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ANALOG OPTICAL LINKS

Analog Optical Links presents the basis for the design of analog links.

Following an introductory chapter, there is a chapter devoted to the de￾velopment of the small signal models for common electro-optical com￾ponents used in both direct and external modulation. However, this is not

a device book, so the theory of their operation is discussed only insofar

as it is helpful in understanding the small signal models that result. These

device models are then combined to form a complete link. With these

analytical tools in place, a chapter is devoted to examining in detail each

of the four primary link parameters: gain, bandwidth, noise figure and

dynamic range. Of particular interest is the inter-relation between device

and link parameters. A final chapter explores some of the tradeoffs among

the primary link parameters.

Charles H. Cox, III Sc.D., is one of the pioneers of the field that is

now generally referred to as analog or RF photonics. In recognition of

this work he was elected a Fellow of the IEEE for his contributions to the

analysis, design and implementation of analog optical links. Dr. Cox is

President and CEO of Photonic Systems Inc., which he founded in 1998.

He holds six US patents, has given 45 invited talks on photonics and has

published over 70 papers on his research in the field of phototonics.

ANALOG OPTICAL LINKS

Theory and Practice

CHARLES H. COX, III

cambridge university press

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press

The Edinburgh Building, Cambridge cb2 2ru, UK

First published in print format

isbn-13 978-0-521-62163-2

isbn-13 978-0-511-19562-4

© Cambridge University Press 2004

2004

Information on this title: www.cambridge.org/9780521621632

This publication is in copyright. Subject to statutory exception and to the provision of

relevant collective licensing agreements, no reproduction of any part may take place

without the written permission of Cambridge University Press.

isbn-10 0-511-19562-1

isbn-10 0-521-62163-1

Cambridge University Press has no responsibility for the persistence or accuracy of urls

for external or third-party internet websites referred to in this publication, and does not

guarantee that any content on such websites is, or will remain, accurate or appropriate.

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

hardback

eBook (NetLibrary)

eBook (NetLibrary)

hardback

To Carol

and

to the memory of Charles H. Cox, Jr. and John A. Hutcheson,

whose combined influences on me defy measure or acknowledgement

Contents

Preface page xi

1 Introduction 1

1.1 Background 1

1.2 Applications overview 8

1.2.1 Transmit optical links 8

1.2.2 Distribution optical links 9

1.2.3 Receive optical links 11

1.3 Optical fibers 12

References 17

2 Link components and their small-signal electro-optic models 19

2.1 Introduction 19

2.1.1 Notation 20

2.2 Modulation devices 20

2.2.1 Direct modulation 20

2.2.2 External modulation 34

2.3 Photodetectors 49

Appendix 2.1 Steady state (dc) rate equation model for

diode lasers 54

Appendix 2.2 Absorption coefficient of an electro-absorption

modulator 63

References 63

3 Low frequency, short length link models 69

3.1 Introduction 69

3.2 Small-signal intrinsic gain 70

3.2.1 Direct modulation 72

3.2.2 External modulation 74

3.3 Scaling of intrinsic gain 75

vii

viii Contents

3.3.1 Optical power 75

3.3.2 Wavelength 79

3.3.3 Modulation slope efficiency and photodetector

responsivity 81

3.4 Large signal intrinsic gain 82

Appendix 3.1 External modulation links and the Manley–Rowe

equations 87

References 88

4 Frequency response of links 91

4.1 Introduction 91

4.2 Frequency response of modulation and photodetection devices 93

4.2.1 Diode lasers 93

4.2.2 External modulators 98

4.2.3 Photodetectors 105

4.3 Passive impedance matching to modulation and photodetection

devices 110

4.3.1 PIN photodiode 112

4.3.2 Diode laser 117

4.3.3 Mach–Zehnder modulator 129

4.4 Bode–Fano limit 138

4.4.1 Lossy impedance matching 139

4.4.2 Lossless impedance matching 142

Appendix 4.1 Small signal modulation rate equation model for

diode lasers 152

References 156

5 Noise in links 159

5.1 Introduction 159

5.2 Noise models and measures 160

5.2.1 Noise sources 160

5.2.2 Noise figure 167

5.3 Link model with noise sources 168

5.3.1 General link noise model 168

5.3.2 RIN-dominated link 169

5.3.3 Shot-noise-dominated link 173

5.4 Scaling of noise figure 178

5.4.1 Impedance matching 179

5.4.2 Device slope efficiency 180

5.4.3 Average optical power 182

5.5 Limits on noise figure 185

5.5.1 Lossless passive match limit 185

Contents ix

5.5.2 Passive attenuation limit 187

5.5.3 General passive match limit 189

Appendix 5.1 Minimum noise figure of active and passive networks 196

References 199

6 Distortion in links 201

6.1 Introduction 201

6.2 Distortion models and measures 202

6.2.1 Power series distortion model 202

6.2.2 Measures of distortion 205

6.3 Distortion of common electro-optic devices 217

6.3.1 Diode laser 217

6.3.2 Mach–Zehnder modulator 222

6.3.3 Directional coupler modulator 225

6.3.4 Electro-absorption modulator 227

6.3.5 Photodiode 228

6.4 Methods for reducing distortion 232

6.4.1 Primarily electronic methods 233

6.4.2 Primarily optical methods 240

Appendix 6.1 Non-linear distortion rate equation model for

diode lasers 249

References 259

7 Link design tradeoffs 263

7.1 Introduction 263

7.2 Tradeoffs among intrinsic link parameters 263

7.2.1 Direct modulation 263

7.2.2 External modulation 268

7.2.3 SNR vs. noise limits and tradeoffs 273

7.3 Tradeoffs between intrinsic link and link with amplifiers 277

7.3.1 Amplifiers and link gain 277

7.3.2 Amplifiers and link frequency response 278

7.3.3 Amplifiers and link noise figure 278

7.3.4 Amplifiers and link IM-free dynamic range 279

References 284

Index 285

Preface

In the preface I think it is better if I abandon the formality of the text and address

you the reader, directly.

As I hope you will have gathered from the title, this is a book that attempts to

lay out the basis for the design of analog optical links. Let me give an example

that should drive home this point. It is customary in books on lasers to start with

an extensive presentation based on the rate equations (do not worry at this point

if you do not know what these are). In this book we also discuss lasers, but the

rate equations are relegated to an appendix. Why? Because in over 15 years of

link design, I have never used the rate equations to design a link! So why all the

emphasis on the rate equations in other texts? Probably because they are targeted

more to, or at least written by, device designers. The view in this book is that you

are a user of devices, who is interested in applying them to the design of a link. Of

course to use a device most effectively, or even to know which device to choose for

a particular link design, requires some knowledge of the device, beyond its terminal

behavior. To continue the laser example, it is important to know not only what the

laser frequency response is, but also how it changes with bias. Hence my intent was

to include sufficient information for you to use various electro-optic devices, but

not enough information to design such devices.

This book is written as an introduction to the field of link design. This was an

easy choice, since, to my knowledge, there are no other books exclusively covering

this topic. In the early days, once the device design was complete, link “design”

consisted simply of connecting a couple of the appropriate devices together with

an optical fiber. However, such links always had performance that was found lack￾ing when evaluated using any one of a number of figures of merit. The traditional

approach to overcome these shortcomings was to augment the link with pre- and/or

post-amplifiers. These amplifiers did improve some aspects of the performance; no￾tably the amplifier gain could overcome the link loss. But these amplifiers introduced

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their own tradeoffs that complicated the task of the system designer. Further, they

obscured for the device designer the impacts on link performance that improved

devices would have.

Hence there emerged the need to evaluate the tradeoffs among device, link and

system parameters of an intrinsic link, i.e. one without amplifiers. This is the best I

can do to define what I mean by link design. Of course to do this I needed some sort

of analytical framework. There are lots of analytical tools I could have used for this.

Given my background in electrical engineering, I chose to apply the incremental,

or small-signal, modeling approach that has been so successfully applied to the

analysis of electronic components, such as diodes, transistors, etc.

To my surprise, the introduction of the incremental modeling approach to link

design permitted design insights that are easy to overlook when you take a purely

device-oriented view. For example, an early demonstration of the impact of the

small-signal link design approach showed that – with proper link design – it was

possible to eliminate high link loss, in the sense of RF out vs. RF in, without

any change in the devices used. This is but one, albeit dramatic, example of the

power of this approach. Hence, once you have worked your way through this

text, you will be equipped with a systematic basis for evaluating link designs and

for understanding the tradeoffs among device, link and system parameters. This

is becoming increasingly important as link designers are pressed to extract the

maximum performance for the minimum cost.

I have tried to write this book so that it would be accessible to three groups

of readers: electrical engineers, who usually do not know much about photonics;

device designers, who typically have more of a physics background that does not

include much about electrical engineering; and system designers, who need a more

in-depth understanding of the relationship between these areas. Take as an example

Chapter 2, which covers electro-optic devices and their incremental or small-signal

models. Those of you who have an electrical engineering background can skim the

incremental modeling parts of this chapter, and focus more on the aspects of the

electro-optic devices. Conversely, those with a device background will likely skim

the device descriptions and focus more on the incremental modeling discussions.

Those of you with a systems perspective may focus on the limits of link performance

in terms of device parameters.

Another dimension of the accessibility space is the familiarity of the reader with

the field. Those of you who are new to the field (and we need all the new blood

we can in this field!) are likely to want to get the basics down – which also tend

to have general applicability – before tackling the more advanced topics – which

often are of interest only in specific applications. As a guide to which sections you

might want to skip on a first reading, I have prepared the following table.

Preface xiii

Introductory Advanced/Reference

Chapter 1 – all

Chapter2– all except as listed at right Sections 2.2.1.2, 2.2.1.3, 2.2.2.2, 2.2.2.3

Chapter 3 – all

Chapter4– all except as listed at right Section 4.4

Chapter5– all except as listed at right Section 5.5

Chapter6– all except as listed at right Sections 6.3.3, 6.3.4, 6.4

Chapter 7 – all

Those new to the field would also probably want to skip all the appendices on a

first reading.

As for background, I have tried to make this book as self-sufficient as possible,

while keeping it to a reasonable length. Where more background was needed than

was feasible to include, I have given you references that can provide the needed

information. I would think that if you have the background equivalent to a senior

level in electrical engineering, you should be able to follow the majority of material

in this book. Those with a background equivalent to a senior level in physics should

also be able to follow most of the text, with perhaps the exception of the frequency

response models of Chapter 4.

I would like to begin the acknowledgements by thanking all the members of

the microwave photonics community. Their numerous questions over the years, not

only of me but of others whom they have asked at conferences, have been invaluable

in sharpening my own understanding of this material.

When this incremental modeling approach was first published, it generated some

controversy, primarily because of the predictions of link RF power gain. How￾ever, there were two people who understood this approach then and have been

instrumental in guiding my thinking of it over the years: hence my deep apprecia￾tion to Professors William (Bill) Bridges of the California Institute of Technology

(Caltech) and Alwyn Seeds of University College London.

Several colleagues graciously agreed to read through an early draft of the entire

manuscript and offered numerous helpful suggestions; thanks to Professors Bill

Bridges, Caltech, Jim Roberge, MIT and Paul Yu, UCSD. I would also like to thank

Professor Paul Yu who used an early draft of the manuscript in teaching his course

on electro-optics at UCSD. Several other colleagues read specific chapters and

offered helpful comments as well; thanks to Ed Ackerman of Photonic Systems,

Chapters 5 and 7; Gary Betts of Modetek, Chapter 6; Harry Lee of MIT, rate

equation appendices and Joachim Piprek of UCSB, Chapter 2. Thanks to Joelle

Prince and Harold Roussell, both of Photonic Systems, for designing several of

xiv Preface

the experimental links and taking the data that are reported in this text. I appreciate

the help of Ed Ackerman, who read through the entire proof copy of the manuscript,

and with red pen at the ready, offered numerous suggestions. Ed also proved to

be a wonderful sounding board to test presentation ideas before they were fully

developed. Thanks also to John Vivilecchia now at MIT Lincoln Laboratory, for

his help with early versions of some of the figures. And finally thanks to my wife

Carol, for all her patience and support, as always.

It is a pleasure to acknowledge the staff at Cambridge University Press with

whom it has been a delight to work; primary among them are Philip Meyler, Simon

Capelin, Carol Miller and Margaret Patterson.

It seems that every time I glance through the manuscript I find another item

I wish I could change. Hence I have no illusions, despite all the expert advice I

have received, that the present version is “perfect” in any respect. Thus I would

appreciate hearing from you with comments, suggestions and corrections. Any

errors that remain are my responsibility alone.