Fundamentals of Laser Diode Amplifiers

250 Pages·1996·13.32 MB·English

by  Dr. H. Ghafouri-Shiraz

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Library of Congress Calaloging-in-Publication Data
Ghafouri-Shiraz, H.
Fundamentals of laser diode amplifiers/H. Ghafouri-Shiraz.
^: P. cm.
~ Includes bibliographical references and index.
ISBN 0471 958727
1. Semiconductor lasers. 2. Optical amplifiers. I. Title.
TA1700.G53 1995
621.36'6 —dc20 95-32238
C!P
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0471 95872 7
Typeset in 10/12pt Times by Dobbie Typesetting Ltd
Printed and bound in Great Britain by Bookcraft (Bath) Ltd
This book is printed on acid-free paper responsibly manufactured from sustainable forestation,
for which at least two trees are planted for each one used for paper production.
This book is dedicated to
My Father, Haji Mansour, for the uncompromising
principles that guided his life.
My Mother, Rahmat, for leading her children into
intellectual pursuits.
My Supervisor: The Late Professor Takanori Okoshi, for
his continuous guidance, encouragement, inspiring discus-
sion and moral support. A distinguished scientist and a
great teacher who made me aware of the immense potential
of optical fibre communications.
My Wife, Maryam, for her magnificent devotion to her
family. My constant companion and best friend, she has
demonstrated incredible patience and understanding dur-
ing the rather painful process of writing this book while
maintaining a most pleasant, cheerful and comforting
home.
My Children, Elham, Ahmad-Reza and Iman, for making
everything worthwhile.
To all of my Research and Undergraduate Students, for
their excellent and fruitful research work, and for many
stimulating discussions, which encouraged and motivated
me to write this book.
CONTENTS
Preface xi
Acknowledgements xv
1 Introduction 1
References 7
Basic Principles of Optical Amplifiers 9
2.1 Introduction 9
2.2 Interaction of Radiation with a Two-Level System 10
2.2.1 Radiative processes 10
2.2.2 Spontaneous emission 11
2.2.3 Stimulated emission 12
2.2.4 Absorption 12
2.2.5 Optical gain 14
2.3 Characterisation of Optical Amplifiers 16
2.3.1 Signal gain 16
2.3.2 Frequency bandwidth 18
2.3.3 Saturation output power 19
2.3.4 Noise figure 20
,2.4 Ideal Optical Amplifiers 22
2.5 Practical Optical Amplifiers 23
2.5.1 Performance limits of the amplifier signal gain 24
2.5.2 Performance limits of the amplifier bandwidth 24
2.5.3 Performance limits of the saturation output power 24
2.5.4 Performance limits of the noise figure 25
2.6 Summary 29
2.7 References 29
Optical Amplification in Semiconductor Laser Diodes 33
3.1 Introduction 33
3.2 Principles of Optical Amplification in Semiconductor Lasers 33
viii CONTENTS
3.2.1 Optical processes in semiconductors 34
3.2.2 Analysis of the optical gain in semiconductors 37
3.3 Semiconductor Laser Diodes as Optical Amplifiers 44
3.3.1 Optical amplification using homojunctions 44
3.3.2 Optical amplification using heterostructures 46
3.4 Types of Semiconductor Laser Amplifiers 48
3.4.1 Operational classification 48
3.4.2 Structural classification 51
3.5 Radiative Transition in Semiconductors 53
3.5.1 Stimulated emissions 53
3.5.2 Spontaneous emissions 55
3.6 Applications of Semiconductor Laser Amplifiers 56
3.6.1 Non-regenerative repeaters 56
3.6.2 Рге-amplifiers to optical receivers 58
3.6.3 Bistable and switching applications 59
3.6.4 Other applications 61
3.7 References 62
Analysis of Transverse Modal Fields in Semiconductor Laser [
Amplifiers (SLAs) 67 I
4.1 Introduction 67 f
4.2 Solution of Transverse Modal Fields in Rectangular Optical I
Waveguides 68 |
4.2.1 Solution for a three-layer slab (planar optical waveguide) 68 j
4.2.2 Solution for a rectangular dielectric waveguide using modal field !
approximations 75 ;
4.2.3 Application of Effective Index Method (EIM) for calculating |
propagation constants for transverse modal fields in rectangular j
dielectric waveguides 78 j
4.2.4 Other methods to solve for transverse modal fields and the
dispersion characteristics of rectangular dielectric waveguides 82
4.3 Applications of Solutions of Transverse Modal Fields in SLAs 83
4.3.1 Analysis of the modal gain coefficients 84 j
4.3.2 Design of a polarisation insensitive Travelling Wave Amplifier }
(TWA) 87 I
4.4 Importance of Transverse Modal Field Properties in SLAs 98 j
4.5 References 99 \
Analysis and Modelling of Semiconductor Laser Amplifiers:
Gain and Saturation Characteristics 103
5.1 Introduction 103
5.2 Analysis of Semiconductor Laser Amplifiers with a Uniform Gain
Profile 104
5.2.1 Amplifier gain formulation in semiconductor laser amplifiers 105
5.2.2 Gain saturation formulation in semiconductor laser amplifiers 110
5.2.3 Appraisal on using a uniform gain profile in analysing SLAs 112
5.3 General Analysis of Semiconductor Laser Amplifiers (A Brief Review) 113
5.3.1 Analysis using rate equations 113
5.3.2 Analysis using travelling-wave equations 114
5.4 Analysis of Semiconductor Laser Amplifiers Using Transfer Matrices 117
5.4.1 A brief review of matrix methods 117
CONTENTS ix
5.4.2 Analysis of longitudinal travelling fields in SLAs using the
Transfer Matrix Method (TMM) 120
5.4.3 Analysis of SLAs with a non-uniform gain profile using the
Transfer Matrix Method (TMM) 125
5.4.4 Computational considerations 127
5.5 An Equivalent Circuit Model for SLAs 130
5.6 Applications 135
5.6.1 Structural effects on amplifier gain 135
5.6.2 System considerations 139
5.7 Analysis of Gain Saturation in a SLA With a Uniform Material
Gain Profile 141
5.8 Summary 143
5.9 References 144
Analysis and Modelling of Semiconductor Laser Amplifiers:
Noise Characteristics 149
6.1 Introduction 149
6.2 Formulation of Noise in Semiconductor Laser Amplifiers 150
6.2.1 Photon statistics formulation 150
6.2.2 Rate equation approach 157
6.2.3 Travelling-wave equations formulation 159
6.3 Analysis of Noise in SLAs Using the Equivalent Circuit Model 159
6.3.1 Representation of spontaneous emissions in a SLA by an
equivalent circuit 160
6.3.2 Validity of modelling spontaneous emissions by an equivalent
circuit 162
6.3.3 Effects of stray reflections on the spontaneous emission power
from a SLA 170
6.4 Applications 175
6.4.1 Device design criteria 176
6.4.2 System considerations 182
6.5 Analysis of SLA Spontaneous Emission Power Using the Green
Function Approach 183
6.5.1 Travelling-wave amplifier (TWA) 184
6.5.2 Fabry-Perot amplifiers 185
6.6 Summary 186
6.7 References 187
Experimental Studies on Semiconductor Laser Amplifiers 191
7.1 Introduction 191
7.2 Basic Set-up for Measurements 191
7.2.1 The laser source 192
7.2.2 Semiconductor laser amplifier 199
7.2.3 Detection circuit 199
7.3 Experimental Studies on Recombination Mechanisms 200
7.3.1 Principles of the experimental measurement 201
7.3.2 Experimental procedures 202
7.3.3 Results and discussions 202
7.4 Measurement of Gain Characteristics 204
7.4.1 Experimental set-up 204
7.4.2 Experimental procedures 209
7.4.3 Results and discussions 211
CONTENTS
7.5 Measurement of Noise Characteristics 214
7.5.1 Experimental set-up 214
7.5.2 Experimental procedures 215
7.5.3 Results and discussions 219
7.6 Summary 221
7.7 References 221
Conclusions 223
8.1 Summary of the Book 223
8.2 Limitations of the Research Study 226
8.2.1 Limitations on theoretical studies 226
8.2.2 Limitations on experimental studies 227
8.2.3 Limitation on the scope of this book 227
8.3 Future Work 227
8.4 References 228
PREFACE
In the latest decade we have witnessed a tremendous advance in telecommu-
nications technology. With the rapid growth and sophistication of digital
technology and computers, communication systems have become more
versatile and powerful. This has given a modern communication engineer
two key problems to solve: (i) how to handle the ever-increasing demand for
capacity and speed in communication systems, and (ii) how to tackle the need
to integrate a wide range of computers and data sources so as to form a highly
integrated communication network with a global coverage.
The foundations of communication theory show that by increasing the
frequency of the carrier used in the system, both the speed and the capacity of
the system can be enhanced. This is especially true for modern digital
communication systems. As the speeds of computers have increased
dramatically over recent years, digital communication systems operating at a
speed which can match these computers have become increasingly important.
Rather than the electronic circuitry, it is now apparent that the upper bound on
the speed of a communication system is limited by the transmission medium.
An example that illustrates this is the 80486 PC, which can perform
computations with a clock speed of 66 MHz or higher. However, the speed
of modems connecting these PCs have just recently reached 1.44 MHz. This is
45 times slower than the electronic clock in the PC. One of the reasons for such
a mismatch is that modems use telephone lines (which are typically twisted-pair
transmission lines) and these cannot operate at very high frequencies. To
improve the speed and hence capacity of the system, we not only need to switch
to a carrier with a higher frequency, but to switch to an alternative
transmission medium.
Given the preceding argument, the reader will not be surprised by the rapid
development of optical communications during the past 20 years. Ever since
Kao and his co-workers discovered the possibility of transmitting signals using
light in circular dielectric waveguides, research in optical communication
systems has developed at an unprecedented pace and scale. Optical
communications offer two distinct advantages over conventional cable or
wireless systems. First, because the carrier frequency of light is in the region of
THz (i.e. 1014 Hz), it is possible to carry many more channels than radio waves
or even microwave systems. Secondly, the former advantage can be realised
because of the development of a matching transmission medium, namely
optical waveguides (including fibres and planar structures). Optical waveguides
not only provide the necessary frequency bandwidth to accommodate a
Xii PREFACE
potentially large number of channels (and hence a huge capacity), but also offer
an immunity from electromagnetic interference from which the traditional
transmission medium often suffers.
In addition to optical waveguides, another key area of technological
development, which plays a crucial role in the success of optical communica-
tion systems, is optical devices. The rapid growth of semiconductor laser diodes
has allowed optical transmitters to be miniaturised and become more powerful
and efficient. Both the fabrication and theoretical research in semiconductor
lasers have given rise to a wide range of components for optical communication
systems. For example, from conventional buried heterostructure laser diodes to
the recent development of multiple quantum-well lasers and from simple
Fabry-Perot structures to (i) distributed feedback (DFB) structures, (ii) single
cavity laser diodes and (iii) multiple cavity laser diodes. Laser diodes are not
only important in compact disc players, but they also provide coherent light
sources which are crucial in enhancing the speed and range of transmission of
optical communication systems.
The technological forces that gave us optical waveguides and semiconductor
laser diodes, have recently explored theoretical research and manufacturing
technology to develop other innovative devices that are crucial in optical
communications, for example optical amplifiers, optical switches and optical
modulators. Previously optical/electronic conversion devices had to be used to
perform these functions, but the bandwidth of these was limited. The
integration of semiconductor laser diodes with optical waveguide technology
allows such components to be developed specifically for optical communica-
tions. This force of integration does not stop here. The advent of photonic
integrated circuits (PICs), which are ICs built entirely with optical components,
such as laser diodes, waveguides and modulators will further enhance the
power and future prospects of optical communication networks.
In view of the increasing pace of development and growing importance of
optical communication technology, I believe that students, researchers and
practicing engineers should be well equipped with the necessary theoretical
foundations for this technology, as well as acquiring the necessary skills in
applying this basic theory to a wide range of applications in optical
communications. There are of course many good books about optical
communication systems, but they seldom direct their readers to concentrate
on the two key aspects behind the success in optical communications which we
have discussed above. I am attempting to fill this gap with this book. I will be
concentrating on the basic theory of optical waveguides and semiconductor
laser technology, and I will illustrate how these two aspects are closely related
to each other. In particular, I will examine how semiconductor laser amplifiers
have been developed based on applications of the basic theory of these two
areas.
Throughout this book it is intended that the reader gains both a basic
understanding of optical amplification and a factual knowledge of the subject
based on device analysis and application examples. I hope that this book will
be beneficial to students aiming to study optical amplification, and to the active
researchers at the cutting edge of this technology.
PREFACE xiii
This book is organised as follows: Chapter 1 explores the state of the art of
optical fibre communication systems in this rapidly evolving field. A short
introduction includes the historical development, the principles and applica-
tions of semiconductor laser amplifiers in optical fibre communications, the
general optical system and the major advantages provided by this technology.
In Chapter 2 the basic principles and important performance characteristics of
optical amplifiers will be outlined. Chapter 3 gives an introduction to optical
amplification in semiconductor laser diodes. Chapters 4-6 deal with the
analysis of semiconductor laser amplifiers (SLAs). In these chapters the
waveguiding properties and the basic performance characteristics of SLAs (i.e.
amplifier gain, gain saturation and noise) will be studied. Also a new technique,
which is based on an equivalent circuit model, will be introduced for the
analysis of SLAs. The implications of SLAs for optical fibre communication
system performance will also be discussed. In Chapter 7 the accuracy and
limitations of the equivalent circuit model will be investigated by comparing
both theoretical and experimental results for actual devices. Finally, Chapter 8
is devoted to some concluding remarks and comments.
The book is referenced throughout by extensive end-of-chapter references
which provide a guide to further reading and indicate a source for those
equations and/or expressions that have been quoted without derivation.
The principal readers of this book are expected to be undergraduate and
postgraduate students who wish to consolidate their knowledge in lightwave
technology, and also researchers and practicing engineers who need to equip
themselves with the foundations to understand and use the continuing
innovations in optical communication technologies. The reader is expected
to be equipped with a basic knowledge of communication theory, electro-
magnetism and semiconductor physics.
Finally, I must emphasise that optical communications is a rapidly growing
technology with very active research. After reading the book I hope that the
reader will be equipped with the necessary skills to apply the most up-to-date
technology in optical communications.
Dr H. Ghafouri-Shiraz
December 1995, Birmingham, UK
ACKNOWLEDGEMENTS
I owe particular debts of gratitude to my former research student, Dr C. Y. J.
Chu, for bis excellent research work on semiconductor laser diode amplifiers. I
am also very grateful indeed for the many useful comments and suggestions
provided by reviewers which have resulted in significant improvements to this
book. Thanks also must be given to the authors of numerous papers, articles
and books which I have referenced while preparing this book, and especially to
those authors and publishers who have kindly granted permission for the
reproduction of some diagrams. I am also grateful to both my undergraduate
and research students who have helped me in my investigations. Finally, my
special thanks go to Jack Henderson, a former senior lecturer at the University
of Birmingham, who kindly reviewed the manuscript. Thanks also to Mr M. S.
Rodger for his excellent drawings.
Dr H. Ghafouri-Shiraz
December 1995, Birmingham, UK