Coupled Semiconductor Optical Amplifier Network for ...

Abdul Rahim

Reservoir ComputingCoupled Semiconductor Optical Amplifier Network for

Academiejaar 2007-2008Faculteit IngenieurswetenschappenVoorzitter: prof. dr. ir. Paul LagasseVakgroep Informatietechnologie

Scriptie ingediend tot het behalen van de academische graad van

Begeleider: Jonathan SchrauwenPromotor: prof. dr. ir. Dries Van Thourhout

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Permission for usage

The author gives the permission to make this work available for consultation and to copy part of the work

for personal use. Any other use is bound to the restriction of copyright legislation, in particular regarding

the obligation to specify the source when using results of this work.

Abdul Rahim

5th June 2008

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Acknowledgements

I would like to thank all the people from the INTEC department of Gent University for their welcome to

this department and their support in my work during my 10 month stay in Belgium. I am thankful to

consortium of Erasmus Mundus Master Program in Photonics, which gave me the opportunity to study in

some of the best European institutes.

I would like to express my gratitude to my promoter Dries Van Thourhout and my supervisor Jonathan

Schrauwen. I am thankful to Steven Verstuyft for his advice, help and contribution in fabrication

processes. I am also very thankful to Liesbet Van Landschoot for her patience and help during FIB

processing. I am especially thankful to Dr. Liu Liu and Shankar Kumar Selvaraja for guiding and helping

me in troubled times. I am thankful to contributions and suggestions from Dirk Taillaert, Joost Brouckaert,

Lieven Vanholme and Pieter Dumon and to all the people in photonics department.

I am thankful for the good company provided by my fellow students of EMMP, Paul Bradt, Diedrik

Vermeulen, Alvaro Martinez Mingo, Juan Antonio Lloret and Gunay Yurtsever.

I am thankful to my friends who always helped and motivated me. I would also like to thank my teachers

throughout my academic career for delivering their best to me. Very special thanks to my parents and

sisters for their support and encouragement through out my life. Without their support it would have been

impossible to achieve all the success I have achieved through out my life.

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Coupled Semiconductor Optical Amplifier Network for Reservoir Computing

By

Abdul Rahim

Final work handed in for obtaining the degree of Masters in Electrical Engineering with emphasis on

Photonics.

Academic Year: 2007-208

Universiteit Gent

Faculty of Engineering

Promotor: prof. dr. ir. Dries Van Thourhout

Abstract

This thesis proposes a coupled semiconductor optical amplifier network, which can be used as an optical

reservoir for a reservoir computing system. The optical reservoir can be power efficient and can provide

more computational power to solve extremely complex temporal problems. Two types of optical

reservoirs are proposed. In one type, the node can either act as an amplifier or as a detector. In the other

type, each node consists of an amplifier and a photo-detector.

This report first explains some fundamental concepts about reservoir computing and a schematic for a

photonic reservoir is proposed. The photonic components that can be useful for the implementation of a

photonic reservoir are discussed. In this work, the semiconductor optical amplifiers are coupled to each

other by using cross-mirrors, which are simulated by using OMNISIM. The dimensions of the cross-

mirrors to split the optical signal into three parts are found. FIB processing is used for the fabrication of

such mirrors. The effect of FIB processing and the losses introduced by it are also discussed in this work.

Measurements to determine the optical coupling between the nodes are carried out and the measurement

results are also part of this report. At the end, few suggestions are made to improve the performance of the

system.

Keywords:

Reservoir Computing, Optical Reservoir, Cross-mirrors, FIB Processing

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Coupled Semiconductor Optical Amplifier Network

for Reservoir Computing Abdul Rahim

Supervisor: Jonathan Schrauwen

Promotor: prof. dr. ir. Dries Van Thourhout

Abstract— The networks of semiconductor optical amplifiers (SOAs) coupled by the semi-transparent mirrors are studied. Such a network can be used as an optical reservoir in a reservoir computing system. Two types of optical reservoirs are proposed. In one type, the node can either act as an amplifier or as a detector. In the other type, each node consists of an amplifier and a photo-detector. This article discusses about the simulation and fabrication of the semi-transparent mirrors. The measurements to determine the optical coupling among the nodes are also part of this article. Keywords— Reservoir Computing, Optical Reservoir, Semiconductor Optical Amplifiers, Semi-transparent mirrors Introduction

The reservoir computing provides faster convergence and computationally efficient mechanism to solve temporal and extremely complex classification and recognition problems. It consists of a reservoir and a readout part. The reservoir is a random and untrained Recurrent Neural Network (RNN) having fixed weights while the readout part is trained and static, which makes the reservoir computing system easy to train. The lack of hardware implementation of the reservoir computing systems motivates for the hardware implementation by using photonic components. The photonic implementation is thought to be much faster, energy efficient and computationally powerful. Photonic components like Lasers, Optical Amplifiers and Photonic Crystals can be useful for the photonic implementation of a reservoir. Due to the

similarities in the transfer function of an optical amplifier and the artificial neuron, which acts as a node of a reservoir, a coupled network of SOAs is proposed as a photonic reservoir. The coupling between the SOAs is achieved by using semi-transparent mirrors.

Figure: 2X2 reservoir coupled by cross mirrors

Simulation of semi-transparent Mirrors The semi-transparent mirrors act as an inter-connection between the optical nodes of the reservoir and are made up of air slits of certain width. Cross-mirrors are used as

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semi-transparent mirrors. 2D simulations using FDTD tool are used to determine the dimensions of the cross mirrors.

Figure: Power splitting by cross-mirror

A large fraction of input signal is transmitted through the cross mirror with thin slits and a small fraction is reflected in the upward, downward and backward dirctions. As the thickness of the slits of the cross mirrors increases, the fraction of transmitted light decreases and the reflection in the upward, downward and backward directions increases. The signal reflected in the upward and downward direcions is the same because of symmetry of the structure. The four powers (power upward, downward, forward and backward) are equal for a cross mirror with slits having width of 109nm.The sum of the four normalized powers is less than unity. The light may spread rapidly in the air slits causing power loss because of divergence, which increases with the increase in the width of the slits. Consequently, the sum of the four powers is less than one. Fabrication of Cross Mirrors FIB process is used to etch the cross mirrors. In order to etch the active region a depth of approximately 2.33µm is needed, which is difficult to achieve with Si-etch program. 10pA of beam current and enhance-etch mechanism, in which iodine gas is flows

over the sample is used to etch the cross mirrors.

Figure: Cross Mirror etched by FIB Process

Measurements Measurements to determine the effect of FIB processing by etching the facet of the laser have shown that the reflectivity of the facet of the laser decrease by using FIB processing. The effect of change in the reflectivity of the facet is more pronounced for Si-etch mechanism than the enhance-gas etch mechanism. Measurements have shown that the optical signal is coupled in the top SOA and bottom SOA after reflection from the cross-mirror. Not enough transmission of optical signal is found in the forward direction, which may be due to much wider air gap at the point of intersection of the two slits of the cross-mirror. Severe leakage current was found in the reservoir in which each node can either act as an SOA or as a detector. This problem was less evident in the reservoir in which each node consists of an amplifier and a detector. Conclusion Cross mirrors can be used to couple optical signal among the nodes of the reservoir. Some other mirror configurations and improvements in the fabrication process can improve the performance of the system.

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Table of Contents 1 ..................................................................................................................................................................... 1

1.1. Introduction .................................................................................................................................... 1

1.2. Fundamentals of Reservoir Computing ......................................................................................... 1

1.2.1. Artificial Neural Networks and Artificial Neurons .................................................................... 1

1.2.2. Feed Forward Neural Networks (FFNN) ................................................................................... 3

1.2.3. Recurrent Neural Networks (RNN) ........................................................................................... 3

1.2.4. Motivation for Reservoir Computing ......................................................................................... 4

1.2.5. Principle of Reservoir Computing ............................................................................................. 4

1.2.6. Reservoir Creation, Training and Dynamics.............................................................................. 5

1.2.7. Applications ............................................................................................................................... 6

1.3. Reservoir Computing and Photonics ............................................................................................. 7

1.4. System Level Architecture of Photonic Reservoir Computing System ......................................... 7

1.5. Conclusion ..................................................................................................................................... 8

1.6. References ...................................................................................................................................... 8

2 ................................................................................................................................................................... 10

2.1. Proposed Photonic Reservoir Implementation ............................................................................. 10

2.2. Optical Nodes for Photonic Reservoir ......................................................................................... 10

2.2.1. Semiconductor Optical Amplifier ............................................................................................ 11

2.2.2. Critical Parameters of an SOA ................................................................................................. 13

2.2.3. Design of the SOA ................................................................................................................... 14

2.3. Connection between Optical Nodes ............................................................................................. 15

2.3.1. Semitransparent Mirrors .......................................................................................................... 15

2.3.2. Technology used for semitransparent mirror fabrication ......................................................... 17

2.3.2.1. Principle ............................................................................................................................... 17

2.3.2.2. Effects and Limitations of FIB Processing .......................................................................... 18

2.4. Structure of Photonic Reservoir ................................................................................................... 19

2.5. Conclusion ................................................................................................................................... 20

2.6. References .................................................................................................................................... 20

3 ................................................................................................................................................................... 21

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3.1. Semi-transparent mirrors ............................................................................................................. 21

3.2. 2D simulation of mirrors using FIMMWAVE and FIMMPROP ................................................ 22

3.3. Vertical and angled mirror simulation in CAMFR ...................................................................... 27

3.4. Mirror simulations in OMINSIM ................................................................................................. 31

3.5. Conclusion ................................................................................................................................... 36

3.6. References .................................................................................................................................... 36

4 ................................................................................................................................................................... 37

4.1. Process Flow for the Fabrication of Photonic Reservoir ............................................................. 37

4.2. Description of the Mask ............................................................................................................... 37

4.3. Fabrication Process ...................................................................................................................... 40

4.3.1. Fabrication of Ridge Waveguides and Metal Contacts ............................................................ 40

4.3.2. Fabrication of Semitransparent Mirrors ................................................................................... 43

4.4. Improved Photonic Reservoir ...................................................................................................... 45

4.5. Conclusion ................................................................................................................................... 47

5 ................................................................................................................................................................... 48

5.1. Quantifying the loss introduced by the FIB processing ............................................................... 48

5.2. Measurements to check optical connection between SOAs ......................................................... 50

5.2.1. Coupling from a 450 air slit ...................................................................................................... 52

5.2.2. Coupling by a cross-mirror ...................................................................................................... 54

5.3. Conclusion ................................................................................................................................... 58

6 ................................................................................................................................................................... 59

Appendix A .................................................................................................................................................. 60

A.1. Relation between laser threshold current and losses .................................................................... 60

Appendix B .................................................................................................................................................. 62

B.I. Simulation Code for Angled Slit in CAMFR .............................................................................. 62

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List of Figures Figure 1—1: Mathematical Model of Artificial Neuron ................................................................................ 2

Figure 1—2: Network of 2 Neurons .............................................................................................................. 2

Figure 1—3: Single Layer (a) and Multi-Layer (b) FFNN ............................................................................ 3

Figure 1—4: Simple RNN .............................................................................................................................. 3

Figure 1—5: Structure of Reservoir Computing System ............................................................................... 5

Figure 1—6: Photonic Reservoir Computing System .................................................................................... 8

Figure 2—1: tanh Sigmoid Function ........................................................................................................... 11

Figure 2—2: Schematic representation of an SOA ...................................................................................... 12

Figure 2—3: Types of SOA .......................................................................................................................... 12

Figure 2—4: Cross-Sectional view of ridge waveguide semiconductor optical amplifier .......................... 14

Figure 2—5: Layer structure of SOA and MQW ......................................................................................... 15

Figure 2—6: Semitransparent cross-mirrors .............................................................................................. 16

Figure 2—7: Principle of FIB Milling [3] ................................................................................................... 17

Figure 2—8: Effects of FIB processing [4] ................................................................................................. 19

Figure 2—9: Layout of the Photonic Reservoir ........................................................................................... 19

Figure 3—1: Mirrors with vertical and angled slits .................................................................................... 21

Figure 3—2: 2D Cross Section of the waveguide ........................................................................................ 23

Figure 3—4: Schematic of FIMMPROP device .......................................................................................... 24

Figure 3—5: Simulation result for FIMMPROP device with simple joint .................................................. 25

Figure 3—7: Simulation result for modified FIMMPROP Device .............................................................. 26

Figure 3—10: Structure with vertical slit in CAMFR.................................................................................. 28

Figure 3—11: Interference in the air slit ..................................................................................................... 28

Figure 3—13: CMFR result for vertical slit ................................................................................................ 29

Figure 3—14: Comparison of CAMFR and FIMMWAVE result for vertical slit ........................................ 30

Figure 3—15: Transmission through angled slit in CAMFR ...................................................................... 30

Figure 3—16: CMFR structure for angled slit simulation .......................................................................... 31

Figure 3—17: Simulation plane of OMNISIM ............................................................................................. 32

Figure 3—18: Simulation result of vertical slit in OMNISIM ..................................................................... 32

Figure 3—19: Angled Slit in OMNISIM ...................................................................................................... 33

Figure 3—20: Transmission through an angled slit .................................................................................... 33

Figure 3—21: Comparison of OMNISIM and CAMFR results for an angled slit ....................................... 34

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Figure 3—22: Cross-mirror structure for simulation in OMNISIM ............................................................ 35

Figure 3—23: Plot of power splitting by cross-mirror ................................................................................ 36

Figure 4—1: Process Flow .......................................................................................................................... 37

Figure 4—2: Ridge Mask ............................................................................................................................. 38

Figure 4—3: Metal Mask ............................................................................................................................. 39

Figure 4—4: Schematic of semi-transparent mirrors on a 2X2 reservoir ................................................... 39

Figure 4—5: Metal Plating Mask ................................................................................................................ 40

Figure 4—6: Ridge waveguide processing .................................................................................................. 41

Figure 4—7: Processing to make metal contacts ........................................................................................ 42

Figure 4—8: 2X2 Reservoir ......................................................................................................................... 43

Figure 4—9: Slit etched by Si-Etch Program .............................................................................................. 44

Figure 4—10: Slit etched by Enhanced Etch Mechanism ............................................................................ 44

Figure 4—11: Cross Mirror Fabricated by FIB .......................................................................................... 45

Figure 4—13: Detector Based Photonic Reservoir ..................................................................................... 47

Figure 5—1: Effect of FIB processing on the laser facet ............................................................................ 48

Figure 5—2: Effect of enhanced gas etching on laser facet ........................................................................ 49

Figure 5—3: Losses due to absorption layer ............................................................................................... 49

Figure 5—4: Effect of polymide heating on threshold of laser.................................................................... 50

Figure 5—5: Leakage Current through SOAs ............................................................................................. 51

Figure 5—6: Conduction current ................................................................................................................ 51

Figure 5—7: Equivalent Electrical Model .................................................................................................. 51

Figure 5—8: Optical Coupling in 45 degree Slit ......................................................................................... 52

Figure 5—9: Modified result of coupling by 45 degree slit ......................................................................... 53

Figure 5—10: Equivalent Model ................................................................................................................. 53

Figure 5—11: Measurement Schematic for cross mirror ............................................................................ 54

Figure 5—12: Optical coupling in the top arm ........................................................................................... 54

Figure 5—13: Optical coupling in the bottom arm ..................................................................................... 55

Figure 5—14: Behavior of top arm SOA as a detector................................................................................ 55

Figure 5—15: Behavior of bottom arm SOA as a detector.......................................................................... 56

Figure 5—16: Leakage current ................................................................................................................... 56

Figure 5—17: Coupling in the right arm ..................................................................................................... 57

Figure 5—18: Dimensions of Cross Mirror .................................................................................. 57

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Abbreviations and Acronyms

Abbreviations Acronyms

ANN Artificial Neural Network

RNN Recurrent Neural Network

ESN Echo State Network

LSM Liquid State Machine

BPDC Back Propagation De-correlation

FFNN Feed Forward Neural Network

SOA Semiconductor Optical Amplifier

TW SOA Travelling wave SOA

MQW Multiple Quantum Well

TE Transverse Electric

TM Transverse Magnetic

FIB Focused Ion Beam

SEM Scanning Electron Microscope

LMIS Liquid Metal Ion Source

Ga Gallium

GUI Graphical User Interface

PML Perfectly Matched Layer

PEC Perfect Electric Conductor

DBPR Detector Based Photonic Reservoir

InP Indium Phosphide

BCB Benzocyclobutene

Au Gold

Ti Titanium

FDTD Finite Difference Time Domain

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1 Reservoir Computing and Photonics

1.1. Introduction

Like a neural network, reservoir computing is a computation system. This system is used to solve

extremely complex classification and recognition problems in an efficient way. The reservoir computing

system has been implemented in the software and it lacks any hardware implementation so far.

The chapter starts with a basic introduction of neural networks, the principle of the reservoir computing

system and its capabilities. The arguments for the need of the hardware implementation using photonics

are also part of this chapter. A system level architecture of the photonic implementation is also mentioned

at the end of this chapter.

1.2. Fundamentals of Reservoir Computing

1.2.1. Artificial Neural Networks and Artificial Neurons

Artificial Neural Networks (ANN) imitate the processes of a human brain. They are made from artificial

neurons. These artificial neurons can be trained to solve complex problems like the classification and the

recognition problems. Many neurons can carry out their computations in parallel.

Like Biological Neural Network, ANN is an interconnection of individual artificial neurons. Every

connection has a certain weight and this weight can be adapted during the learning process. The way the

neurons are connected with each other determines the architecture or the topology of the ANN [1, 2]. Each

neuron (node) performs a simple job. Some nodes receive input signals from the external world. These

nodes are called the input nodes. The output obtained from the input nodes can feed many other neurons.

The neurons that give the output or the response of the network are called the output nodes. Usually, a

neural network consists of input, output and working (hidden) neurons.

Consider an artificial neuron that consists of n inputs. The weighted sums of the inputs determine the

excitation level ζ of the neuron.

∑ == n

ni ii xwξ

Here, wi

and xi correspond to the ith weight and input of the neuron. When ζ reaches a certain threshold

level h, it produces the output y of the neuron. The output y depicts the state of the neuron. The

mathematical formulation of the neuron is given by the following expression.

1)( == ξσy if 1≥ξ

Chapter 1 Reservoir Computing and Photonics

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0)( == ξσy if 0<ξ

σ is called the activation function that shows the non-linear growth of the output y when the threshold h is

reached. Figure 1 shows a mathematical model of an artificial neuron.

Figure 1—1: Mathematical Model of Artificial Neuron

The neuron's states, weights and the connections among the neurons change with time. This evolution of

an ANN with time makes them dynamic in nature. Due to the dynamic nature of the ANN, different

models have evolved. The ANN is specified by defining the dynamics of the ANN, which includes

computational dynamics, architectural dynamics and adaptive dynamics [1, 2]. Computational,

architectural and adaptive dynamics correspond to the state, topology and configuration.

Figure 1—2 shows how two neurons can be connected. We can connect any number of neurons in any

way. The connections between neurons define the topology of the neural network. Two famous topologies

are the recurrent (cyclic) neural network topology and the feed-forward (acyclic) network topology [1, 2

and 3].

Figure 1—2: Network of 2 Neurons


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1.2.2. Feed Forward Neural Networks (FFNN)

FFNNs do not contain any cycle and all paths lead in one direction. Figure 1—3 shows an example of a

FFNN. The neurons in the FFNN can be split into layers. These layers are arranged over each other to

form a multi-layer FFNN.

Figure 1—3: Single Layer (a) and Multi-Layer (b) FFNN A network with one input layer and one output layer and having no feedback connections is called a single

layer FFNN [1, 3]. If there are one or more hidden layers of neurons then a multi-layer FFNN is formed.

The connections among layers go from lower layers to the higher layers and the lower layer may skip

some of the higher layers and make a connection with some other higher layer.

1.2.3. Recurrent Neural Networks (RNN)

In recurrent network topology a group of neurons is connected into a ring. That is the reason why it is also

called cyclic neural network topology. In this topology the output of one neuron becomes the input to a

second neuron and the output of this neuron becomes the input of a third neuron and so on while the

output of the last neuron becomes the input of the first neuron. The simplest cycle is a feedback of the

neuron whose output serves simultaneously as its input. The maximum number of cycles is contained in

the so-called complete topology in which the output of each neuron represents the input for all neurons [1,

3]. An example of a general cyclic neural network is shown in figure 1—4.

Figure 1—4: Simple RNN


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1.2.4. Motivation for Reservoir Computing

The feed-forward neural networks have been employed extensively to solve problems which are

independent of time in the domain of machine learning. As mentioned above, FFNNs have connections

made only in one direction and as a result the information flows only in one direction. Consequently, they

do not have any feedback and are usually non-dynamic.

Many problems in the world are temporal. Weather predictions, adaptive filtering, noise reduction and

voice recognition are some examples of temporal problems. In comparison to feed-forward neural

networks, Recurrent Neural Networks (RNN) are dynamic, more complex and have feedback. RNNs are

considered to be very powerful for solving temporal machine learning problems. Although RNN has many

applications, it is not always feasible to use it due to its high computational trainings and slow

convergence [4]. Buonomano in 1995 and Laurenco in 1994 were the first scientists who investigated a

solution to these problems. The solution employed a RNN with fixed (random and untrained) topology

operating in correct dynamic regime and a separate trained output layer with linear readout function. Other

scientists have also come up with some other solutions. All these ideas are brought into a single research

stream that is referred as Reservoir Computing. These ideas constitute the three implementations (types) of

Reservoir Computing system namely:

1. Echo State Network (ESN)

2. Liquid State Machine (LSM)

3. Back Propagation and De-correlation (BPDC)

The intention of Reservoir Computing is to solve extremely complex classification tasks like recognition

of speech or images.

1.2.5. Principle of Reservoir Computing

A key difference between RNN and reservoir computing, however, is that the input in the reservoir

computing is not represented using static algorithmic rules, which ultimately end up in a steady state. This

steady state represents the solution of the classification problem. Rather, a Reservoir Computing system

converts its input into highly complex dynamic behavior. This behavior is then interpreted by a simple

memory-less readout function to get the solution of the classification problem (Figure1—5).


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Figure 1—5: Structure of Reservoir Computing System Reservoir computing system consists of a so called reservoir and a readout part. The reservoir is a RNN

and is constructed in a random fashion. The inputs are fed to the reservoir. The reservoir is not trained at

all but the so called readout part is. The structure of a Reservoir Computing system is shown in figure 1—

5. The readout function can employ any type of pattern classification or regression algorithm. The state of

the reservoir depends on the inputs to the reservoir and the readout part looks at the state of the reservoir

and computes the output of the system. The algorithm used by the readout part is not complex because

readout part is static. Since, it is a simple algorithm so it requires little time and less effort to train as

compared to the training time required by RNN, while the temporal processing capabilities of the RNN are

also preserved by the system. Hence, reservoir based neural networks can provide an efficient way of

analyzing dynamic patterns without requiring complex and computationally intensive training procedures

[5].

1.2.6. Reservoir Creation, Training and Dynamics

In all three types of reservoir computing systems named above, the reservoirs are random network of

neurons. The original concept of reservoir computing uses fixed random network of neurons. Recent

research has shown that instead of using RNNs FFNNs can also be used for the implementation of a

reservoir.

The output of the reservoir is fed as input to the read out part, which is trained to process the dynamic

reservoir states. A variety of statistical classification or regression techniques can be used as readout

function. A large number of training algorithms have been developed for FFNNs and RNNs [4]. The same

learning rules can be used by the reservoir computing systems [6]. The purpose of the training algorithms

is to adjust the weight and the bias of the neurons making the neural network. The correct adjustment of

the weight and bias of the neurons ensures correct output to be activated at the output part. In reservoir

computing systems the training techniques are implemented in the readout part that is a FFNN, which is

easy due to its non-dynamic nature.


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In general there are two broad categories of learning or training algorithms. One is the supervised learning

algorithms and the other is called the unsupervised learning algorithms [4]. In supervised learning

algorithms, data is sent at the input units. The output of the networks is compared with the expected output

pattern. The difference between the actual output and the expected output is used to adjust the weight and

bias of the network. The learning process is repeated until the network is considered to be trained

sufficiently. The training process is an attempt to reduce the error between the actual output and the

expected output. In order to train a network some defined set of training examples are fed to the output

part many times. The error function for the network is iteratively reduced by adjusting the weights of the

readout part by some amount determined by the value of the error function [4]. In reservoir computing

systems, the weight of the reservoir is kept fixed so the training of the reservoir computing system reduces

only to the training of the feed forward readout part. This is the reason that reservoir computing systems

have fast learning and convergence. In the case of unsupervised learning algorithms the readout part is

trained to respond to the features in the input data. This type of training is used in classifying systems.

The performance of a reservoir system is determined by the dynamics of the system and the readout part.

For this reason it is very important to determine the dynamics of the reservoir. The network dynamics is

affected by a large number of parameters such as the weight of the nodes, the connection topology, the

time constant associated with the response function, the number of processing elements, the system

dynamics etc [2, 4]. A large number of processing elements make the reservoir more dynamic [4].

1.2.7. Applications

Reservoir computing is a very suitable candidate to solve temporal classification and prediction tasks. The

good thing about reservoir computing is that it provides a very good performance because once it is

trained there is no need to set any reservoir parameter. Reservoir computing systems have been used in a

large number of engineering applications and are providing state of the art performance. Below is a brief

collection of applications mentioned in the literature.

Reservoir computing can be used for dynamic pattern recognition and classification [2]. ESNs are also

used for the complex system modeling [7]. A large scale ESN with 3000 internal neurons is used to model

the pH-neutralization process, which is an example of complex system modeling. pH-neutralization is a

process of neutralization of strong acid with a strong base in a continuously stirred tank reactor. The

results have shown that ESN has better performance as compared to RNN [7]. Motor speed control has

been accomplished by using ESN and the results are published in [8, 10]. It has been shown by simulation

results in [8] that ESN can be trained orders of magnitude faster and better than RNNs. ESNs have also

been employed for noise-robust automatic speech recognition [9]. ESNs have also been used for Brain

Machine Interface (BMI). ESN provides better generalization of BMI model and simplified and efficient


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learning [11, 10]. ESNs are also used to develop macro-models to assess signal integrity effects in high

speed digital systems [12]. In robotics, LSMs and ESNs have been used to control a robot arm, to model

an existing robot controller, and to perform object tracking and motion prediction [1]. ESN are also in

used in underwater robot applications [13]. Reservoir computing has also been used in chaotic time series

prediction and isolated word recognition [5, 14].

1.3. Reservoir Computing and Photonics

Reservoir computing has been implemented in the software but the hardware implementation is still

missing. Software computing has made a lot of progress in the last few decades. It has evolved as a field

with strong scientific methodology and mathematical foundations. Photonics, the science of harnessing of

light, is also booming and 21st century is attributed to the century of photonics. Due to rich dynamics and

enthralling physics, Photonics has the capability to solve problems where today’s conventional technology

has reached to its limit. Photonics and Information Processing have met in the past to enable processing

and transport of data. Photonic implementation of reservoir computing can be considered as a new

encounter of photonics and information processing. The hardware implementation of reservoir computing

is essential due to the high computation cost of the large neural networks on sequential instruction

machines [3]. By a hardware implementation, each neuron can be computed in parallel. The photonic

implementation of reservoir computing system can provide a number of advantages. Firstly, in photonics

the advantages of a large bandwidth and non-linear effects can lead to computationally efficient reservoir

computing systems. Secondly, as compared to software based implementation of reservoir computing

system, photonic implementation can be much more energy efficient and faster

It is worth mentioning that it is not an essential condition to have a network of neurons for reservoir

computing; a more important condition for a reservoir is that the input signal should not fade away

quickly, rather it should disappear slowly.

1.4. System Level Architecture of Photonic Reservoir Computing System

A block level architecture of a photonic reservoir computing system is shown in figure 1—6. Like the

software based reservoir computing system, the photonic implementation has a reservoir and a readout

part. The system shown in figure 1—6 consist of a photonic reservoir and the software based readout part.

The photonic reservoir is made up of optical nodes. The photonic components like optical amplifiers,

lasers or photonic crystals can serve as the optical nodes. These optical nodes are connected to each other

to form a network. The output of the optical node is fed to the software based readout part. Generally the

computing power of the reservoir computing system lies in the reservoir so the focus of this research is on

the photonic implementation of reservoir.


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Figure 1—6: Photonic Reservoir Computing System

1.5. Conclusion

The reservoir computing provides faster convergence and computationally efficient mechanism to solve

temporal and extremely complex classification and recognition problems. It consists of a reservoir and a

readout part. The reservoir computing systems exists in three forms called LSM, ESN and BPDC. The

reservoir is a random and untrained RNN having fixed weights while the readout part is trained and static,

which makes the reservoir computing system easy to train. The lack of hardware implementation of the

reservoir computing systems motivates for the photonic implementation by utilizing the dynamically rich

photonic components like SOAs, Lasers or Photonics Crystals.

1.6. References

[1] B. Kröse and Pattrick van der Smagt; “An introduction to Neural Networks”; Eighth edition,

November 1996

[2] J.Sima; “Introduction to Neural Networks”; Technical report No. V-755, Institute of

Computer Science, Academy of Sciences of the Czech Republic

[3] Lectures by Dr. John A. Bullinaria; “Introduction to Neural Networks”;

www.cs.bham.ac.uk/~jxp/inn.html

[4] Master Thesis by Jeff Riley, “An Evolutionary Approach to Training Feed-Forward and Recurrent

Neural Networks”; Department of Computer Science Royal Melbourne Institute of Technology

Australia.

[5] B. Noris, M. Nobile, L. Piccinini, M. Berti,E. Mani, M. Molteni, F. Keller, D. Campolo; A. G.


9 | P a g e

Billard; “Gait Analysis of Autistic Children with Echo-State Networks"

[6] Ganesh K. Venayagamoorthy; “Online design of an echo state network based wide area monitor

for a multimachine power system Real-Time Power and Intelligent Systems”;Laboratory,

Department of Electrical and Computer Engineering, University of Missouri-Rolla.

[7] Zhidong Deng, Member, IEEE, and Yi Zhang; “Complex Systems Modeling Using Scale-Free

Highly-Clustered Echo State Network”; 2006 International Joint Conference on Neural Networks

July 16-21, 2006.

[8] Matthias Salmen and Paul G. Plöger; “Echo State Networks used for Motor Control”; FHG

Institute of Autonomous Intelligent Systems Schloss Birlinghoven Proceedings of the 2005 IEEE

International Conference on Robotics and Automation Barcelona, Spain, April 2005

[9] Mark D. Skowronski and John G. Harris; “Noise-Robust Automatic Speech Recognition Using a

Predictive Echo State Network”; IEEE Transactions on Audio, Speech, and Language processing,

vol. 15, no. 5, July 2007.

[10] Aysegul Gunduz, Mustafa C. Ozturk, Justin C. Sanchez, and Jose C. Principe; “Echo State

Networks for Motor Control of Human ECoG Neuroprosthetics”; Proceedings of the 3rd

International IEEE EMBS Conference on Neural Engineering Kohala Coast, Hawaii, USA, May

2-5, 2007.

[11] Yadunandana N. Rao, Sung-Phil Kim, Justin C. Sanchez, Deniz Erdogmus, Jose C. Principe, Joser

M. Carmena, Mikhail A. Lebedev, Miguel A. Nicolelis; “Learning Mappings in Brain Machine

Interfaces with Echo State Networks”; Computational NeuroEngineering lab, University of

Florida, FL 32611, Dept. of Neurobiology, Duke University.

[12] I. S. Stievano, C. Siviero, I. A. Maio, F. G. Canavero C. Duca Abruzzi; “Guaranteed Locally-

Stable Macromodels of Digital Devices via Echo State Networks”; 2006 IEEE Electrical

Performance of Electronic Packaging, 24, 10129 Torino, Italy.

[13] K. Ishii, van der Zant, V. Becanovic, P. Ploger; “Optimization of parameters of echo state

network and its application to underwater robot”; SICE 2004 Annual conference Volume 3, 4-6

Aug. 2004 Page(s):2800 - 2805

[14] Jianhui Xi; Zhiwei Shi; Min Han; “Analyzing the state space property of echo state networks for

chaotic system prediction”; Neural Networks, 2005. IJCNN '05,. Proceedings, IEEE International

Joint Conference

*Figures in this chapter are drawn by taking inspiration from literature

10 | P a g e

2 Photonic Reservoir

Different photonic components like Optical Amplifiers, Lasers or Photonic Crystals can be used for the

implementation of photonic reservoir. In this chapter, the choice of photonic component and its design for

the implementation of reservoir are addressed. Possible method to make a network of photonic

components connected to each other is also addressed in this chapter. The technology needed for the

implementation of the connection mechanism is briefly introduced in the last part of this chapter.

2.1. Proposed Photonic Reservoir Implementation

Since the 1990s there has been a lot of interest in the development of optical processing elements for

optical computing and neural networks [1]. These devices are expected to exploit the high parallelism

possible with the optical systems. The photonic recipe of a reservoir has the following major ingredients:

1. Optical Nodes

2. Connection between optical nodes

The Semiconductor Optical Amplifiers (SOAs) are used as optical nodes of the reservoir. To connect the

SOAs, semitransparent mirrors can be used, which can couple the output of one SOA (one optical node of

network) to the neighboring nodes.

For the fabrication of semi transparent mirrors, Focused Ion Beam (FIB) etching is used. FIB is a mask-

less and resist-less process, which has the ability to produce geometric shapes with nanometer scale

precision.

2.2. Optical Nodes for Photonic Reservoir

The transfer function of the neurons in a reservoir is usually sigmoid or spiking. The sigmoid function can

be approximated by the transfer function of an SOA in the region with positive values of the excitation

levels. Hence, we can use optical amplifiers as the nodes of a photonic reservoir. A plot of the tanh

sigmoid function is shown in figure 2—1.

Chapter 2 Photonic Reservoir

11 | P a g e

Figure 2—1: tanh Sigmoid Function

In figure 2—1, ζ is the excitation level and y is the output of the node. Apart from using SOAs as nodes of

the reservoir, lasers and photonic crystal cavities can also be used. The SOAs provide ease of modeling

and fabrication; while photonic crystal based nodes provide smaller size and more interesting dynamics.

2.2.1. Semiconductor Optical Amplifier

Like an electronic amplifier the SOA is a device used to amplify the optical signal under suitable

operating conditions. The gain in an SOA is generated by stimulated emission in the active region (gain

medium). To confine the signal in the active region, a waveguide is embedded. An external current source

is needed to enable the stimulated emission process. The current source pumps electrons into the active

region. If the injected current is sufficiently high then the electron population in the conduction band can

exceed the electron population in the valance band. This situation is called as population inversion. An

existing photon of suitable energy can stimulate an electron in the conduction band to return to the valence

band. The suitable energy needed for this process is called as the band gap energy given by the expression

below:

hvEEEg =−= 12

where E2 is the energy of the conduction band, E1 is the energy of the valence band, v is the frequency of

emitted photon, and h is the Plank’s constant. This process results in the emission of a second photon,

which is exactly identical (i-e, has the same frequency, phase, and direction of propagation) to the incident

photon. The newly emitted photon and the original photon leads to more stimulated emissions and the

process goes on. This process leads to optical gain. By suppressing the feedback due to reflection from the

end facets of the cavity, the power lost from the cavity becomes more than the gain. This results in

prevention of laser action and the device works as an optical amplifier. Hence, a laser can be made to

work as an SOA if the feedback from the optical cavity is suppressed and it is biased below laser

threshold. A schematic representation of an SOA is shown in figure 2—2.


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Figure 2—2: Schematic representation of an SOA

The feedback from end facets of the cavity can be suppressed by using an anti-reflective coating, tilted

stripe structures (also called angled facets) or a combination of both [5]. On the basis of the quality of

feedback suppression, SOAs can be divided into two types namely:

1. Fabry Perot SOA (FP SOA)

2. Travelling wave SOA (TW SOA)

In FP SOA, the feedback (reflection) from the end facets is significant and the signal passes through the

active region a number of times. On the other hand, in a TW SOA the reflections from the end facets are

very small and the signal takes a single pass through the amplifier and travels in the forward direction

only. Both types of SOAs are shown schematically in figure 2—3. The reflections from the end facets of

an SOA cause ripples in the gain spectrum due to interference.

Figure 2—3: Types of SOA


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2.2.2. Critical Parameters of an SOA

The SOAs are the basic building block of the reservoir. They have to obey certain performance parameters

so that they can act as optical nodes efficiently. A brief account such parameters is given below:

Gain and Bandwidth: The gain of an amplifier is the ratio of the power at the input facet to the power at

the output facet and is also called intrinsic gain. If the coupling losses at the input and output facets are

taken into account then one can define fiber-to-fiber gain. High gain is a desirable feature of an SOA. In

photonic reservoir, the gain of the SOAs should be enough to overcome the losses introduced by the

coupling mechanism of the SOAs. If the gain is less than the losses introduced then the information signal

will be damped in the SOAs and the effective number of the SOAs acting as the nodes of the reservoir will

be reduced. It is not an essential condition that there exists some net gain out of the network of the SOAs

acting as a reservoir. The gain of SOA depends on structure, material and operational parameters.

The bandwidth of an amplifier is the frequency range over which the signal gain is not less than half of its

peak value. It is desirable to have a high gain bandwidth for an SOA because it supports a wider frequency

range of input signals that can be amplified by the SOA.

Gain Saturation and Dynamic Effects: Gain saturation of an SOA is defined as the amplifier output

signal power at which the amplifier gain is reduced by 3dB from the small signal gain of the amplifier.

The decrease in the gain with the increase in the signal power is due to the depletion of carriers in the

active region. The fast gain dynamics of the SOA is due to the fast carrier recombination lifetime. Carrier

recombination lifetime is the average time for an electron to recombine with a hole in the valence band.

The dynamic effects increase with the increase in the modulated signal bandwidth. These are the rich

dynamic effects which provide an encouragement to use the SOAs in the implementation of the reservoir.

Polarization effects in an SOA: Polarization sensitivity is an undesired feature of an SOA and it should

not be present. As a result of the polarization sensitivity the gain of an SOA is different for Transverse

Electric (TE) and Transverse Magnetic (TM) polarization of the input signal. The waveguide structure, the

gain material and the nature of anti-reflection coatings can affect the polarization sensitivity of the SOA.

Noise: There exists a probability that conduction band electrons relax spontaneously to the valence band

by emitting the band gap energy in the form of a photon: spontaneous emission. These photons are emitted

in random directions and have no phase relationship among them. This process leads to the noise in an

SOA and results in the reduction of the electron population available for optical gain. Spontaneous

emission is difficult to avoid. Hence, it is difficult to make noiseless amplifier. However, noise in the

SOAs can be reduced by increasing the level of the population inversion.


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2.2.3. Design of the SOA

It is very important to select a proper structural design of an SOA because it has an impact on the

performance of an SOA. The structural design of an SOA can put emphasis on certain characteristics

needed for the implementation of the reservoir [6].Along with the structural design, the material used as

the active layer of an SOA is also very important because it can influence the gain spectrum of an SOA.

The SOA selected as the optical node of the reservoir has:

• Ridge waveguide structure

• Compressively strained Multiple Quantum Well (MQW) material as the active layer

The ridge waveguide structure is selected because it makes the SOA gain independent of the polarization.

The polarization sensitivity is due to the difference between the confinement factor of the TE and the TM

polarization. This difference can be reduced by optimizing the active waveguide structure and the

geometry of the ridge

The ridge waveguide structure consists of an active layer that is buried between the n-type substrate and

the p-type cladding. The structure confines the light to the active region and keeps it away from the etched

regions [6]. The structure of a ridge waveguide SOA with ridge width WR is shown schematically in

figure 2—4.

Figure 2—4: Cross-Sectional view of ridge waveguide semiconductor optical amplifier

Bulk or Quantum Well material can be used as an active layer in an SOA. 1% compressively strained

MQW material is selected as the active layer of the SOAs because it provides a superior gain bandwidth,

polarization insensitivity and saturation output power than the bulk material. [6].


15 | P a g e

The MQW structure is made up of a stack of thin active layers (well) separated by non-active layers

(barrier). The thickness of the well layer is less than the de-Broglie wavelength (λB=h/p, where p is the

momentum of the carriers) of the carriers. An outer cladding layer with a higher energy gap than the

MQW barrier layers is used to achieve a better confinement of the optical mode in the active region. This

outer cladding layer is called as Separate Confinement Hetro-structure (SCH). A lattice mismatch between

the well and the adjacent barrier layers can introduce strain in the quantum well. In a compressively

strained MQW material, the band edge of the heavy holes (holes with a higher effective mass) is more

close to the conduction band edge than the band edge of the light holes (holes with a lower effective

mass). This fact can be used to equalize the TE and the TM gains and to achieve the polarization

insensitivity. The layer structure of material used in the fabrication of the SOA for reservoir is shown in

figure 2—5.

Figure 2—5: Layer structure of SOA and MQW

2.3. Connection between Optical Nodes

2.3.1. Semitransparent Mirrors

As it has been aforementioned in the previous chapter, photonic reservoir has optical nodes, which are

connected to each other by some suitable mechanism. The connection between the optical nodes is meant

to couple the output power of one optical node with its neighboring nodes. The connection between the

optical nodes determines the weight function of the reservoir. To connect or couple the SOAs with each

other, the coupling mechanism should:

• Change the direction of propagation of signal


16 | P a g e

• Compact in size

• Introduce minimal losses

In optoelectronic research, a curved optical waveguides or the reflection from a mirror is used to change

the propagation direction and to interconnect the optoelectronic components. The curved waveguides have

low radiation loss [2] but they are large in size due to the large bending radius. On the other hand, the

mirrors are compact in size but they have large losses [3]. The losses in the mirrors are produced due to:

• Surface roughness of the facet of the etched mirror.

• Lack of facet verticality of the mirror can cause loss of the light by reflecting it into the substrate.

• Lateral displacement with respect to the SOA or Laser by deviating from a 450 angle.

An important characteristic of the connection mechanism is to couple the output power of the SOA to all

of its neighboring SOAs. This characteristic invokes the need of the semitransparent mirrors in which a

part of the signal is transmitted and a part of it is transmitted. In order to couple one SOA with its

neighboring SOAs, different semi-transparent mirror implementations are possible.

The implementation of the semitransparent mirrors consists of a pair of air slits that are etched at right

angle to each other but make an angle of 450 with respect to the facet of the SOAs or the lasers. The air

slits completely etch through the active layer of the SOAs. The slits should be narrow enough that the

exponentially decaying field is non-zero at the back interface of the slits. As a result of this some of the

signal is transmitted through the slits while rest of the signal is reflected. The fraction of the signal that is

transmitted or reflected depends on the width ‘W’ of the slits. Hence, these mirrors behave as the

semitransparent mirrors. Such mirrors are shown schematically in figure 2—6 and will be termed as cross-

mirrors in the report after words. The implementation shown in figure 2—6 can couple the amplified

signal of one SOA to three other SOAs labeled as SOA2, SOA3 and SOA4.

Figure 2—6: Semitransparent cross-mirrors


17 | P a g e

In another implementation, the semitransparent mirrors are fabricated by partially etching down the active

region. This implementation allows the lower portion of the guided wave to go straight through to one of

the output waveguides and reflects the upper portion into another waveguide. In this way the light is

divided into two parts. The etch depth determines the amount of the light that is reflected or transmitted.

To have a 50-50 division of the light, the etching should be half way down the active (guiding) region.

A fraction of light is reflected back by the semitransparent mirrors and is coupled back to the same SOA

(i-e; SOA1 in figure 2—6). When this “back-reflection” increases beyond a certain limit then the SOA will

start to behave as a laser. This laser action can lead to unpredictable behavior of the reservoir. Hence, it is

very important to have minimum “back-reflection”.

2.3.2. Technology used for semitransparent mirror fabrication

Focused Ion Beam (FIB) milling is used for the fabrication of semitransparent mirrors. This process is

carried out by the FIB instrument that is commercially introduced about a decade ago. FIB instrument has

precisely localized milling and deposition abilities. FIB processing can also be used for imaging.

2.3.2.1. Principle

FIB instrument is like a Scanning Electron Microscope (SEM). Instead of an electron beam, it uses a

Gallium (Ga) ion beam. The milling or removal of the material is done by the high current Ga ion beam.

The sputtering process takes place as a result of this ion beam. The ion beam is scanned over the sample to

mill away the material and to etch any shape. The principle of FIB process is schematically shown in

figure 2—8.

Figure 2—7: Principle of FIB Milling [3]


18 | P a g e

Some suitable gas is used during the milling of the sample in order to improve the etching process. This

helps in the removal of the reaction products and as a result the etching rate is increased [3, 4]. Gas

Assisted Etching (GAE) also improves the selectivity of the etching towards different materials.

2.3.2.2. Effects and Limitations of FIB Processing

Let there be an ion incident on the sample. The kinetic energy and the momentum of the ion are

transferred to the atoms and the electrons of the sample by elastic and inelastic interaction. The transfer of

energy from the impinging ion to the sample atom leads to a number of physical processes, which lead to

physical effects.

The inelastic interaction results in the transfer of the ion energy to the electrons in the sample. This causes

the ionization and the emission of the electrons & electromagnetic radiations. The emission of electrons

from the sample is used for the imaging of the sample and also results in the charging of the sample.

If the elastic energy transferred to the sample is above a certain threshold then it leads to the sputtering

process and the damage of the sample by displacing the sample atoms from their original locations. The

displaced atoms collide with the other atoms to displace them, hence resulting in the increase of the

number of displaced atoms. If the ion collides with an atom near the surface of the sample then this

collision causes the sputtering of the atom from the sample [4]. This sputtering is used for the milling of

the sample. The sputtering rate depends on the material, the crystal orientation, the extent of re-deposition,

and on the angle between the surface normal and the ion-beam direction. Larger incidence angle of the ion

beam leads to larger sputtering [4]. The sputtered material can re-deposit on the area being sputtered and

needs to be sputtered once again. Hence, re-deposition leads to the low sputtering yield. The re-deposition

also results in the change of the sputter profile. That is the reason why perfectly vertical sidewalls cannot

be etched with a FIB machine unless tilting the sample to avoid re-deposition. One consequence of using

FIB milling is the implantation of the Ga ions on the surface of the sample and sometimes these ions

diffuse into the sample. The atom displacement, the sputtering, the implantation of Ga ions, and the

electron emission as a result of the FIB processing on a sample are shown in figure 2—9.

A major affect and the drawback of the FIB process is the formation of an amorphous layer on the surface

of the sample. This formation of amorphous layer depends on the material of the sample. The heating of

the sample due to the ion bombardment is also caused by the FIB process because only a small part of the

kinetic energy of the ions is lost as the energetic particles or the radiations. The heating by the ion beam

depends on the power of ion beam, geometry of the sample and thermal conductivity of the sample. The

beam heating of sample can be reduced by placing the sample in good contact with heat sink.


19 | P a g e

Figure 2—8: Effects of FIB processing [4]

2.4. Structure of Photonic Reservoir

In a photonic reservoir, the SOAs act as the nodes of the reservoir and the semitransparent mirrors are

used to couple or connect these optical nodes. A blueprint of the photonic reservoir using SOAs and

semitransparent mirrors is shown in figure 2—10.The input signal is fed to one SOA, which is amplified

and coupled to the neighboring SOAs through the cross mirrors. The fraction of the signal coupled to the

neighboring SOAs determines the weight of the optical nodes. As mentioned earlier, one requirement for

the reservoir is the fading memory, which means that the input signal should not fade away quickly, rather

it should disappear slowly. This requirement is met in photonic reservoir by tweaking the electrical

biasing of the optical nodes.

Figure 2—9: Layout of the Photonic Reservoir


20 | P a g e

2.5. Conclusion

SOA connected by semitransparent mirrors are selected for the implementation of photonic reservoir. The

SOA has a ridge waveguide structure with MQW active material so that it can provide the necessary

features needed by the optical node of a reservoir. Cross-mirrors or partially etched active regions can act

as semitransparent mirrors. For the fabrication of semitransparent mirrors, FIB etching can be used.

2.6. References

[1] J. F. Heffernan, M. H. Moloney, and J. Hegarty, “All optical, high contrast absorptive modulation

in an asymmetric Fabry-Perot etalon” in Applied Physics Letters, Vol. 58, No. 25, 24 June 1991.

[2] L.H. Spiekman, Y.S. Oei, E.G. Metaal, F.H. Groen, P. Demeester, M.K. Smit, “Ultrasmall

waveguide bends: the corner mirrors off the future?” in IEE Proc.-Optoelectronics., Vol. 142, No. 1,

February 1995.

[3] P. Albrecht, W. Doldissen, U. Niggebriigge, H.P. Nolting, H. Schmid, “Waveguide mirror

components in InGaAsP/InP” Heinrich-Hertz-Institut fbr Nachrichtentechnik Berlin GmbH, Einsteinufer

37, D-1000 Berlin 10 , Federal Republic of Germany.

[3] Steve Reyntjens and Robert Puers, “A review of focused ion beam applications in microsystem

technology” in Journal of Micromechanics and Microengineering Vol.11, Page 287–300, 2001.

[4] C.A.Volkert and A.M. Minor, “Focused Ion Beam Microscopy and Micromachining” in MRS

Bulletin, Volume 32, May 2007.

[5] G.P Agarwal, “Fiber Optic Communication Systems, 3rd Edition, Wiley Series in Microwave and

Optical Engineering”.

[6] Michael J. Connelly, “Semiconductor Optical Amplifiers”, Kluwer Academic Publishers.

*Few figures in this chapter are drawn by taking inspiration from literature

21 | P a g e

3 Simulation of Semi-transparent mirrors

In this chapter the methods used for the simulation of semitransparent mirrors are discussed. As a first step

vertical slits are simulated by using FIMMAVE. CAMFR is used to simulate angled slits because it is

difficult to simulate angled slits in FIMMWAVE. CAMFR results can have some errors due to the

approximations made in structure used to simulate very narrow slits. Hence, OMNISIM simulations are

carried out. The results obtained for the simulations done using these three tools are part of this chapter.

3.1. Semi-transparent mirrors

The semi-transparent mirrors act as an inter-connection between the nodes of the reservoir and are made

up of air slits of certain width. If the air slit is narrow enough such that the exponentially decaying

evanescent field is non-zero at the back interface of the slit, then a fraction of the signal is transmitted and

some of it is reflected. The width of the air slit determines the fraction of the signal going straight through

the slit. Depending on the angle between the mirror and the axis of the waveguide (or SOA) the light can

be reflected backward or at a certain angle as depicted in figure 3—1, where ‘W’ corresponds to the width

of the slit.

Figure 3—1: Mirrors with vertical and angled slits

For the reservoir application, the cross mirror configuration described in section 2.3 has been used. As

shown in figure 2—6, the cross mirror consist of two air slits which are perpendicular to each other and

Chapter 3 Simulation of Semitransparent Mirrors

22 | P a g e

make an angle of 450 with the axis of the SOA. Depending on the width of the cross-mirrors, a fraction of

signal is transmitted in forward direction, a fraction is reflected in upper SOA and a fraction is reflected to

the lower SOA. Some part of the signal is also reflected in the backward direction. The amount of light

reflected, transmitted or backscattered for a certain width of the slit can be determined by simulations.

3.2. 2D simulation of mirrors using FIMMWAVE and FIMMPROP

FIMMWAVE is a simulation tool to design 2D and 3D waveguide structures and it is based around a fully

vectorial waveguide solver/mode solver [1]. The vector mode solver can locate almost any horizontal or

vertical mode of arbitrary or mixed polarization.

FIMMPROP is a propagation module integrated with the FIMMWAVE. It can be used to construct

complex structures and allows visualizing propagating fields in the structures. FIMMPROP uses

eigenmode expansion algorithm. In this algorithm the optical properties of the structure are characterized

by the local modes of the structure and the coupling matrix between the local modes.

A FIMMPROP device with two identical waveguides separated by an air gap is constructed. The air gap

will act as a mirror. The material used for the simulation of the waveguide is the same as used for the

fabrication of SOA. The detailed layer structure of the material used for the simulation of the waveguides

is shown in the table 3—1.

It is assumed that the material has no absorption. Hence, the excitation field in the waveguide propagates

without any attenuation. When the excitation field reaches the interface between the waveguide and the air

gap, fraction of it is reflected and a part of it is transmitted. The reflection takes place due to the difference

of index at the waveguide and the air gap interface.

For the sake of simplicity in simulation, the material stack shown in the table below is reduced to 3 layers

by ignoring the refractive index change in the quantum well structure. The simplified model of the above

material stack has been shown in table 3—2.

Thickness (nm) Layer Layer Type

180nm InGaAs Contact Layer

1350nm InP

75nm InP 75nm InP 90nm InGaAsP SCH layer 8nm InGaAsP QW (+1%) Active Layer (8X) 15nm InGaAsP Barrier Layer (7X) 90nm InGaAsP SCH Layer 90nm InP 1500nm InP InP Substrate

Table 3—1: Layer Structure of the material [3]


23 | P a g e

The infrared refractive index for InxGa1-xAsyP1-y is found by using the following approximate expression:

yn 46.01.3~ += [4]

By using the above expression, the infrared refractive index for In0.78Ga0.22As0.79P 0.21 is found to be 3.46.

InP has a refractive index of 3.1 in the infrared region [4]. The cross-sectional view of the ridge

waveguide constructed in FIMMWAVE is shown in figure 3—2.

Thickness Layer Type 1500nm InP Top Cladding 349nm InGaAsP Core 2400nm InP Bottom Cladding

Table 3—2: Simplified Layer Structure

Figure 3—2: 2D Cross Section of the waveguide

Simulation results in FIMMWAVE have shown that there are 3 guided modes for a ridge width of 3

microns. It has also been verified by the simulation that the number of guided modes decreases with the

decrease in the ridge width and vice versa. The simulation has shown that a waveguide with ridge width of

2 micron supports 2 guided modes while a waveguide with 5 micron ridge width supports 4 guided modes.

The modes which have a modal index greater than the lowest index in the waveguide are the guided

modes while the modes which have an index smaller than the lowest index in the waveguide are the

unguided modes.

For a 2D simulation, the 2D cross-section shown in figure 3—2 has been converted to a 1D cross section.

This is done by finding the effective indices of the three slices of 2D cross section. These effective indices

are then used to construct a 1D cross section as shown in figure 3—3.


24 | P a g e

Figure 3—3: 1D Cross-section of the waveguide

A FIMMPROP device is created by using the 1D structure separated by a free space joint. A schematic of

the FIMMPROP device is shown in the figure 3—4.

Figure 3—4: Schematic of FIMMPROP device

Figure 3—5 shows the transmission, reflection and loss for a normalized input at the left facet of the

FIMMPORP device. The amplitude of the input remains constant in the first section because the

absorption in this section is assumed to be zero. Once the input (excitation field) reaches the free space

joint, a part of it is reflected due to the index difference at the interface of the waveguide and the free

space joint. A part of input is transmitted while the rest is lost in the free space joint. The plot in figure

3—5 shows that 27% of excitation field at a wavelength of 1550nm is transmitted, 28% is reflected and

45% is lost in the free space joint. Simulation results for the waveguides connected with a free space joint

have shown that the amount of reflection is fixed at 28.29% and it does not change with the change in

length of the joint. In real world, the amount of reflection increases with the increase in the size of the slit.

In general, there is interference between the reflection off the first and the second facet of the waveguides

(see figure 3—4). The free space joint does not take the second reflection into account and therefore the

reflection does not change with the change in the slit size. The amount of reflection at the facet of the

waveguide can be found by the following expression:


25 | P a g e

2

1

1

+−=

n

nR where n is the refractive index of the medium. The refractive index of air is taken as 1. As

shown in figure 3—3, the refractive index of the core of the waveguide is 3.274 and by using above

expression a reflection of 28.3% has been found. Hence, the FIMMPROP device with free space joint

does not take multiple reflections into account

Figure 3—5: Simulation result for FIMMPROP device with simple joint

The FIMMPROP device has been modified to reduce the amount of power lost in the free space joint and

to take the multiple reflections into account. Figure 3—6 shows this modified device.

Figure 3—6: Modified FIMMPROP Device

In the modified structure, the waveguides are connected to each other by using a so called ‘air-

waveguide’. The structure of this air-waveguide is shown in figure 3—6. The air-waveguide serves the


26 | P a g e

purpose of an air slit. The simple joints shown in figure are the FIMMPROP joints to connect the two

waveguides. For this modified device with an air waveguide of 100nm length, the amount of transmitted

power has been increased to 74.5% for an excitation wavelength of 1550nm. The reflection becomes 25%

and the loss has become negligible (< 1%). The results are shown in figure 4—7.

Figure 3—7: Simulation result for modified FIMMPROP Device

The plot in figure 3—8 shows comparison of the amount of transmission through the air slit, which is

simulated by using free space joint and by using the air waveguide. The length of the air slit is swept from

53nm to 163nm. A significant difference in transmission is evident for the two different configurations of

the FIMMPROP device.

Figure 3—8: Free Space Joint based FIMMPROP device vs the modified FIMMPROP device


27 | P a g e

The FIMMPROP device with the air waveguide takes the multiple reflections into account. Increase in the

amount of reflection with the increase in the size of the air waveguide is shown in figure 3—9.

Figure 3—9: Reflection from modified FIMMPROP device

3.3. Vertical and angled mirror simulation in CAMFR

CAMFR is a Maxwell solver based on frequency domain eigenmode expansion technique and is used to

simulate optical devices. CAMFR can be used to find the scattering matrix of a structure. [5] Therefore, it

can be used to simulate the air slits, which act as the semi-transparent mirrors. The simulations in CAMFR

have been carried out at a wavelength of 1550nm. The excitation signal is TE polarized. The thickness of

the perfectly matched layer (PML) is set to -0.1. The PML layer assigns an imaginary component of -0.1j

to the thickness of the cladding, which implements the PML boundary condition. The PML can absorb

radiation travelling toward the walls of the waveguide without introducing any additional parasitic

reflections regardless of wavelength, incidence angle or polarization of the incident light [5]. A larger

value of PML leads to stronger absorption. Without PML, the Perfect Electric Conductor (PEC) walls

would reflect all the incoming radiation and would send it back to the structure and this can adulterate the

simulation results. The structure used to simulate a vertical slit is shown in figure 3—10.


28 | P a g e

Figure 3—10: Structure with vertical slit in CAMFR

An interference pattern is achieved when the width of the air slit is swept from zero. The pattern for a

sweep from zero to 3λ is shown in figure 3—12. This interference pattern is produced by multiple

reflections of the signal from the two facets of the structure and is shown schematically in figure 3—11.

The phase difference between the succeeding reflections is given by:

( )θλπδ cos2

2nw=

Where λ is the wavelength of the signal, n is the refractive index of the medium and w is the width of the

slit.

Figure 3—11: Interference in the air slit

Assuming that the reflection from surface 1 and surface 2 are equal then the transmission T is given by the

expression:

δcos21

)1(2

2

RR

RT

−+−=

Assuming θ=0 and w=λ, transmission becomes 1. Hence, the transmission is maximum when the width

of slit is integral multiple of wavelength λ. Similarly, the reflection is maximum when the width of the slit

is equal to quarter wavelength. This concept has been shown in figure 3—12. According to law of


29 | P a g e

conservation of energy, the sum of reflected power and transmitted power should be equal to 1. It is

evident from the plot shown in figure 3—12 that as the width of the slit increases, the sum of reflected and

transmitted power starts to go below 1. This may be because of power loss as a result of divergence in the

air slit.

Figure 3—12: Simulation result for Interference pattern in vertical slit

If w=0.103µm, θ=0, n=1, λ=1.55µm and R=0.283 then the transmitted power is calculated to be 0.736,

which is very close to the value found by the FIMMWAVE simulation of air slit using air waveguide

(Modified FIMMPROP device). Simulation in CAMFR also leads to the same approximate value.

CAMFR result for the reflected and transmitted power through a vertical slit is shown in figure 3—13.

This graph is nothing more than a zoomed in version of the interference pattern shown in figure 3—12.

Figure 3—13: CMFR result for vertical slit


30 | P a g e

A comparison of the transmitted and reflected power from a vertical slit determined by FIMMWAVE and

CAMFR is shown in figure 3—14.

Figure 3—14: Comparison of CAMFR and FIMMWAVE result for vertical slit

After simulation of the vertical slit, a slit at an angle of 450 is simulated by using CAMFR. The structure is

similar to the one shown in figure 3—10 but the slit is now at an angle of 450 with respect to the

waveguide axis. The power that is transmitted through the angled slit is shown in figure 3—15.

Figure 3—15: Transmission through angled slit in CAMFR

A strange peak at 113nm is visible in the plot for transmission through the angled slit as shown in figure

3—15 This may be due the approximations made in the structure used for the simulation of angled slit.

The structure is shown in figure 3—16.


31 | P a g e

Figure 3—16: CMFR structure for angled slit simulation

As seen in figure 3—16, the facet appears as a staircase and may lead to errors in the simulation result.

This staircase shape is due to the discritization of structure done by CAMFR. Secondly, there are not

enough modes available in CAMFR for very narrow slits to compute an exact scattering matrix. Another

problem is the grid size used for simulation. For very narrow slits, the grid should be small enough so that

few grid points lie in the air slit. Extremely small grid size in CAMFR leads to a very slow simulation.

3.4. Mirror simulations in OMINSIM

FIMMAVE helps to find the scattering matrix of a vertical air slits but it is difficult to determine the

trasnmission and reflection from an angled slit. Similarly,it is not possible to find the trasnmission and

reflection for the cross mirror using FIMMWAVE. CAMFR can be used to simulate angled slits but for

narrow slits the simulation is very slow and approximations in the structure constructed for simulation can

also lead to some erroneous results. In order to address these critical issues ,OMNISIM has been used. It is

an FDTD tool to simulate the propagation of light through devices. Every simulation in OMNISIM is

carried at a wavelength of 1550nm and the polarization of the excitation signal is TM. In OMNISMI, the

TM polarization is the one in which the magnetic field is in the zx-plane (i-e; horizontal plane of

OMNISIM simulation environment) and electric field is in the y-direction. It is worth mentioning that the

definitions of TE and TM polarizations are opposite for CAMFR and OMNISIM. That is why the

simulations done with TE polarization in CAMFR are done with TM polarization in OMNISIM. Grid size

of 15nm is used for the simulations. The grid size is selected in such a way that some of the grid points

should lie in the air slit. This is important to get good simulation results. A structure similar to the one

shown in figure 3—17 is constructed in OMNISIM. The axes shown in figure 3—17 show the simulation

plane of OMNISIM.


32 | P a g e

Figure 3—17: Simulation plane of OMNISIM

The normalized power reflected from the slit and transmitted power through the slit are shown in figure

3—18.

Figure 3—18: Simulation result of vertical slit in OMNISIM

The configuration with a single slit at 450 is illustrated in figure 3—19, whereas figure 3—20 shows the

fraction of signal transmitted and reflected for slits with different widths. For an angled slit, the amount of

signal reflected backward is very small. The angled slit reflects the light in the vertical direction and a

fraction is transmitted in the forward direction.


33 | P a g e

Figure 3—19: Angled Slit in OMNISIM

Figure 3—20: Transmission through an angled slit

The transmission results of an angled slit using CAMFR and OMNISIM are shown in figure 3—21 for

comparison. It is evident from the plot that for larger slit sizes the transmission computed by the two tools

is approximately same.


34 | P a g e

Figure 3—21: Comparison of OMNISIM and CAMFR results for an angled slit The cross mirror configuration simulated in OMNISIM is shown in figure 3—22. Input signal is reflected

vertically in upward, downward and backward directions. From the plots shown in figure 3—23, one can

see that a large fraction of input signal is transmitted through the cross mirror with thin slits and a small

fraction is reflected in the upward, downward and backward dirctions. As the thickness of the slits of the

cross mirrors increases, the fraction of transmitted light decreases and the reflection in the upward,

downward and backward directions increases. The signal reflected in the upward and downward direcions

is the same because of symmetry of the structure. The four powers (power upward, downward, forward

and backward) are equal for a cross mirror with slits having width of 109nm.The sum of the four

normalized powers is less than unity. The light may spread rapidly in the air slits causing power loss

because of divergence. Consequently, the sum of the four powers is less than one. Simulation result in

table 3—3 shows that the power loss due to divergence increases with the increase in the width of the slit.


35 | P a g e

Figure 3—22: Cross-mirror structure for simulation in OMNISIM

Slit widht

(nm) P up P down

P

forward

P

reflected Sum

175.0 0.164 0.167 0.057 0.520 0.908

165.0 0.178 0.181 0.069 0.482 0.909

155.0 0.191 0.194 0.086 0.441 0.911

145.0 0.203 0.207 0.106 0.397 0.913

135.0 0.214 0.218 0.132 0.351 0.914

125.0 0.223 0.227 0.166 0.300 0.916

115.0 0.228 0.232 0.202 0.256 0.917

109.0 0.229 0.233 0.232 0.224 0.918

93.0 0.220 0.228 0.317 0.154 0.920

83.0 0.214 0.214 0.386 0.112 0.925

73.0 0.189 0.197 0.457 0.079 0.922

63.0 0.165 0.169 0.541 0.049 0.923

53.0 0.134 0.138 0.624 0.028 0.924

Table 3—3: Power splitting by the cross mirror


36 | P a g e

Figure 3—23: Plot of power splitting by cross-mirror

3.5. Conclusion

Different simulation tools can be used to determine the reflected and transmitted optical signal through an

air slit. OMNISIM is used to simulate vertical, angled and cross mirror configuration of mirrors. CAMFR

and OMNISIM have approximately similar results for angled slits. It is difficult to simulate very narrow

slits in CAMFR and angled slits are difficult to simulate in FIMMWAVE. Simulation results in

OMNISIM have shown that the cross mirrors with a slit width of 109nm split the optical power equally in

backward, forward, up and down directions.

3.6. References

[1] “FIMMWAVE manual”, Version 4.00.

[2] “OMNISIM Manual”, Version 4.00.

[3] Jan De Merlier, “Optical Signal regeneration based on integrated amplifying interferometers2,

Academic Year 2002-2003, University of Gent, Belgium.

[4] http://www.ioffe.ru/SVA/NSM/Semicond/ accessed in November 2007.

[5] Peter Bienstman, “CAMFR Manual”, version 1.3, September 2007

37 | P a g e

4 Fabrication

This chapter describes the different masks prepared for the fabrication of the photonic reservoir. The

fabrication process is briefly described in this chapter.

4.1. Process Flow for the Fabrication of Photonic Reservoir

It has been mentioned in chapter 2 that the photonic reservoir consists of optical nodes connected with one

another by semitransparent mirrors. The optical nodes are made up of SOAs, which have ridge waveguide

structure. A schematic of ridge waveguide structure has been shown in figure 2—4. The top-down process

flow for the fabrication of reservoir is shown in figure 4—1. The mask layout and the masking layers can

be determined from this process flow.

Figure 4—1: Process Flow

4.2. Description of the Mask

The fabrication of the reservoir consists of four processes as shown in figure 4—1. The fabrication of

semi-transparent mirrors is done by using FIB process, which is a resist-less and mask-less process. A

mask is designed for the remaining processes. Hence, the mask for the reservoir has three layers.

Chapter 4 Fabrication

38 | P a g e

The ‘Ridge Mask’ is designed to fabricate the ridge waveguides and the ridge mask to fabricate a 2X2

reservoir is shown in figure 4—2. The length and width of the ridge waveguides are defined by the ridge

mask.

Figure 4—2: Ridge Mask

In this work, the ridge masks for a 2X2 and a 6X6 reservoir have been designed. Important specifications

of these ridge masks are listed in table 4—1.

2X2 Reservoir

Number of Optical Nodes 8

Ridge Length 450 microns

Ridge Width 3 microns

6X6 Reservoir

Number of Optical Nodes 72

Ridge Length 150 microns

Ridge Width 3 microns

Table 4—1: Specifications of 2X2 and 6X6 ridge mask

The metal contacts are needed to electrically pump the SOAs of the reservoir. The ‘Metal Mask’ is

designed for this purpose.. It is very important that the size of these metal contacts should be large enough

that they can be contacted easily with the needles. Generally, a metal contact of 60X60 microns can be

contacted by using needles. The spacing between the contacts should be large enough to provide isolation

among them. If the spacing between the two contacts is very small then the contacts can be short circuited,

leading to the damage of the device and the test equipment. The minimum spacing among the contacts is

determined by the resolution of the lithography process. The metal mask is designed in such a way that it


39 | P a g e

can compensate for any miss-alignment between the ridge mask and the metal mask. The metal mask for a

2X2 reservoir is shown in figure 4—3. The ridge mask is shown by the dotted lines in the background of

figure 4—3 to represent overlapping of ridge mask and metal mask to compensate for miss-alignment.

Figure 4—3: Metal Mask After fabrication of the ridge waveguides and the metal contacts, air slits are etched by using FIB milling.

These slits serve as the semi-transparent mirrors. As mentioned previously, FIB milling is a mask-less

and resist-less process, therefore it does not need any mask. A schematic of 2X2 reservoir after the etching

of mirrors is shown in figure 4—4.

Figure 4—4: Schematic of semi-transparent mirrors on a 2X2 reservoir

The metal contacts fabricated by using metal mask are very fragile. Electroplating of the metal contacts is

done to make them thick and robust for probing them with a needle and for wire bonding. ‘Metal Plating


40 | P a g e

Mask’ is designed to achieve this goal. It is important that the metal plating process is carried out after the

etching of the semi-transparent mirrors as mentioned in the process flow, which is shown in figure 4—1.

The electroplating process makes the metal contacts thick. The thick metal layer results in the increase of

the etch depth for the FIB process to etch the MQW active layer. It is difficult for the FIB etching process

to etch slits with nanometer width and with few microns depth. The electroplating process also makes the

surface rough, which makes it difficult to control the etch depth for the fabrication of the air slits. Hence,

it is very important to carry the electroplating process after the etching of semi-transparent mirrors. The

metal plating mask is shown in figure 4—5. The red dots in this figure show the ridge mask in the

background whereas the metal contact mask is shown by white area with continuous lines. The grey area

shows the metal plating mask.

Figure 4—5: Metal Plating Mask

4.3. Fabrication Process

4.3.1. Fabrication of Ridge Waveguides and Metal Contacts

The first step in the fabrication of the reservoir is the etching of the ridge waveguides. A deep etch process

is needed to etch the ridge waveguides because the top InP cladding of the wafer is 1500nm thick (see

figure 2—5). To meet this requirement, hard mask processing is selected. Hard mask processing gives

additional benefits of providing less roughness and better slope of the walls of the waveguides. The first

step to make ridge waveguides using hard mask processing is to deposit a 100nm thick layer of Titanium


41 | P a g e

(Ti) on the wafer. Positive photo-resist is deposited on the thin Ti layer and lithography is performed by

using the ridge mask. After the lithography, dry etching is performed to remove Ti and InP. A cycle of dry

etching and oxygen plasma etching is used to remove thin layer of Ti. Only using the dry etching process

results in the formation of a polymer, which can stop the etch process. Therefore, it is important to etch Ti

by using a cycle of dry etching and oxygen plasma etching. Dry etching is performed by using a mixture

of methane and hydrogen gas and it is performed until 100nm to 200nm of InP is left, which is removed

by selective wet etching. For wet etching, a mixture of hydrochloric acid and phosphoric acid is used.

Finally the photo-resist is stripped off and Ti is removed by selective wet etching. Figure 4—6 depicts the

complete process of fabrication of ridge waveguides.

P++ InGaAs

p type InP

InGaAsP MQW

n type InP

P++ InGaAs

p type InP

InGaAsP MQW

n type InP

100nm Ti

Bare Wafer 100nm Ti Deposited

P++ InGaAs

p type InP

InGaAsP MQW

n type InP

100nm Ti

Photo-resisted Deposted

Photo-resist

p type InP

InGaAsP MQW

n type InP

Exposure

p type InP

InGaAsP MQW

n type InP

Develop

p type InP

InGaAsP MQW

n type InP

Ti etched by cycle of dry etch and oxygen

plasma etch

InGaAsP MQW

n type InP

Dry etch unitl 100nm to 200nm of InP

is left

InGaAsP MQW

n type InP

Selective wet etch to remove 100nm

to 200nm of InP

InGaAsP MQW

n type InP

Strip off photo-resist and remove Ti

by using selective wet etching Figure 4—6: Ridge waveguide processing


42 | P a g e

After completing the processing for ridge waveguides, the next step is to make metal contacts. The first

step in the fabrication of the metal contacts is to deposit layer of Benzocyclobutene (BCB). BCB layer is

so thick that the height variations of the ridge waveguide will have minimum impact and a planarized top

is achieved. Dry etching of BCB is carried out by using a mixture of SF6 and O2. The 180nm thick p++

InGaAs layer acts as an etch stop layer for the process and thus self-aligned BCB etching is achieved. A

37nm thick Ti layer is deposited by evaporation after the dry etching of BCB. Photo-resist is deposited on

top of the Ti layer and the image reversal process is carried out to get negative tone from a positive photo-

resist. After this process, 3nm Ti and 150 nm gold (Au) layer are deposited by evaporation. Finally, lift-off

process is carried out as the last step to get metal contacts on top of the ridge waveguides. The process of

fabrication of metal contacts is schematically illustrated in figure 4—7. Figure 4—8 shows a device after

the ridge waveguides and metal contacts have been made.

InGaAsP MQW

n type InP

Planarization uisng BCB

BCB BCB

InGaAsP MQW

n type InP

Self Alligned BCB Etching

BCB BCB

InGaAsP MQW

n type InP

Deposit 37nm Ti

BCB BCB

Ti

InGaAsP MQW

n type InP

Image Reversal Process

BCB BCB

TiPhoto-resist

InGaAsP MQW

n type InP

Develop

BCB BCB

Ti

InGaAsP MQW

n type InP

BCB BCB

Ti

Ti+Au

Depost 150nm of Ti+Au

InGaAsP MQW

n type InP

BCB BCB

Ti

Ti+Au

Lift-off Process

InGaAsP MQW

n type InP

BCB BCB

Ti+Au

Remove Ti layer

Figure 4—7: Processing to make metal contacts


43 | P a g e

Figure 4—8: 2X2 Reservoir

4.3.2. Fabrication of Semitransparent Mirrors

After the fabrication of metal contact the cross mirrors can be etched by FIB processing. As discussed in

chapter 3, a slit of 109nm width is needed to split the incoming signal equally into four parts. It was found

by making a cross-section on fabricated device that the metal contact has a thickness of approximately

200nm. An etch depth of approximately 2.33µm is needed in order to etch the active layer completely (see

table 3—1). One of the most important things is to determine the appropriate FIB process parameters

which can give the required width and depth of the slits.

FIB process uses the ion beam to etch the sample. As the current of the ion beam increases, the goal to

make slits of the order of 100nm becomes difficult to achieve. Generally, a smaller beam current is used to

etch narrow slits but it is usually hard to focus ion beam with small current on the smooth surface of the

sample. An ion beam current of 10pA is used for the etching of slits.

The FIB process can be carried out by using either the Si-Etch program or the Enhanced Etch mechanism.

In enhanced etch mechanism Iodine gas is used, which flows over the sample. It was found by using the

Si-etch program that it can provide very narrow slits with nearly vertical walls but it was difficult to get

depth of 2.33µm (see figure 4—9). A slit of only 840nm depth was etched by the Si-etch program for an

ion beam current of 10pA and etch depth of 5µm. Desired etch depth of 2.33µm was not achieved even for

an etch depth of 15µm. The slit etched by the Si-etch program for an etch depth of 5µm is shown in figure

4—9.


44 | P a g e

Figure 4—9: Slit etched by Si-Etch Program

It is possible to etch very deep slits by using the enhanced etch mechanism but it is not possible to have

very steep walls of the slits. The slits appear as tapers, which are broad at the top and becomes narrow at

the bottom. An etch depth of more than 2.33µm was achieved for an ion beam current of 10pA and etch

depth of 4.5µm. The result is shown in figure 4—10. The width of the slit was found to be 150nm. The

yellow lines are meant to show the active region.

Figure 4—10: Slit etched by Enhanced Etch Mechanism


45 | P a g e

As mentioned earlier, a cross mirror consist of two slits. In few devices both slits of depth more than

2.33µm are etched, but for few devices one of the slit is etched less deep. Since, all the nodes are short

circuited due to the metal contacts so the less deep slits are used to provide electrical isolation between the

nodes. The less deep slits should have depth enough to prevent any leakage/diffusion current among the

nodes. It will not be possible to use the nodes as detector in case of a large leakage current. Therefore, slits

are etched which etches till the active layer. Such slit are etched by using an etch depth of 2.5µm for an

ion beam current of 10pA. A picture of the cross mirror etched by using the FIB process is shown in the

figure 4—11. One can observe that the air gap is much wider at the center where the two slits intersect

each other.

Figure 4—11: Cross Mirror Fabricated by FIB

After the etching of the cross mirrors, lithography and electroplating are carried out to make the metal

contacts thick. The photo-resist is stripped off and the thin Ti layer acting as a short circuit is also

removed.

When the processing on the top side is complete, the bottom side is thinned to 150micrometers and an n-

contact is made by using an alloy of gold, germanium and nickel. As a result of fast alloying process, the

metal diffuses into the n-type InP, which consequently results in a good ohmic contact.

4.4. Improved Photonic Reservoir

It was mentioned earlier that a 6X6 reservoir has 72 optical nodes. In order to use this device as a

photonic reservoir in a reservoir computing system, the output power of these nodes should be fed to the

software based read-out part. To read the output power, at least half of these nodes will be used as a

detector . Therefore, the effective number of nodes will be reduced to half. The computation power of a


46 | P a g e

reservoir computing system generally decreases with the decrease in the number of the nodes of the

reservoir.

A new design has been proposed in order to solve this problem of using half of the optical nodes as

detectors. The proposed design will be termed as Detector Based Photonic Reservoir (DBPR) in the report

afterwards. In this design, a small section of every optical node is used as a detector by reverse biasing it

so that it can absorb a fraction of the power. The amount of power absorbed can be calculated by:

)exp()0()( zzPzP Γ−== α

For a detector of length L,

)exp()0()( LzPLP Γ−== α

where α is the absorption coefficient and Γ is the confinement factor. 4% power is absorbed by a detector

of 2micron length for an absorption coefficient of 10000/cm and a confinement factor of 2%. DBPR uses

the same ridge mask as used by the previous design. The metal contact mask is modified to include the

contacts for the detectors and the metal plating mask is also modified accordingly. Snapshot of the metal

contact mask used for the fabrication of the DBPR is shown in figure 4—12. The white region in figure

4—13 represents the metal plating mask. The ridge waveguide mask is shown in the background. The

fabrication process for the detector based photonic reservoir is the same as described in section 4.3.

Important characteristics for the detector based photonic reservoir are listed in table 4—2.

Detector based Photonic Reservoir

Length of detector 2 microns Amount of power absorbed 4% Ridge Width 3 microns Spacing between the SOA and the detector 2 microns Size of contact pads Minimum 60X60 microns

Table 4—2: Important features of DBPR

Figure 4—12: Mask for Detector Based Photonic Reservoir


47 | P a g e

A picture of the 2X2 DBPR is shown in figure 4—13.

Figure 4—13: Detector Based Photonic Reservoir

4.5. Conclusion

The process flow for the fabrication of coupled SOA network can be used to determine the masking layout

and the masking layers. Two types of mask are prepared. In one type, the optical node can either act as an

SOA or as a detector. In the other design, each node consists of an SOA and a detector. Fabrication

process is carried out in three steps. Ridges are fabricated in the first step. Then the metal contacts are

fabricated. After that the cross mirrors are etched by using the FIB processing.

48 | P a g e

5 Measurements

Measurements are taken to determine the effect of FIB processing to etch slits of the cross mirrors.

Different measurements were taken in order to test the fabricated device and the working of the cross

mirrors. These measurements and the results of the measurements are discussed in this chapter.

5.1. Quantifying the loss introduced by the FIB processing

As mentioned previously, FIB processing is used to etch cross mirrors. Plot in figure 3—23 shows that a

significant fraction of power is reflected backwards by the cross mirrors. If the back reflection is large

then the SOA can start to behave as a laser, which is not desired for the reservoir discussed in this work.

The transmission through an air slit can be found by the expression:

δcos21

)1(2

2

RR

RT

−+−= , where it is assumed that the two surfaces of the air slit have equal reflectance R

(see figure 3—11). One can easily see from this equation that as the reflectance decreases the transmission

increases. It was found that the reflectance R of the facet of the laser changes by FIB processing. This

change can be determined from the change in threshold current of the laser. A plot of the laser threshold

before and after FIB etching by using Si etch program is shown in figure 5—1.

Figure 5—1: Effect of FIB processing on the laser facet

A model to determine the change in reflectivity from the change in threshold current of a laser is

mentioned in Appendix A. The material used for the fabrication of the laser has an internal loss

coefficient of 20/cm [ref. 3 in chapter 3] and the cleaved facet of the laser has a reflectivity of

approximately 30%.If the left facet of the laser is etched then the threshold of the laser is changed from

Chapter 5 Measurements

49 | P a g e

29mA to 37mA. The change in reflectivity from 30% to 12.24% is found by using equation 9 in appendix

A.

When the facet of the laser was etched by using enhance gas etch mechanism a relatively smaller increase

in threshold was observed. This means that enhance gas etch mechanism produce a relatively smaller

change in reflection as compared to Si-etch program. The change in laser threshold by etching the facet

using enhance gas etch mechanism is shown in figure 5—2. The reflectivity of the facet changed from

30% to 22.1%. Although, Si etch mechanism reduces the reflection of the facet by a significant amount

but deep etching is not possible with this mechanism (see figure 4—9).

Figure 5—2: Effect of enhanced gas etching on laser facet

The increase in the laser threshold and the decrease in the reflectivity of the facet are due to the formation

of a back-sputtered amorphous layer on the wall of the facet. The amorphous layer acts as an absorbing

layer. The amount of absorption in this layer can be found by doing a simulation in FIMMWAVE. The

simulation mechanism is shown in figure 5—3.

20nm

absorbing

layer

R = 30%

R = 22.1%

Transmission

Transmission

Input

Input

Absorption = 0

Absorption = 0

Figure 5—3: Losses due to absorption layer

The change in the reflectivity is attributed to the amorphous layer formed by the FIB processing. The

value of the absorption in the amorphous layer is selected in such a way that the reflectivity has changed


50 | P a g e

from 30% to 22.1%. The value of α is found to be 2500000/m. From this value of absorption the value of

imaginary index is found to be j308519 by using the expression: π

αλ4

=jn .

The loss due to absorption in the amorphous layer is found by using the expression:

)(log10

)/( 10in

outP

PL

cmdBLoss −= where )exp( LP

P

in

out α−=

In the above equation L is the length of the absorbing layer and is taken to be 20nm.The value of the loss

(dB/cm) calculated by the above expressions is found to be approximately -10,000dB/cm.

This loss introduced by the FIB process can be reduced by using some post processing. Heating in

polymide oven for 2 hours at a temperature of 300oC was carried out. A decrease in the threshold current

of the laser has been observed and the result is shown in plot of figure 5—4. A decrease in the threshold

current means that the reflectivity of the facet of the mirror has increased once again. In other words, the

losses due to absorption in the amorphous layer have decreased.

Figure 5—4: Effect of heating in polymide oven on threshold of laser

5.2. Measurements to check optical connection between SOAs

It is important to check the electrical isolation between SOAs before checking the optical coupling

between the SOAs. If the electrical isolation between the nodes is not good then there will be leakage

current, which makes the detection of optical coupling difficult. A voltage source is connected between

two nodes in order to check the electric isolation between SOAs. Some typical results obtained by

connecting the voltage source across the two SOAs are shown in figure 5—5 and figure 5—6.


51 | P a g e

Figure 5—5: Leakage Current through SOAs

Figure 5—6: Conduction current

It is easy to analyze the plots shown in figure 5—5 and 5—6 by considering a model shown in figure 5—

7.

Figure 5—7: Equivalent Electrical Model


52 | P a g e

The diodes shown in figure 5—7 represent the SOAs which are connected back to back as they are placed

on the same copper plate. The resistance R represents the electrical connection between the two SOAs,

which may be provided by the gold sputtered during the FIB processing. This gold can be deposited in the

narrow air slits and may provide a conduction path. The resistances R1 and R2 are some parasitic

resistance of the diode because the diodes are not the perfect ones. If the resistance R is much higher than

the equivalent impedance of the two diodes then the current will flow through the resistance paths

provided by the diodes. The applied voltage will make SOA1 forward biased and SOA2 will be reverse

biased. As a result, only leakage/conduction current will flow through the conduction paths of the SOAs.

This corresponds to the situation shown in the plot of figure 5—5. If the equivalent impedance of the

SOAs is larger than the resistance R then the current will flow through resistance R and it will linearly

increase with the increase in the voltage. This situation is depicted in plot of figure 5—6.

5.2.1. Coupling from a 450 air slit

The result for the photo detection of an optical signal after reflection from a 450 air slit is shown in figure

5—8. The measurement is done by pumping one SOA and another SOA is reverse biased so that it can be

used as a detector. The pump current leads to stimulated emission, which can be detected by a photo-

detector.

Figure 5—8: Optical Coupling in 45 degree Slit

The SOA is pumped with a pump current of 2mA, 3mA and 4mA. The plot shows that the current of the

photo-detector increases with an increase in the electrical pumping of the SOA. The current of the photo

detector when no pump current is applied to the SOA represents the leakage current due the parasitic


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resistances shown in figure 5—10. When the reverse voltage across the SOA is zero then there is no

leakage current. The leakage current increases with an increase in the reverse voltage. This is shown by

the first curve of the plot in figure 5—8. If this leakage current is very large then it will not be possible to

detect any optical signal. The current of the photo-detector increases with an increase in the pump current

of the SOA. The slope of the leakage current curve (curve with no pump) is approximately the same as is

for the remaining curves. The photocurrent detected by the photo-detector can be obtained by subtracting

the no pump curve from the other curves. The result is shown in figure 5—9.

Figure 5—9: Modified result of coupling by 45 degree slit

When the SOA is pumped and no voltage is applied across the photodetector then there is still some

current detected by the detector, which tells that the optical signal generated by the SOA is coupled to the

detector and the detector detects it even if no reverse current is applied to it. The same has been depiceted

in figure 5—9. An equivalent model of the amplifier and detector is shown in figure 5—10.

Figure 5—10: Equivalent Model


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5.2.2. Coupling by a cross-mirror

The configuration used to detect the coupling by using the cross mirror is shown in figure 5—11. The

SOA on the left most side was pumped and the optical signal was detected at the top and bottom detectors.

The results for the measurements are shown in figure 5—12 and 5—13.

Figure 5—11: Measurement Schematic for cross mirror

It is evident from the plot shown in figure 5—12 that the detector current of the top arm detector increases

with an increase in the pump current of the SOA. It means that the optical signal generated by pumping

the SOA has been coupled to the top arm after reflection from the cross-mirror.

Figure 5—12: Optical coupling in the top arm

Similarly an optical signal is detected by the bottom arm detector as shown by figure 5—13. Hence, the

optical signal is coupled to the top and the bottom SOAs. The top and bottom detector are identical and


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are located at identical distance on the respective SOAs. For the same pumping of the SOA, the top

detector and bottom detector have different currents. At a reverse voltage of -1V, the top detector has a

current of approximately 1µA while the bottom detector has a current of approximately 4µA at a pump

current of 4mA. This means that although the two slits of the cross mirror are etched by using the same

FIB process but the two slits are not identical. As a result more optical signal is coupled in one arm than in

the other arm.

Figure 5—13: Optical coupling in the bottom arm

The top and bottom SOAs were also used as photo-detectors by reverse biasing them. The response given

by them are shown in figure 5—14 and 5—15. It is evident from the plots that by using the top and bottom

SOAs as detectors the response is not good. The leakage current is so high that the optical signal is hidden

in the leakage current, which makes the detection of optical signal difficult. This is more evident in the

plot shown in figure 5—15.

Figure 5—14: Behavior of top arm SOA as a detector


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Figure 5—15: Behavior of bottom arm SOA as a detector The reason for high leakage current can be attributed to the conduction path provided by the resistance R

shown in figure 5—7. The two SOAs were short circuited before the etching of the mirrors by using FIB

processing. So, it is only the very narrow slit etched by FIB process which has isolated the SOAs. The re-

deposition of gold can provide a conduction path that can lead to a large value of leakage current. The

same has been observed by the measurements done on the network that has optical nodes which consist of

SOAs only (see figure 4—8).

Figure 5—16: Leakage current The optical signal is detected better by the top and the bottom photo-detectors of figure 5—11 because the

contact pads are isolated from the SOA contact pad by a gap of 2µm. It is important to mention here that

the p++ InGaAs is still connecting the SOA with the detector. So, it can be interesting to measure the

device after etching the p++ InGaAs between the contact pad of the SOA and the detector. p++ InGaAs

behaves just like a conductor and can lead to leakage current. The same has been shown in the schematic

shown in figure 5—16. In the reservoir, the purpose of the detectors shown in figure 5—11 is to detect a


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fraction of the power of the SOA, which can be fed to the readout part of the reservoir. A large leakage

between the detector and SOA can lead to difficult detection of optical signal.

The response of the right arm detector to check optical coupling through the cross mirror has been shown

in figure 5—17.

Figure 5—17: Coupling in the right arm

It was not possible to detect optical coupling through the cross mirror. The problem may be due to a large

width of the slit in the center of the cross mirror as shown in figure 5—18. The cross mirror has a width of

approximately 246.8nm at top but the walls are not perfectly steep and the width is approximately 150nm

at the bottom. It can be seen in figure 5—18 that the slit is approximately 516.7nm wide at the location

where the two slits intersect each other. The results for the simulation of cross mirror in table 3—3 show

that less than 6% of the optical signal goes forward for a slit width of 175nm. The cross mirror may have a

dimension more than 175nm, which hampers the coupling of optical signal in the forward direction.

Figure 5—18: Dimensions of Cross Mirror


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5.3. Conclusion

The measurements are done to determine the effect of the FIB processing on the facet of a laser. The

losses introduced by FIB processing have been quantified. It was found that the Si-Etch mechanism

produces a larger change in the reflectivity of the facet than the enhanced-etch mechanism. The coupling

of the optical signal by the cross mirror has been determined and it was found that the cross-mirror

provides coupling in the upward and downward direction but the signal was not coupled in the forward

direction, which might be due to a wider air gap at the intersection of the two slits.

Chapter 6 Conclusion and Future Work

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6 Conclusion and Future Work

In this work a network of SOAs is proposed to work as a reservoir for a reservoir computing system. The

SOAs are coupled to each other by semi-transparent cross-mirrors, which can split the optical signal into

three parts (ignoring the optical signal that is reflected backwards). Such mirrors can be simulated by

using FDTD simulation tools. Simulation results have shown that a significant amount of optical signal is

reflected backwards by the cross mirror. The cross-mirrors were fabricated by using FIB etching. It was

found that the reflectivity of a facet decreases by FIB processing. The decrease was more pronounced by

using Si-etch mechanism than enhance etch mechanism. The decrease in the reflectivity can be attributed

to the lossy amorphous layer formed at the facet. The losses introduced by the amorphous layer are

computed. Measurements were done to determine the working of the cross mirrors. It was found that the

reservoirs in which a node can either act as an amplifier or as a detector had a lot of parasitic leakage

current. This current rode over the optical signal and prevented the detection of optical signal.

Measurements were done on the reservoir in which each optical node consisted of an amplifier and a

detector. It was found that the optical signal was coupled in the top SOA and the bottom SOA. The optical

signal was not coupled in the forward direction, which may be due to the much wider air gap at the point

of intersection of the two slits of the cross mirrors.

Considering the fact that the DBPR can provide optical coupling in the top and the bottom directions,

following suggestions are made for the improvement of the performance of the system:

• It can be interesting to investigate some other mirror configurations which can provide optical

coupling in three directions with very small back reflections.

• The fabrication process might be changed to etch the p++InGaAs, which acts as a short circuit

between the detector contact pad and the SOA contact pad.

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Appendix A A.1. Relation between laser threshold current and losses

The threshold current of the laser is given by:

+==

pNcc

thth G

NqqN

Iτττ

10 ……………………………….1

If we neglect N0, then the expression reduces to

==

pNcc

thth G

qqNI

τττ1

……………………………….2

Here, Ith is the threshold current, q is electron charge and τc is the carrier life time, Nth is the threshold

value of the carrier population and τp is the photon life time.

A schematic of Fabry Perot laser is shown in the figure below with L as the length of the cavity and RR

and RL is the reflectivity of the right and left mirror of the cavity respectively.

Photon life time can be associated to the losses in the cavity by the following expression:

)( int1

ernalmirrorgcavitygp ααναντ +==−……………………………….3

αmirror accounts for the losses induced by the mirrors and is called as mirror loss coefficient. It can also be

written as αmirror= αleft+ αright. The loss introduced by one of the mirror is given by:

)1

ln(2

1

Lleft RL

=α ……………………………….4

If two mirrors have same reflectivity then the above expression becomes:

)1

ln(1

RLmirror =α ……………………………….5

Appendix A

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Hence, expression 3 can also be written as:

)( int1

ernalrightleftgcavitygp αααναντ ++==−……………………………….6

By changing the reflectivity of one of the mirrors of the laser, the threshold current will change. If the

reflectivity of left mirror (for example) is changed, then we can reach to expression:

2

1

1

2

p

p

th

th

I

I

ττ

= ……………………………….7

Here Ith1 refers to the situation where the cavity has equal reflectivity on both facets and Ith2 corresponds to

the case when the reflectivity of the left facet is altered (i-e, by etching).

Then by using expression 6, expression 7 can be written as:

=1

2

th

th

I

I

)2(

)(

int

int

ernalright

ernalrightleft

ααααα

+++

……………………………….8

Or

ernalrightth

ernalrightthleft I

Iint

1

int2 )2(αα

ααα −−

+= ……………………………….9

By using this expression, we can find the loss induced by changing the reflectivity of the left mirror

provided we know the threshold current for the laser with equal and known mirror reflectivity and the

internal loss of the material.

Appendix B

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Appendix B B.I. Simulation Code for Angled Slit in CAMFR

This is the CAMFR code to determine the amount of back reflection and transmission through an angled

slit.

___________________________________________________ ___________________

#!/usr/bin/env python

#### Parameters ####

from camfr import *

outfile = file("new.txt",'w')

set_lambda(1.55)

pml=0.1

set_polarisation(TE)

set_lower_PML(-pml)

set_upper_PML(-pml)

slit = 2.96

set_N(800)

#set_precision(10000) #100000 does not help

#set_precision_enhancement(500)

#set_dx_enhanced(.0001)

#set_orthogonal(0)

#### Define Material stack####

InGaAsP = Material(3.274)

InP = Material(3.214)

Air = Material(1.0)

#for slit in arange(0.1, 1, 0.1):

####Define geometry####

#### Left tilted waveguide is defined first__define d Top To BOTTOM ####

#### Right tilted waveguide is defined second__ defined Bottom to

TOP ####

# Left side Tilted Waveguide defined top to bottom

my_geo = Geometry(Air)

my_geo += Rectangle(Point(0.0,1.5), Point(4.0, 5.5) , InP)

Appendix B

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my_geo += Rectangle(Point(0.0,-1.5), Point(8.0,1.5) , InGaAsP)

my_geo += Rectangle(Point(0.0,-5.5), Point(11,-1.5) , InP)

my_geo += Triangle (Point(4.0,1.5), Point(8.0,1.5), Point(4.0,5.5), InP)

my_geo += Triangle (Point(8.0,1.5), Point(8.0,-1.5) , Point(11.0,-1.5),

InGaAsP)

my_geo += Triangle (Point(11.0,-1.5), Point(11.0,-5 .5), Point(15.0,-5.5), InP)

# Right side Tilted Waveguide defined bottom to top

my_geo += Triangle (Point(15.0+slit,-5.5), Point(15 .0+slit,-1.5),

Point(11.0+slit,-1.5), InP)

my_geo += Rectangle(Point(15.0+slit,-5.5), Point(19 .0+slit, -1.5), InP)

my_geo += Triangle (Point(11.0+slit,-1.5), Point(11 .0+slit,1.5),

Point(8.0+slit,1.5), InGaAsP)

my_geo += Rectangle(Point(11.0+slit,-1.5), Point(19 .0+slit, 1.5), InGaAsP)

my_geo += Triangle (Point(8.0+slit,1.5), Point(8.0+ slit,5.5),

Point(4.0+slit,5.5), InP)

my_geo += Rectangle(Point(8.0+slit,1.5), Point(19.0 +slit, 5.5), InP)

#### finding the guiding modes####

#slab.calc()

#guided = 0

#niguided = 1

#for t in range (0,40):

#if abs(slab.mode(t).n_eff().imag) < niguided :

#guided = t

#niguided =abs(slab.mode(t).n_eff().imag)

#### Defining Stack###

prop0, prop1, d_prop = 0.0, 19+slit, 0.2

trans0, trans1, d_trans = -5.5, 5.5, 0.2

exp = my_geo.to_expression(prop0, prop1, d_prop,

trans0, trans1, d_trans)

s = Stack(exp)

#s.plot()

#### Excitation####

inc = zeros(N())

inc[0] = 1

s.set_inc_field(inc)

#s.plot()

### Reflection and Transmission Coefficients####

s.calc()

Appendix B

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Reflection = abs(s.R12(0,0))

Transmission = abs(s.T12(0,0))

#print abs(s.T12(0,0))

#### Print the results####

print >> outfile, " ",slit," ",Transmission*Trans mission,"

",Reflection*Reflection

print >> outfile

outfile.close()

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