FREQUENCY MODULATION RESPONSE OF 「

FREQUENCY MODULATION RESPONSE OF 「

SEMICONDUCTOR LASERS AND OPTICAL FSK COMMUNICATION SYSTEM S

by

SANDEEP DILWALI

Department of Electrical Engineering

刀柾汚盾 ^SUB ルガ ^T た ^D

IN FULFILMENT OF THE REQUIRE相匠NTS FOR かだ DEGREE OF

DOCTOR OF PHILOSOPHY

to the

INDIAN INSTITUTE OF TECHNOLOGY, DELHI IND!A

I 992

Dedicated to

my wife,Sun ita and

our children

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CERTIF.

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This s to certi

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that the thesis entitied

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'FREQUENCY MODULATION RESPONSE OF SEMICONDUCTOR LASERS AND OPTICAL FSK COMMUNICATION SYSTEMS",which is being submitted by SANDEEP DILWALI to the Department of

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ee trica] Engirieerin

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Indian Institute of Technoiog

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Delhi, in fulfi

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^{men t} foi

・

the award of the degree of Doctor of Philosophy, is a bonafide i

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^{ecord of} the reseax

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ch work cai

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ⁱ

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led out by him under my su pez

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vision and guidance. He has fu

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filled all the require

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>ents foi

・

the submission of the thesis, which has reached the requisite s

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^{n dard.}

The results con

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in ed in this thesis have not been submitted in any foi

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m to any other Univez'sitj

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or Institute for awai

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Dr. G. SOUNDRA PANDIAN Asst. Professor

Departme nt of Electrical Engineerin g Indian Institute of Technology, Delhi India

ACKNOWLEDGEMENTS

I wish to express my profound gratitude and indebtedness to Dr. G. SOUNDRA PANDIAN, Asst. Professor in the Department of Electrical Engineering for his perfect supervision and endless patience without which this research work would not have been possible.

I am also grateful to Professor S. N. Gupta for providing aft the laboratory facilities for the experimental work. I would like to thank Professor Fl.M. Gupta and Professor S.C. Dutta Roy for the stimulating discussions and encouragement.

I am thankful to Mr. A.P. Thukral, Mr. J.P. Nautiyal, Mrs. N. Asija and Mr. Verabhadra Sastry for all their help in the Optical Communication Lab. A very special thanks is due to my colleague Mr. Vikram Gadre for all the help rendered by hirn.

The re8earch programme was sponsored by the Indian Army, and I am greatly indebted to the Indian Army for encouraging me to take up this challenge and for all the support provided. I would especially like to acknowledge the encouragement and moral support given by Maj Gen J.S. Ahiuwalia, Maj Gen I. Krishnan, Brig S.C. Bahuguna and Col Mahendra Kumar.

il

Mr. R.E. Epworth of STC Technology Ltd. (now BNR Europe) is thanked for suggesting to study a possible application of the FORH for optica' fiber equalization. Dr. Hadjifotiou and Mr. J. Xing of STC Technology Ltd. (now BNR Europe) are a'so thanked for their help in donating an optical fiber directional coupler.

Finally, the patient understanding and cooperation extended by my wife Sunit.a, and my children Sahil, Sagar, and Sonam are gre

吐

ly appreciated.

eep Dfiwafr

August 1992

Department of Electrical Engineering lIT, New Delhi

月

BSTR

^月

CT

A theoretical expression for the transfer function of the thermal FM response of laser diodes is given, that is in excellent agreement with the experimentally measured FM response and agrees in general with an empirical expression reported earlier in the literature. The characteristic dip in the FM response and the time-domain step-response of the laser frequency are analyzed theoretically as a function of a thermal cutoff frequency and the ratio of thermal FM at dc to the carrier FM at dc. Fromn the step response analysis, the lower bound on the bitrate for penalty-free AMI-FSK transmission is derived which tallies well with the experimental observations.

A theory given in the literature for the equalization of FM response using passive RC ladder networks is questioned. It is shown that if an additional low-pass filter is used along with the suggested RC ladder network, an acceptable equalization is possible at low bit rates less than the frequency at which the FM phase angle becomes 900.

A novel method of equalizing the FM response of a laser diode is proposed for optical FSK transmission. It is shown that a complete equalization is possible when the ratio of thermal FM to carrier FM at dc,β

，

is less than 1. Whenβ

と

i,it is theoretically ot possible to achieve a 100% equalization, since an ideal equalizing filter required in this case represents an unstable system. However, an approximate equalization is proposed forβ

と

1. A closed

X

loop system with an RC transmission line is proposed as an equalizing filter forβ

く

i and a low-pass filter cum adder circuit

お

^rβ

と

i. The low-pass filter cum adder circuit is useful at higher bit rates gre

吐

er than the frequency at which the laser FM phase response is 90. For lower bit rates, the low-pass filter cum ladder network is desirable.

A bit-error-rate (BER) analysis for two types of optical FSK transmission systems using a Mach-Zehnder interferometer as a discriminator is done. In one case the discriminator is assumed to be kept on the transmitter side and in the second case, on the receiver side, The analysis takes into account the linewidth of the source and other noises in the system. The discriminator disperses the input pulse, and an optimum fi

比

er required to produce a raised cosine output pulse spectrum is proposed. Such an optimum filter gives the minimum noise bandwidth without causing any ISI at the decision instant. The values of the equivalent noise-bandwidth factors '2 and 1 , of the filter vary between 0.563 to 0.822 and 0.086 to 0.193, respectively, when the interferometer delay time

て

is varied from zero to bit time. BER curves are given for various conditions of the FSK systems. To avoid an error floor the linewidth of the source should be less than 0.01/t .

When s

血

bilising a fiber optic Mach-Zehnder interferometer using a PZT the maximum possible closed ioop bandwidth is limited by the resonance frequency of the PZT. A PZT control circuit using a current source drive is proposed

xi

that gives an improved control bandwidth when compared to a vol

切

^{ge source} drive. Equations are given to select the parameters of the system to get an optimum second order response, along

柳

th experimental results.

Results of a theoretical simulation on the dynamic response of a dispersion equalizing scheme employing a ring resonator are given, when transmitting chirped Gaussian optical pulses over a long distance fiber. It is shown that two pulses which merge into each other due to dispersion are recovered by the resonator. The selection of the optimum resonator parameters in relation to the overall response is described.

xii

C 〇 NTENTS

CERTI

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WATE

ACKNOWLEDGEM

勇四

rTs ABS7沢ACT

Chapter 1

1よ つ一 IA Iよ

INTRODUCTION INTRODUCTION

HISTORICAL BACKGROUND AND IDENTIFICATION OF RESEARCH

・ ・

PROBLEMS

1.3 STATEMENT OF AIMS OF THE WORK 1.4 STATUS OF THE WORK

1.5 ORGANIZATION OF THE THESIS

Chapter 2

FM RESPONSE OF LASER DIODES 2.1 INTRODUCTION

2.2 THERMAL FM RESPONSE OF LASER DIODES 2.2.1 Empirical Equation for the Thermal FM 2.2.2 Derivation for the Thermal FM Response at

Frequencies Close to DC

2.2.3 Derivation for the Thermal FM Transfer Function 2.3 CARRIER INDUCED FM RESPONSE

lo

1上 つム つ」 一」 11 『 1

11 咽1 一hU 喝1 1上 2

つ一

8 りム つ」 OU 1ょ 4一つ一 qV CJ d昌 1ょ つ」 JサっV d一 d昌 d一 一1

ロ」 d昌 d一

51 2.4 DIP IN THE FM RESPONSE

2.5 ESTIMATION OF fc AND (3 FROM THE EXPERIMENTAL FM RESPONSE

2.6 COMPARISON OF THEORY WITH EXPERIMENTAL RESULTS 2.7 SIMPLIFIED EXPRESSION FOR THE THERMAL FM RESPONSE 2.8 ELECTRICAL EQUIVALENT CIRCUIT FOR THE THERMAL FM

RESPONSE

2.9

FSK STEP RESPONSE

2.10

LOWER BOUND ON THE BIT RATE FOR PENALTY FREE OPERATION

2.11

CONCLUSION APPENDIX 2.1

Chapter 3

COMMENT ON PASSIVE EQUALIZATION OF THE FM RESPONSE OF LASER DIODES REPORTED IN THE LITERATURE

3.1 INTRODUCTION

3.2 PROOF THAT PASSIVE NETWORKS CANNOT GIVE COMPLETE EQUALIZATION WHENβ

と

I

3.3 PROOF THAT A HIGH PASS NETWORK DOES NOT GIVE AN EQUALIZATION

3.4 PASSIVE EQUALIZATION SCHEME BASED ON LADDER NETWORKS 53 3.5 PULSERESPONSE OF AN EQUALIZATION SCHEME BASED ON AN 65

RC LADDER NETWORK FOLLOWED BY A LOW一PASS FILTER

3.6 COMMENTS ON THE THEORY OF FM EQUALIZATION 77 PROPOSED IN [59]

1よ つ山 一D S り

U Jり 一D lb

3.7 CONCLUSION APPENDIX 3.1 APPENDIX 3,2 APPENDIX 3.3

n一 1よ 一D S 8 8 8 8

Chapter 4

NOVEL SCHEMES FOR EQUALIZATION OF THE FM RESPONSE OF A LASER DIODE

4.1 INTRODUCTION 91

4.2 IDEAL EQUALIZATION OF THE FM RESPONSE WHENβ

く

ⁱ 92 4.3 IDEAL EQUALIZATION OF THE FM RESPONSE WHENβ

と

^{1 99}

4.4 COMPARISON OF EQUALIZING SCHEMES 106

4.5 CONCLUSION 107

Chapter 5

BER ANALYSIS ON OPTICAL DIRECT DETECTION P5K TRANSMISSION SYSTEMS USING A MACH-ZEHNDER rNTERFEROMETER AS A DISCRIMINATOR

INTRODUCTION

・

・

DESCRIPTION OF BLOCK DIAGRAM OF THE SYSTEM PULSE RESPONSE OF THE SYSTEM

、

・

OPTIMUM RAISED COSINE FILTER 5.5 NOISE ANALYSIS

6 7 5 5 BER ANALYSIS

CONCLUSION

109 ilo 112 115 118 i 18 i 24

vi

11 0一 6 6 qU 4 ・ ・

一O rU

6.5

Chapter 6

OPTICAL PHASE STABILIZATION OF A MACH-ZEHNDER INTERFEROMETER USING A PZT WITH A PROVISION TO LOCK TO THE CENTER

INTRODUCTION

・ ・

PROPOSED SYSTEM

6.2.1 Open Loop Transfer Function

6.2.2 Reduction of the Spurious Resonance Gain

Below Unity: Comparison of the Current Source Drive and the Voltage Source Drive.

6.2.2.1 Selection of the Low-Pass Filter i 38

6.2.3 Closed Loop Transfer Function 139

6.2.3.1 Sinewave Response 141

6.2.3.2 Root Locus Plot 143

6.2.3.3 Step Response 145

METHOD OF SELECTING SYSTEM PARAMETERS 148

CONTROLLING THE OPERATING FRINGE 149

CONCLUSION 159

i 25 i 27 i 32 i 36

vil

Chapter 7

OPTICAL EQUALIZATION OF FIBER DISPERSION BASED ON AN OPTICAL RESONATOR

7.1 INTRODUCTION

7.2 DESCRIPTION OF THE OPTICAL RESONATOR

7,3 DERIVATION FOR THE ELECTRIC FIELD AT THE OUTPUT OF FIBER

OPTICAL SIGNAL AT THE OUTPUT OF RESONATOR 7.4.1 Electric Field at the Output of Resonator

7.4.2 Electric Field at the Output of Resonator for Chirped 173 Pulses

・ ●

DERIVATION FOR THE ELECTRIC FIELD AT THE OUTPUT OF 175 FIBER FOR TWO PULSES

7.6 CONCLUSION 176

APPENDIX 7.1 179

4 5 け1 り1

161 162 168

170 170

Chapter 8

CONCLUSION

8.1 MAJOR ACHIEVEMENTS 182

8.2 SUGGESTIONS FOR FUTURE WORK 184

PUBLISHED WORK OUT OF THE PRESENT THESIS 187

REFERENCES 188

BIOGRAPHY 223