I–R–1000–A–7–F(data provided by themanufacturer)

SpecificationsOuter dimension 120 × 120 × 8.5 mmPraseodymium doped fibreGlass composition InF3-based fluoride glassPraseodymium concentration 1000 ppmFibre length 7 ± 0.1 mFibre core diameter 1.8 – 2.0 µmRefractive index difference 2.5 %Cut-off wavelength 0.95 µmScattering Loss ≤ 0.1 dB/mBackground loss ≤ 0.1 dB/mSplicingSplicing loss ≤ 0.5 dB/pointReturn loss ≥ 50 dB/pointPigtail fibre (silica)Cut-off wavelength 0.95 µmRefractive index difference 0.45 %Connector type FC-PC

223


0.000

0.010

0.020

0.030

0.040

0.050

900 1000 1100 1200 1300 14000.00

0.10

0.20

0.30

0.40

0.50

Abs

orpt

ion

cros

s se

ctio

n x

1024

[m

2 ]

Em

issi

on c

ross

sec

tion

x 10

24 [

m2 ]

wavelength [nm]

Pump GSASignal GSA

Signal emission

Figure B.1: Cross sections for pump ground state absorption, signal ground stateabsorption and stimulated emission of NEL praseodymium doped InF3-based fluorideglass fibre.

The emission life time is 130 µs (data provided by the manufacturer). The absorp-tion and emission cross sections are shown in figure B.1. No data is available for theexcited state absorption cross-section.

B.2 Dual output ytterbium fibre laser

Table B.2: Specifications of the ytterbium doped fibre laser typeIPG Laser YLM–1030–500×2 (data provided by the manufacturer)

SpecificationsOuter dimension 90 × 160 × 20 mmOptical CharacteristicsMaximum output power 2 × 500 ± 5 mWOperation wavelength 1029.5 ± 0.1 nmBandwidth 0.1 ± 0.01 nmOperation mode CWOutput polarisation state RandomOutput fibre Flexcor – 1060Connector type FC-APC

Appendix C

Light guiding in single-mode

fibres

The propagation of light through a step index single-mode fibre is determined usingMaxwell’s equations. A comprehensive derivation of the characteristic equation (so-lution of the wave equations) for a step index fibre can be found in e.g. Van Etten etal. [1].The electro-magnetic field that is associated with a particular (transmission) modeof a step index fibre depends on the normalised frequency V of the light, which isdefined [1] as

V =2πa

λ

√

n21 − n2

2 (C.1)

in which λ is the wavelength, a is the core radius and n1, n2 are the refractive indicesof the core and cladding respectively.In the case of a weakly guiding fibre, i.e. the relative difference between the index ofrefraction of the core and cladding material is small, the optical intensities of the pumpand signal modes are given by the eigenvalues (discrete solutions) of the characteristicequation [1].

(

1

ut

J ′m(ut)

Jm(ut)+

1

wt

K ′m(wt)

Km(wt)

)

= ±m

(

1

u2t

+1

w2t

)

(C.2)

in which ut is the transverse propagation constant and wt is the transverse decayconstant [1, 2] and m is an integer number. Jm and Km are Bessel functions andmodified Bessel functions of order m and of the first and second kind respectively.Eigenvalues of the characteristic equation are found for each positive integer modenumber m.For a real argument, the ordinary Bessel functions Jm are oscillating and are givenby [4]

Jm(z) = Σ∞l=0

(−1)l

22l+ml!(m + l)!z2l+m (C.3)

225


The modified Bessel functions of the second kind Km show exponential decay and aregiven by [4]

Km(z) =π

2

I−m(z) − Im(z)

sin(mπ)(C.4)

where Im are modified Bessel function of the first kind, which are given by [4]

Im(z) = i−mJm(iz) (C.5)

At the interface between core and cladding (r = a), the magnitude of the electro-magnetic field in the core is equal to the magnitude of the field in the cladding. Thiscondition is satisfied [1] when

V 2 = u2t + w2

t (C.6)

For values of V , which are smaller than 2.405, only one transmission mode can existin the waveguide [1]. Hence, the fibre is single-mode for wavelengths longer than thecut-off wavelength of the fibre. The cut-off wavelength λc is given by [1]:

λc =2πa

√

n21 − n2

2

2.405(C.7)

The characteristic equation C.2 can be solved, to find the optical intensity within thefibre, using equation C.6 for the condition of continuity of the field at the interface ofthe core and cladding. The normalised intensity I(r, ν) in the fibre core [1, 3], for asingle-mode is

I(r, ν) =1

π

[

wt

aV

J0(utr/a)

J1(ut)

]2

(C.8)

in which ut is the transverse propagation constant and wt is the transverse decayconstant [1, 2], r is the radial distance and the frequency is given by ν = λ/c. Thevalue of the transverse propagation constant wt as a function of V is tabulated byJeunhomme [2]. J0, J1 denote Bessel functions (equation C.3) of the first kind.Equation C.8 is used to determine the intensity distribution of pump, signal and ASElight in the fibre core in the radial direction.

C.1 Bibliography

[1] W. Etten and J. Plaats, Fundamentals of optical fiber communications. London:Prentice Hall, 1991. ISBN 0-13-717521-3.

[2] L. Jeunhomme, Single-mode fiber optics - principles and applications. MarcelDekker, Inc., 1983. ISBN 0-8247-7020-X.

[3] C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Light-wave Technol., vol. 9, pp. 271–283, February 1991.

[4] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with For-mulas, Graphs, and Mathematical Tables. New York: Dover, 9th dover printing,10th gpo printing ed., 1964. ISBN 0-486-61272-4.

Appendix D

Noise in optical amplifiers

In this appendix, expressions for the noise caused by amplified spontaneous emission(ASE) at the output of an optical amplifier are derived.In Figure D.1 a schematic representation of an optical amplifier connected to a trans-mitter (Tx) and receiver (Rx) is shown. The optical power spectra as a function ofoptical frequency ν at the left hand side of the the figure indicate a) the signal priorto amplification, b) the amplified signal and amplified spontaneous emission (gener-ated by the amplifier) and c) the amplified signal and amplified spontaneous emissionwithin the optical bandwidth Bo of the optical bandpass filter (BPF). These spectracan be measured using an optical spectrum analyser. At output of the amplifier, theelectric fields of both the amplified signal and the ASE are simultaneously detectedusing a photo detector within the receiver. This process is schematically depicted inthe optical spectrum (d) at the bottom of the figure. Upon opto-electronic conversionat the photo detector, interference between light of different frequencies occurs. Thisinterference (so-called beating) of the signal with ASE and also interference of ASEwith ASE is generating interference signals at frequencies which equal the differenceof the two interfering frequencies. This is indicated by the shaded areas in the opticalspectrum. However, only the frequencies within the electric bandwidth Be of thereceiver (also indicated in the spectrum) are converted to an electrical signal. Theelectrical spectrum (e) as a function of the base-band frequency f after opto-electronicconversion is shown on the righthand side of the figure. In this spectrum, which canbe measured using an electrical spectrum analyser, the contributions of the signalpower and noise power are indicated. The shaded area represents the signals andnoise components within electric bandwidth Be of the receiver.

The interference of light of different frequencies at the detector is explained by thenature of the electro-magnetic field and the opto-electronic conversion at the photodetector. The total electric field Etot at the detector is the sum of the electrical fieldsoriginating from the signal light Es (at frequency νs) and the amplified spontaneousemission light Esp (within the the optical bandwidth Bo) [3].

Etot = Es + Esp (D.1)

227


BoBeG, Pase

Amplifer RxBPF

SignalASE

ν

PSignal

ASE

ν

P

Signal

ν

P Is+Isp

sp-sp beat noise

f

P

Optical power spectra Electrical power spectrum

sig-sp beat noise

ASE-ASEBeating

Signal ASEBeating

νs

ν

P

BeUpon opto-electronic conversion at the photo detector, mixing of signal and ASE and mixing of ASE with ASE is generatinginterference signals at frequencies ν=ν2-ν1

ν1

Tx

ν2

νs νs νs

<Be

Bo

BoBe

a b c e

d

Figure D.1: A schematic representation of an optical amplifier connected to a trans-mitter (Tx) and receiver (Rx). In the optical spectra a–c, the signal and amplifiedspontaneous emission are indicated. The optical filter bandwidth is Bo. The interfer-ence (beating) of the light at different frequencies is indicated in the optical spectrumd. The electrical noise power density of spontaneous-spontaneous (triangular) andsignal-spontaneous (rectangular) beat noise are indicated in the electrical spectrume. The shaded area represents the noise contributions within the electrical bandwidthBe of the receiver.

Appendix D. Noise in optical amplifiers 229

The detector response is proportional to |Etot|2. The signal and ASE components ofthe electro-magnetic field mix. Mixing results in so-called beat noise, at a frequencywhich equals the difference of the optical frequencies of the ASE that mixes witheither the signal or the ASE itself. Note that mixing is limited to signal and ASEwhich have exactly the same polarisation state [3]. The photo-electric current i isproportional to

i ∝[

|Es|2 + (|EsE∗sp| + |E∗

sEsp|) + |Esp|2] e

hν(D.2)

where * denotes the complex conjugate. The first term represents the signal intensity,the second term correspond to so-called signal-spontaneous (s-sp) beat noise and thelast term is the so-called spontaneous-spontaneous (sp-sp) beat noise.

Here, the signal-spontaneous and spontaneous-spontaneous beat noise power at theoutput of an optical amplifier will be derived. For simplicity, it is assumed that theoptical amplifier under consideration has uniform gain G (and thus ASE) over anoptical bandwidth Bo. The average signal input power Ps,in at optical frequency1 ω0

is centred in the optical passband Bo. The length of the amplifier equals L and thecoupling efficiencies at the amplifier input and output are unity.The power spectral density per unit length of the spontaneous emission, generated bythe optical amplifier, is [1]

Pse = hνgs∆ν (D.3)

where gs is the gross gain factor due to stimulated emission. The optical energy ofone photon with frequency ν equals hν. The net gain factor g is obtained from thedifference between the gross gain factor gs and the stimulated absorption factor αs [1]

g = gs − αs (D.4)

Note that the induced rate for absorption is equal to the induced rate of emission.The induced rate of emission is proportional to the intensity of the electro-magneticfield, whereas the spontaneous emission rate is independent of the intensity of theelectro-magnetic field [2].Substitution of equation D.4 in equation D.3 gives

Pse = hνgs

gs − αsg∆ν = hνnsp∆ν (D.5)

where nsp = gs/(gs − αs) is the so-called population inversion factor.In the stationary state (∂/∂t = 0), the amplification of light propagating in thepositive z direction is described by

∂P

∂z= (g − α)P (D.6)

The gain G of the amplifier is given by

G = e(g−α)L (D.7)

1The radian frequency ω is to be distinguished from the real frequency ν = ω/2π.


The gain factor g is assumed to be constant along the amplifier length, which assump-tion is valid for an unsaturated amplifier.The spontaneous emission generated at location z is amplified as it travels to theamplifier output at z = L of the amplifier. Application of equation D.6 and takingall spontaneous emission contributions over the entire amplifier length (i.e. betweenz = 0 and z = L) into account, the power spectral density of the amplified sponta-neous emission PASE at the amplifier output can be calculated.

PASE =

∫ L

0

PseeR

L

z(g−α)dz′

dz

=

∫ L

0

hνnspg∆νeR

L

z(g−α)dz′

dz

= hνnspg

g − α

[

e(g−α)L−1]

∆ν

= hνnspKx(G − 1)∆ν (D.8)

where the factor Kx accounts for population inversion due to internal losses (e.g.scattering losses), excluding stimulated absorption within in the amplifier. Whenthe internal losses may be neglected with respect to the gain (i.e. α ≈ 0), Kx isapproximately 1.The spontaneous emission power in the optical bandwidth Bo, in a single polarisationmode, is then given by [4]

Psp = nsp(G − 1)hνBo (D.9)

Equation D.9 represents a fundamental result needed to understand noise in opticalamplifier systems.A detailed derivation of the amplifier noise terms from the (total) intensity of theelectric field is given by Olsson [4].The electrical field Esp, representing the spontaneous emission at the output of theamplifier, can be written as a sum of cosine terms spaced at an arbitrarily smallfrequency width δν. For the purpose of this analysis, δν is chosen so that Bo/2δν isan integer value. The total electric field of the spontaneous emission equals the sumof monochromatic waves over the frequency bandwidth Bo and is given by [4]

Esp(t) =

Bo/2δν∑

k=−Bo/2δν

√

2nsp(G − 1)hνδν cos ((ω0 + 2kπδν)t + Φk) (D.10)

where Φk is a random phase for each component of the spontaneous emission. Allcomponents of the electric field have the same amplitude, due to the assumption ofuniform gain. By introducing the short notations N0 = nsp(G − 1)hν and M =Bo/2δν, the total electric field at the output of the amplifier is given by

E(t) =√

2GPin cos (ω0t) +

M∑

k=−M

√

2N0δν cos ((ω0 + 2kπδν)t + Φk) (D.11)


The photo-electric current i(t) generated by photo detector with a unity quantumefficiency is proportional to the intensity [4]

i(t) = E2(t)e

hν(D.12)

where the bar indicates time averaging over optical frequencies at the photo detector.Hence, the photo-electric current is given by

i(t) = GPine

hν

+4e

hν

M∑

k=−M

√

GPinN0δν cos (ω0t) cos ((ω0 + 2kπδν)t + Φk)

+2eN0δν

hν

[

M∑

k=−M

cos ((ω0 + 2kπδν)t + Φk)

]2

(D.13)

The consecutive terms in equation D.13 represent the current due to signal, signal-spontaneous beat noise and spontaneous-spontaneous beat noise, respectively for asingle polarisation.In the following derivation of the signal-spontaneous and spontaneous-spontaneousnoise power, all terms at frequencies of approximately 2ω0, which average to zero andare outside the system passband will be neglected.The photo-electric current of the signal-spontaneous beat noise (see equation D.13) is

is−sp(t) =4e

hν

M∑

k=−M

√

GPinN0δν cos (ω0t) cos ((ω0 + 2kπδν)t + Φk)

=2e

hν

√

GPinN0δν

M∑

k=−M

cos (2kπδνt + Φk) (D.14)

where the terms that are proportional to cos(2ω0t), which average to zero, have beenneglected. For each (non-optical) difference frequency, 2kπδν, the sum has a positivefrequency component and a negative frequency component, witch have a randomphase. Therefore, the power spectrum of is−sp(t) is uniform in the frequency interval−Bo/2 – Bo/2 and has an equivalent single-sided noise power density of

N ′s−sp =

4e2

hνPinGnsp(G − 1) (D.15)

Substitution of equation D.9 into equation D.15 and taking the electrical bandwidthBe of the photo detector into account results in [4]

Ns−sp =4(isisp)Be

Bo(4.22)


The photo-electric current of the spontaneous-spontaneous beat noise (see equa-tion D.13) is

isp−sp(t) = 2N0δνe

hν

[

M∑

k=−M

cos ((ω0 + 2kπδν)t + Φk)

]2

=2eN0δν

hν

M∑

k=−M

cos(βk)M∑

j=−M

cos(βj)

(D.16)

where βk = ((ω0 + 2kπδν)t + Φk) and βj = ((ω0 + 2πjδν)t + Φk). Rewriting equa-tion D.16 results in

isp−sp(t) = 2N0δνe

hν

M∑

k=−M

M∑

j=−M

(

1

2cos(βk − βj) +

1

2cos(βk + βj)

)

(D.17)

In this equation, the terms proportional to cos(βk + βj) have frequencies of approx-imately 2ω0 and average to zero. The limits of the summations are −M and M ,respectively. Using cos(−αt) = cos(αt), the limits of the summation can be shiftedto 0 and 2M . Hence, equation D.17 can be simplified to yield

isp−sp(t) =N0δνe

hν

2M∑

k=0

2M∑

j=0

cos ((k − j)2πδνt + Φk − Φj) (D.18)

When k equals j, a DC term is obtained. In total, 2M +1 of such terms are obtained,which do not represent a noise term in itself but which are the values of the detectedspontaneous emission (per polarisation state).

iDCsp =

e

hνN0δν(2M + 1) = nsp(G − 1)eBo (D.19)

because (2M + 1) ≈ 2M for large M . Note that the iDCsp term will contribute to the

shot noise [4].Listing the terms of equation D.18 according to their frequency gives


frequency # terms−2Mδν 1

(−2M + 1)δν 2(−2M + 2)δν 3

......

−mδν 2M-m+1...

...−δν 2Mδν 2M...

...mδν 2M-m+1

......

(2M − 2)δν 3(2M − 1)δν 2

2Mδν 1

The terms with the same absolute frequency but of opposite sign add in phase. There-fore, the power spectrum of the spontaneous-spontaneous beat noise extends from 0to Bo with a triangular shape and single-side power density near dc of

N ′sp−sp = 2n2

sp(G − 1)2e2Bo (D.20)

Substitution of equation D.9 into equation D.20 and taking the electrical bandwidthBe of the photo detector into account results in [4]

Nsp−sp =2i2sp(BoBe − 1

2B2e )

B2o

(4.23)

The electrical power spectrum of the noise terms, presented in equations 4.22 and4.23, is depicted in Figure D.2. The spontaneous-spontaneous noise power density,within the electrical bandwidth Be of the receiver, is reduced by using an optical filterwith a smaller passband Bo, while the signal-spontaneous noise power density is notaffected. In practice, the optimum electrical bandwidth Be and the optical bandwidthBo are related to the bandwidth needed to transmit signals at a given bit rate.

D.1 Bibliography

[1] J. Jennen, Noise and saturation effects in high-speed transmission systems withsemiconductor optical amplifiers. PhD thesis, Eindhoven University of Technology,2000. ISBN 90-386-1760-7.



2i2sp

Bo

4(isisp)Bo

0 Be BoBo/2

Frequency [Hz]

Ele

ctri

calnoi

sepow

erden

sity

[A2/H

z]

Figure D.2: Electrical noise power density of spontaneous-spontaneous (triangular)and signal-spontaneous (rectangular) beat noise, after Olsson [4]. The shaded arearepresents the noise contributions within the electrical bandwidth Be. The opticalfilter bandwidth is Bo.

[3] P. Becker, N. Olsson, and J. Simpson, Erbium-doped fiber amplifiers. Fundamen-tals and Technology. Optics and photonics, San Diego, CA: Academic Press, 1999.ISBN 0-1208-4590-3.


Scientific publications

related to this thesis

Chapter 2 & 3

R.C. Schimmel and A.J. Faber, “Germanium Gallium Sulphide Glasses as host ma-terials for Pr-doped optical fiber amplifier,” in Proceedings of the 1997 IEEE/LEOSsymposium Benelux Chapter, Eindhoven, The Netherlands, pp. 241–244, November1997.

R.C. Schimmel, A.J. Faber, H. de Waardt, R.G.C. Beerkens and G.D. Khoe, “De-velopment of a Praseodymium Doped Fibre Amplifier based on Germanium GalliumSulphide Glass Fibres,” in Proceedings of the International Commission on GlassAnnual meeting, Amsterdam, The Netherlands, pp. S5.3, May 2000.

R.C. Schimmel, A.J. Faber, H. de Waardt, R.G.C. Beerkens and G.D. Khoe, “Devel-opment of Germanium Gallium Sulphide Glass Fibres for the 1.31 µm PraseodymiumDoped Fibre Amplifier,“ in Proceedings of the XII International symposium on non-oxide glasses and advanced materials, Florianopolis SC, Brazil, pp. 318–321, April2000.

R.C. Schimmel, A.J. Faber, H. de Waardt, R.G.C. Beerkens and G.D. Khoe, “Devel-opment of Germanium Gallium Sulphide Glass Fibres for the 1.31 µm PraseodymiumDoped Fibre Amplifier,” Journal of Non-Crystalline Solids vol. 284, pp. 188–192,2001.

Chapter 4

R.C. Schimmel, H.J.D. v.d. Sluis, R.J.W. Jonker and H. de Waardt, “Characterisationand modelling of praseodymium doped fibre amplifiers,” in Proceedings of the 2001IEEE/LEOS symposium Benelux Chapter, Brussel, Belgium, pp. 133–136, December2001.

235


Chapter 5

R.J.W. Jonker, R.C. Schimmel and H. de Waardt, ”Experimental assessment of aPraseodymium Doped Fibrer Amplifier (PDFA) for amplifier applications in the sec-ond telecommunication window,” in Proceedings of the 2001 IEEE/LEOS symposiumBenelux Chapter, Brussel, Belgium, pp. 137–140, December 2001.

R.C. Schimmel, R.J.W. Jonker, P.K. van Bennekom, G.D. Khoe and H. de Waardt,“Experimental assessment of 1.3 µm telecommunication system incorporating aPraseodymium Doped Fibre Amplifier (PDFA),” in Proceedings of SPIE/5th. In-ternational Conference on Applications of Photonic Technology, Quebec, Canada,vol. 4833, pp. 940–947, June 2002.

List of abbreviations

AOS acousto-optical switchASE amplified spontaneous emissionB2B back-to-back configurationBER bit-error-rateBERT bit-error-rate testsetBPF bandpass filterCATV common antenna televisionCW continuous waveDC direct currentDDFA dysprosium doped fibre amplifierDSC differential scanning calorimetryDRA distributed Raman amplifierEDFA erbium doped fibre amplifierESA excited state absorptionETDM electrical time domain multiplexingFP Fabry-PerotFWHM full width at half maximumGSA ground state absorptionHH horizontal-horizontalIR infraredJ-O Judd-OfeltLD laser diodeLPF low-pass filterMMF multi mode fibreNA numerical apertureNDFA neodymium doped fibre amplifierNIR near infraredNRZ non-return-to-zeroOSA optical spectrum analyserOSNR optical signal to noise ratioOTDM optical time domain multiplexingPDFA praseodymium doped fibre amplifierPPG pulse pattern generator

237


PM powermeterPRBS pseudo-random bit sequenceQCE quantum conversion efficiencyRB resolution bandwidthRF radio frequencyRx receiverRZ return-to-zeroSOA semiconductor optical amplifierSOP state of polarisationSMF single mode fibresSMF standard single mode fibreSNR signal to noise ratioTDFA thulium doped fibre amplifierTLS tuneable laser sourceTE transverse electricTG thermogravimetryTM transverse magneticTx transmitterUV ultravioletVIS visibleVH vertical-horizontalWDM wavelength-division multiplexingWSC wavelength selective coupler

Samenvatting

Met zeldzame aarden gedoteerde optische versterkers zijn, door hun hoge versterkings-efficientie (d.w.z. een grote signaalversterking per eenheid pompvermogen), potentieelzeer geschikt om in optische telecommunicatiesystemen toegepast te worden. Om inde toekomst volledig gebruik te kunnen maken van de transparante golflengtegebiedenvan de reeds geınstalleerde glasvezels, in het bijzonder in het golflengtegebied rond1,31 µm, is het van belang om over krachtige versterkers te kunnen beschikken.De praseodymium gedoteerde glasvezelversterker (praseodymium doped fibre ampli-fier, PDFA) is sinds het einde van de jaren negentig commercieel verkrijgbaar. Dezeversterker, welke is gebaseerd op fluoride glazen, is toepasbaar in het golflengtegebiedvan 1290 tot 1340 nm. Een nadeel van deze, op fluoride glas gebaseerde versterker isde lage versterkingsefficientie. Het doel van dit onderzoek is het ontwikkelen van eenop sulfide glas gebaseerde PDFA met een verbeterde efficientie.Daarnaast is het doel van dit werk om de eigenschappen van PDFAs (zoals verster-king, verzadiging en ruiseigenschappen) in telecommunicatiesystemen in de O-band(het golflengte gebied van 1290 tot 1340 nm) te analyseren door middel van model-berekeningen en metingen van onder andere de versterkingsfactor en het ruisgetal.

Praseodymium gedoteerde germanium gallium sulfide glazen

Germanium gallium sulfide glazen kunnen uit de zuivere elementen worden bereiddoor deze bij 1000 C in kwartsglazen ampullen te smelten. Het zuiveren van degrondstoffen, met name zwavel, is van essentieel belang om glazen met een hogetransparantie te verkrijgen in de golflengtegebieden die gebruikt worden voor de teversterken signalen (1290–1340 nm) en voor het optisch pompen van de versterker(1010–1040 nm). Germanium gallium sulfide glazen zijn transparant in het golfleng-tegebied van 0,5 tot 8,0 µm. De golflengte-afhankelijkheid van de brekingsindex vande glazen is bepaald met behulp van ellipsometrie en door meting van de Brewsterhoek. De brekingsindex bepaalt voor een groot deel de breking van licht in de glas-vezel. De brekingsindex van de in dit onderzoek ontwikkelde glazen is ongeveer 2,07en is een functie van de samenstelling.De optische eigenschappen (absorptie en emissie) van praseodymium in de germani-um gallium sulfide glazen werden kwantitatief bepaald met behulp van de Judd-Ofelttheorie. De Judd-Ofelt parameters voor de optische overgangen binnen de praseody-mium ionen zijn gebruikt om de werkzame doorsnede voor gestimuleerde emissie en

239


voor absorptie vanuit de aangeslagen toestand te bepalen. Naast absorptie en emissievan fotonen, kan de excitatie-energie van het praseodymium ion door niet-stralendverval worden overgedragen aan het glas in de vorm van roostertrillingen (fononen).De hoogst voorkomende fononenergie in het glas is circa 490 cm−1. Het energiever-schil tussen de 1G4 en 3F4 toestand van het praseodymium in het germanium galliumsulfide glas is ongeveer 2945 cm−1. Bij kamertemperatuur is de geschatte multi-fononrelaxatiesnelheid van het 1G4 niveau ongeveer 1150 s−1. Dit komt overeen met eenniet-stralende levensduur van 870 µs. De (gemeten) emissie levensduur van de 1G4 –3H5 overgang is circa 400 µs.

Glasvezelfabricage van chalcogenide glazen

Het verschil tussen de glastransitietemperatuur en de kristallisatietemperatuur (detemperatuur waaronder geen kristallisatie plaatsvindt binnen redelijke tijdsduur) ismaatgevend voor de stabiliteit van het germanium gallium sulfide glas tijdens hetbewerken bij hoge temperatuur. De glastransitietemperatuur van de hier ontwikkeldeglazen is ongeveer 360 C en de kristallisatietemperatuur is circa 185 C hoger dande glastransitietemperatuur.In dit werk is de staaf-in-buis methode voor het maken van germanium gallium sulfideglasstaafjes met een kern-mantel structuur onderzocht. Deze relatief eenvoudige me-thode voor het vezeltrekken werd verkozen boven het proces op basis van een dubbelesmeltkroes, omdat de glasstaafjes al beschikbaar zijn als halffabrikaten. In het staaf-in-buis proces worden de staafjes met kern-mantel structuur gemaakt door een dunstaafje van sulfide kernglas in een buisje van sulfide mantelglas (van een iets anderesamenstelling) te steken.Voorafgaand aan het samenstellen van de staafjes met een kern-mantel structuur enhet glasvezeltrekken is het noodzakelijk om de glasoppervlakken te etsen. Door teetsen wordt de vorming van defecten op de overgang van kern- en mantelglas tegengegaan. Dit is nodig om glasvezels met een lage demping te kunnen maken. Wateri-ge, alkalische oplossingen kunnen worden gebruikt om het oppervlak van germaniumgallium sulfide glas te etsen. In dit onderzoek werden de beste etsresultaten behaaldmet verdunde natronloog (0,02 M). De snelheid van etsen met meer geconcentreerdeoplossingen (>0,5 M) is te hoog voor een controleerbaar proces. Door de te verwaar-lozen reactiviteit tussen (geconcentreerde) sterke zuren en germanium gallium sulfideglas kan dit glas niet met zuren worden geetst. Zuren zijn wel geschikt om het opper-vlak van het glas te reinigen.Voor de vervaardiging van germanium gallium sulfide mantelglasbuisjes is een hogetemperatuur vervormingsproces ontwikkeld. In dit proces worden de visco-elastischeeigenschappen van het glas gebruikt. Mantelglasstaafjes worden in een mal opge-warmd en door indrukking met een naald onder isotherme condities omgezet in buis-jes. Het bepalen van de werktemperatuur is van cruciaal belang om scheuren vanhet materiaal (bij lage temperatuur en hoge viscositeit) en kristallisatie (bij te hogetemperatuur) of het bezwijken van de buisvorm tijdens het verwijderen van de naald(bij te lage viscositeit) te voorkomen. Dunne staafjes van kernglas kunnen wordengemaakt door dikkere staven in de glasvezeltrekmachine uit te trekken tot de gewenste

Samenvatting 241

diameter.Het samenstellen van germanium gallium sulfide staafjes (met kern-mantel structuur)en het trekken van glasvezels hieruit is zeer gecompliceerd en kon niet worden gerea-liseerd gedurende dit onderzoek vanwege de beperkte hoeveelheid geschikte glasmon-sters met de vereiste dimensies.Met behulp van een wiskundig model zijn de geschikte procescondities voor het trek-ken van vezels van germanium gallium sulfide glazen bepaald. Het in dit onderzoekgebruikte tweedimensionale model is gebaseerd op de axiale symmetrie van de glas-staafjes en oplossing van de massa-, impuls- en warmtebalansen met de bijbehorenderandvoorwaarden. Bovendien worden de eigenschappen van de germanium galliumsulfide glazen in het model gebruikt.Het glasvezeltrekmodel is gebruikt om, voor verschillende vezeltreksnelheden en oven-temperaturen, het temperatuur-, spannings- en snelheidsprofiel in de zone van insnoe-ring te bepalen. Het werkgebied (d.w.z. de toepasbare vezeltreksnelheid als functievan de oventemperatuur) werd op basis van de berekende resultaten vastgesteld. Denauwkeurigheid van het model kan waarschijnlijk worden verbeterd door een gedetail-leerde beschrijving van de warmteoverdracht door straling in zowel het glas als tussenhet glas en de oven toe te voegen. Het vezeltrekken van germanium gallium sulfideglazen is mogelijk, hoewel het werkgebied klein is. Het werkgebied wordt begrensddoor kristallisatie (beperking van de maximaal toepasbare oventemperatuur) en despanningen die in de axiale richting van de vezel optreden (waardoor de maximaaltoepasbare treksnelheid wordt beperkt).Mantelloze germanium gallium sulfide vezels met een buitendiameter tussen 200 en300 µm en een lengte van 17,5 m werden verkregen in een pilotschaal vezeltrekmachi-ne. Op basis van modelberekeningen is de verwachting dat het trekken van germaniumgallium sulfide vezels met een kerndiameter van minder dan 4 µm en een manteldi-ameter van minder dan 150 µm mogelijk is. Om deze vezeldimensies te verkrijgenmoet de hier gebruikte glasvezeltrekmachine wel worden voorzien van een verbeterdebesturing.

Optische eigenschappen van germanium gallium sulfide vezels

De verzwakkingverliezen, bij de pompen signaalgolflengte van de versterker, in de indit onderzoek geproduceerde glasvezels zijn gemeten. De praseodymium concentra-tie in deze glasvezel, met samenstelling Ge28.8Ga1.2S70.0, is 370 ppm (mg/kg). Hetabsorptieverlies bij de signaal golflengte (1300 nm) in deze vezel is 0,2 dB/cm. Deabsoptieverliezen bij 1030 nm bedragen 0.43 dB/cm. Deze verliezen kunnen gedeelte-lijk worden toegeschreven aan pompabsorptie vanuit de grondtoestand. De piekgolf-lengte van het spontane emissiespectrum is 1335 nm, met een 50% bandbreedte vanongeveer 70 nm.


Eigenschappen en ontwerp van PDFAs voor optische telecommunicatiesys-

temen

De eigenschappen van een PDFA werden experimenteel bepaald in een optisch trans-missiesysteem werkend bij 1,3 µm. De versterker, gebaseerd op fluoride glasvezels,werd samengesteld uit commercieel verkrijgbare componenten. De prestaties van deversterker werden geanalyseerd voor verschillende toepassingen (vermogensversterker,tussenversterker en voorversterker) en configuraties (met betrekking tot de voortplan-tingsrichting van signaal- en pomplicht binnen de versterker) bij datatransmissiesnel-heden tot 10 Gbit/s. De versterkingsfactor van de experimentele PDFA (gebaseerdop fluoride glasvezels) is onafhankelijk van de polarisatietoestand van het signaallicht.Als de experimentele PDFA wordt gebruikt als een vermogensversterker dan zal, doorde hoge signaalvermogens, verzadiging van de versterker optreden. PDFAs zijn zeergeschikt voor het gebruik als vermogensversterker, omdat verzadiging in een PDFAniet resulteert in verstoring van het bitpatroon (als gevolg van veranderingen van deversterkingsfactor).Een testopstelling, waarin het optische signaal kan worden gerecirculeerd, werd ge-bruikt om de eigenschappen van een PDFA in een systeem met meerdere PDFAs(welke als tussenversterker worden gebruikt) en vezelverbindingen (van 2×12,5 kmlengte) te meten bij datatransmissiesnelheden van 622 Mbit/s en 10 Gbit/s. Toena-me van het aantal rondgangen (d.w.z. afgelegde afstand) resulteert in een degradatievan de signaal-ruis-verhouding. Deze degradatie wordt veroorzaakt door zelfregulatievan het optische vermogen (d.w.z. het gemiddelde optische uitgangsvermogen vande versterker blijft constant, terwijl het vermogen van de versterkte spontane emissie(ruis) toeneemt ten koste van het signaalvermogen). Bij een datatransmissiesnelheidvan 622 Mbit/s kan een totale afstand van circa 2000 km (80 rondgangen) wordenoverbrugd. Voorversterking van het optische signaal bij de ontvanger bleek noodzake-lijk. Bij hogere datatransmissiesnelheden (b.v. 10 Gbit/s) is fout vrije datatransmissiealleen mogelijk voor afstanden tot 25 km. Dit wordt veroorzaakt door het gebrek aanoptische voorversterking bij de ontvanger en de lagere gevoeligheid van de 10 Gbit/sontvanger (-15,5 dBm) in vergelijking tot die van de gebruikte 622 Mbit/s ontvanger(-32 dBm).Met een optische voorversterker kan de gevoeligheid van de ontvanger worden verbe-terd. De gevoeligheid van de ontvanger met de op fluoride glasvezel gebaseerde PDFAvoorversterker bij een datatransmissiesnelheid van 10 Gbit/s is ongeveer -30 dBm, of-wel een verbetering van 15 dB vergeleken met de gevoeligheid van dezelfde ontvangerzonder optische voorversterker. De hier gebruikte, op fluoride glasvezel gebaseerdePDFA voorversterker had een versterkingsfactor voor signalen met een laag vermogenvan circa 20 dB en een ruisgetal van 9 dB.

Modellering van versterking in praseodymium gedoteerde glasvezels

Een spectraal model voor de bepaling van versterking, gebaseerd op de vier-niveaulaser werking van praseodymium, werd gebruikt om de werking van de versterkerte bepalen. Het versterkermodel maakt gebruik van de optische eigenschappen vande praseodymium doping en het toegepaste glas in verschillende configuraties. Het

Samenvatting 243

(steady-state) versterkermodel beschrijft de ontwikkeling van het signaal, de versterk-te spontane emissie en het pompvermogen als functie van de afgelegde weg binnen depraseodymium gedoteerde glasvezel. Bovendien kan het ruisgetal worden bepaald.De resultaten van het model werden gevalideerd met metingen van de versterkingsfac-tor en het ruisgetal van een PDFA die was samengesteld uit commercieel verkrijgbarecomponenten. De statische versterkingsfactor en het ruisgetal van deze versterker,gebaseerd op fluoride glasvezels, werden bepaald met behulp van monochromatischetestsignalen, door toepassing van de interpolatie-verminderingsmethode op het optischspectrum gemeten aan de versterkeruitgang. Over het algemeen is de versterkings-factor berekend met het versterkermodel lager dan de gemeten versterkingsfactor.Trends in de versterkereigenschappen worden goed beschreven door het model.De golflengte afhankelijke verliezen, welke worden veroorzaakt door signaalabsorptievan praseodymium ionen in de grondtoestand, worden enigszins te hoog ingeschatals er geen pompvermogen aan de versterker wordt toegevoerd. Met name bij lagepompvermogens resulteert dit effect in een te lage berekende waarde voor de verster-kingsfactor. Het gemeten maximum in de versterkingsfactor wordt bij een iets korteregolflengte gevonden dan het maximum dat door het versterkermodel wordt berekend.De kleine verschillen die gevonden worden bij de meting van de versterkingsfactor enhet ruisgetal van de versterker in verschillende configuraties, met betrekking tot devoortplantingsrichting van signaal- en pomplicht binnen de versterker, worden beves-tigd door het versterkermodel.De resultaten van het versterkermodel geven een goede beschrijving van de waargeno-men trends in de experimentele metingen, waarbij de beperkte nauwkeurigheid van deexperimenteel bepaalde optische eigenschappen en metingen van de versterkingsfac-toren in beschouwing zijn genomen. Het versterkermodel is geschikt voor het ontwerpen de ontwikkeling van PDFAs gebaseerd op verschillende glassamenstellingen (zoalsgermanium gallium sulfide glazen) en/of verschillende configuraties.Het ontwerp van de versterker, gebaseerd op germanium gallium sulfide glas, voor toe-passing als vermogensversterker of voorversterker is geoptimaliseerd met behulp vanhet versterkermodel. De belangrijkste variabelen die werden gebruikt voor optimalisa-tie van de praseodymium gedoteerde glasvezel zijn numerieke apertuur, kerndiameteren lengte. De optimale lengte van de praseodymium gedoteerde glasvezel, die nodig isom een maximale versterking bij een gegeven pompvermogen te verkrijgen, is omge-keerd evenredig met de praseodymium concentratie. Voor praseodymium gedoteerdesulfide glasvezels met een kerndiameter van 4 µm (welke met een pilotschaal glasvezel-trekmachine kunnen worden gemaakt) is de berekende versterkingsfactor maximaalvoor een numerieke apertuur van 0,182 en een afbreekgolflengte van 950 nm. De be-rekende maximale versterking wordt verkregen bij een signaalgolflengte van 1342 nm,welke overeenkomt met de piek in het emissiespectrum van de met praseodymiumgedoteerde germanium gallium sulfide glazen. Uit de berekeningen blijkt onder an-dere dat het verzadigde signaaluitgangsvermogen voor een vermogensversterker circa30 dBm is, wanneer 1700 mW pompvermogen wordt toegepast. Een versterkingsfac-tor voor lage signaalvermogens van 30 dB kan worden gerealiseerd met behulp van165 mW pompvermogen.Het signaal uitgangsvermogen van een verzadigde versterker, gebaseerd op sulfide ve-


zel, is nagenoeg onafhankelijk van het signaalingangsvermogen, d.w.z. de helling vande versterkingscurve is ongeveer -1 dB/dBm. Deze eigenschap maakt het mogelijkom het signaalvermogen in een optisch datatransmissiesysteem met meerdere tussen-versterkers te stabiliseren. Met behulp van het versterkermodel werden de prestatiesvan versterkers gebaseerd op germanium gallium sulfide glazen en fluoride glazen metelkaar vergeleken. Over het algemeen is de berekende efficientie van de sulfide ver-sterkers veel hoger dan de efficientie van fluoride versterkers. De berekende efficientievan een vermogensversterker (signaal ingangsvermogen 0 dBm, signaal uitgangsver-mogen 20 dBm) gebaseerd op sulfide glazen is bijvoorbeeld 0,5 mW/mW en dat istwee keer zo groot als dat van een op fluoride glazen gebaseerde vermogensversterker.De berekenende versterkingsefficientie van een voorversterker (signaalingangsvermo-gen −30 dBm, versterkingsfactor 20 dB) gebaseerd op sulfide glazen is 0,134 dB/mWhoger dan dat van een voorversterker gebaseerd op fluoride glazen. Als gevolg van dehogere efficientie van de sulfide versterker is er minder pompvermogen nodig om eenhoge versterking te behalen. Als gevolg van de langere emissie levensduur van prase-odymium in sulfide glazen vergeleken met fluoride glazen (d.w.z. circa 400 versus 130µs), is de efficientie van versterkers gebaseerd op sulfide glazen veel hoger, hetgeenleidt tot een afname van het benodigde pompvermogen. De piekgolflengte van desulfide versterker is ongeveer 1340 nm en is, in vergelijking met de piekgolflengte bijfluoride versterkers (1310 nm), naar langere golflengten verschoven. Deze verschui-ving van de maximale versterkingsfactor naar langere golflengten wordt als een nadeelvan het gebruik van sulfide versterkers voor optische telecommunicatiesystemen bij1,31 µm beschouwd.

Conclusies

Op basis van de waargenomen prestaties van de experimentele PDFA gebaseerd opfluoride glasvezels en de hoge berekende efficientie van de PDFA gebaseerd op ger-manium gallium sulfide glazen, is het te verwachten dat het laatst genoemde verster-kertype een goede kandidaat is voor de optische glasvezelversterker voor de O-band(1290–1340 nm). De experimentele techniek voor de productie van mono-mode pra-seodymium gedoteerde glasvezels gebaseerd op germanium gallium sulfide glazen meteen kerndiameter van minder dan 4 µm en verliezen door absorptie en verstrooiingvan minder dan 0,1 dB/m moet nog worden verbeterd.De ontwikkeling van een versterker met hoge versterkingsfactor en een hoog verzadi-gingsuitgangsvermogen is mogelijk door de beschikbaarheid van krachtige pomplasersmet een golflengte tussen 1010 en 1040 nm. Wanneer de versterkers gebaseerd opsulfide glasvezels beschikbaar komen, is de keuze om de versterker op basis van sul-fide glas of op basis van fluoride glas in te zetten sterk afhankelijk van de beoogdetoepassing.De versterker gebaseerd op sulfide glasvezels levert potentieel betere prestaties dande versterker gebaseerd op fluoride glasvezels, wanneer deze wordt toegepast als ver-mogensversterker (b.v. de versterking van analoge CATV signalen). In tegenstellingtot halfgeleider optische versterkers en Raman versterkers, is de PDFA geschikt voorde versterking van amplitude gemoduleerde signalen, omdat signaal vervorming door

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de verzadigde versterker (b.v. bitpatroon effecten) verwaarloosbaar zijn.Het uitgangssignaal van de verzadigde versterker gebaseerd op sulfide vezel is na-genoeg onafhankelijk van het ingangsvermogen. Dit is een gunstig effect voor detoepassing van de versterker als tussenversterker. De stabiliserende werking van deversterker op het signaalvermogen in een datatransmissiesysteem met meerdere tus-senversterkers is sterker voor versterkers gebaseerd op sulfide glazen dan voor verster-kers gebaseerd op fluoride glazen.Door de hoge versterkingsfactor voor laag vermogensignalen en een laag ruisgetal isde PDFA ook zeer geschikt voor toepassing als optische voorversterker bij een ontvan-ger. In deze toepassing zijn de prestaties van de sulfide en fluoride glasvezelversterkernagenoeg gelijk en is het verschil in efficientie van ondergeschikt belang.

Dankwoord

Het promotieonderzoek “Towards more efficient praseodymium doped fibre amplifiersfor the O-band” is uitgevoerd in samenwerking tussen de leerstoelen Electro-OpticalCommunications (faculteit Elektrotechniek) en Glastechnologie (faculteit Scheikun-dige Technologie) aan de Technische Universiteit Eindhoven en TNO-TPD afdelingGlastechnologie. Op deze interdisciplinaire samenwerking en het nu afgeronde werkkijk ik met pezier terug. Graag wil ik de collegas waarmee ik de afgelopen jaren hebsamengewerkt bedanken.In het bijzonder wil ik mijn beide promotoren hartelijk bedanken. Ten eerste prof.Djan Khoe, omdat hij mij in de gelegenheid heeft gesteld om binnen zijn groep hetpromotieonderzoek uit te voeren en het werk altijd met belangstelling volgde. Doorzijn goede contacten kon ik al snel beschikken over de experimentele PDFA. Ik wilprof. Ruud Beerkens bedanken voor zijn inhoudelijke inbreng en zijn grote persoonlij-ke betrokkenheid, met name bij de totstandkoming van dit proefschrift. De dagelijksebegeleiding was in goede handen van Huug de Waardt en Anne-Jans Faber. Van mijncopromotor Huug de Waardt heb ik zeer veel geleerd op het gebied van optische tele-communicatie. Ik wil hem bedanken voor de nuttige discussies en zijn enthousiasmewanneer ik mooie of verrassende resultaten met de experimentele PDFA behaalde.Anne-Jans Faber wil ik bedanken voor het initieren van de contacten met prof. Khoedie tot dit promotieonderzoek hebben geleid en zijn suggesties met betrekking tot defysische eigenschappen van de chalcogenide glazen.Graag wil ik de professoren D. Lenstra, R.A.J. Janssen, H. Thienpont, A. Driesen enP.M. Koenraad bedanken voor hun bereidheid zitting te nemen in de promotiecom-missie.Verder gaat mijn dank uit naar Peter Kik, Christof Strohhofer, Hans Mertens en prof.A. Polman van FOM-instituut AMOLF voor de gastvrijheid en hulp bij de bepalingvan de fotoluminescentie eigenschappen van mijn samples.I am greatly acknowledged to Dr. Izawa of NTT Electronics Corp. for providingdetailed information about the optical properties of the praseodymium doped fibremodules.Vele collega’s om mij heen, bij zowel de TUE als TNO-TPD, hebben mede bijge-dragen aan de resultaten van dit onderzoek. Ik wil Tom van der Heijden en GerardHaagh bedanken voor hun behulpzaamheid bij programmeren van de beide modellenin Fortran en Sepran. Verder wil ik Peter van Nijnatten bedanken voor de nuttigediscussies over de optische eigenschappen van gedoteerde glazen. Daarnaast wil ik

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Peter van Bennekom en Frans Huyskens bedanken voor de technische ondersteuningbij de lastige metingen aan de praseodymium gedoteerde vezels.Verder gaat mijn dank uit naar mijn overige collega’s van de glastechnologie, Electro-Optical Communications en van TNO-TPD voor de prettige samenwerking, in hetbijzonder Yingchao Yan en Rik Koch voor de stimulerende discussies over de eigen-schappen van chalcogenide glazen aan het begin van mijn promotie werk en Marcovan Kersbergen bij het oplossen van vele praktische problemen.Daarnaast wil ik mijn afstudeerders en stagiaires bedanken voor hun inzet. SteffenUhlig heeft de basis gelegd voor de volautomatische verwerking van de meetgege-vens uit de optische spectrum analyser. Jacco van der Suis is verantwoordelijk voorhet aansturen van de experimentele PDFA. Hierdoor kon ik vele metingen efficientuitvoeren. Mathijs Vermeulen heeft zich gericht op het etsen van de sulfide glazen.Serge Timmermans heeft geholpen bij het opzetten van verkennende proeven op deglasvezeltrekmachine. Pim Havermans was betrokken bij de aanpassingen m.b.t. hetvezeltrekken vanuit preforms aan het glasvezelmodel, waarmee ik later het werkgebiedvoor het trekken van sulfide vezels heb kunnen vaststellen.Graag wil ik Wieke Boon en Renard Chaigneau bedanken voor de ruimte die zij mijhebben gegeven om dit werk, naast een volledige baan bij Corus RD&T, af te ronden.Met veel plezier kijk ik terug op de tijd die ik met Oscar Verheijen en Roland Groe-nen op de laboratoria van TNO heb door gebracht. Oscar, bedankt voor de fijnesamenwerking, leuke discussies en de nuttige adviezen. Roland, bedankt voor de veleontspannende uurtjes onder het genot van een hapje en drankje. Zoals je ziet heb ikzelfs een aanbeveling uit jouw boekje kunnen gebruiken.Veel goede herinneringen heb ik ook aan mijn kamergenoten John Kennis en ReneJonker. Onder het genot van een bak verse koffie was er altijd voldoende tijd om velenuttige en soms erg leuke onderwerpen te bespreken. John, bedankt dat je de werk-zaamheden in mijn laserlab zo goed in kaart hebt gebracht. Rene, bedankt voor devele nuttige discussies over optische versterkers en het wel en wee van de Xiphophorushelleri. Ik heb zeer goede herinneringen overgehouden aan de bijzondere metingen diewij samen hebben uitgevoerd, met name aan die met de recirculating loop.Oscar, Rene en Roland, ik wil jullie in het bijzonder bedanken voor de goede raad diejullie mij hebben gegeven en voor het minutieus doorlezen van het manuscript.Daarnaast heb ik veel steun gehad van mijn vrienden en familie, die mijn werkzaam-heden met veel interesse volgden en altijd met raad en daad voor mij klaar stonden.In het bijzonder wil ik mijn zus Nicoline, haar man Marcel en natuurlijk Robin be-danken voor de steun, maar zeker ook voor de nodige afleiding die zij mij de afgelopenperiode hebben gegeven. Robin, nu kun je eindelijk eens komen logeren om te spelenop het strand van IJmuiden.Tenslotte wil ik mijn ouders bedanken voor hun begrip, geduld en steun gedurendede tijd die ik aan het promotieonderzoek besteed heb. Zij hebben ervoor gezorgd datik dit promotieonderzoek kon uitvoeren.

Ronald SchimmelIJmuiden, September 2006

Curriculum Vitae

Ronald Schimmel werd op 30 juni 1973 geboren te Veldhoven. Hij behaalde in 1990het HAVO-diploma aan het Eindhovens Protestants Lyceum. Daarna begon hij metde studie Chemische Technologie aan de Hogeschool Eindhoven. Deze opleiding rond-de hij in 1994 af. Van 1994 tot 1997 volgde hij de verkorte opleiding ScheikundigeTechnologie aan de Technische Universiteit Eindhoven (TUE). Aansluitend verrichttehij een promotieonderzoek onder leiding van prof.ir. G.D. Khoe en prof.dr.ir. R.G.C.Beerkens. Dit onderzoek vond plaats in de vakgroep Electro-Optical Communications(faculteit Elektrotechniek, TUE) in nauwe samenwerking met de vakgroep Glastech-nologie (faculteit Scheikundige Technologie, TUE) en TNO-TPD afdeling Glastech-nologie. De resultaten van dit onderzoek zijn beschreven in dit proefschrift.Vanaf 2001 werkte hij gedurende twee jaar als toegevoegd onderzoeker bij de vak-groep Electro-Optical Communications aan glasvezelversterkers. Sinds januari 2003is hij werkzaam als researcher bij de afdeling Ironmaking van Corus Research, Devel-opment & Technology met als voornaamste werkgebieden sinteren en pelletiseren vanijzerertsen.

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