noise in laser

8/11/2019 Noise in Laser

1/6

5'

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LASER

D I O D E

M O D U L A T I O N

AND NOISE

K. Petermann

lnstitutfiirHochfrequenztechnik

e hnis heUn iversitdt Berlin

Kluwer Academ ic Publishers i

Dordrecht / Boston / London

KTK Scientific Publishers / Tokyo


2/6

CONTENTS

PREFACE xi

Chapter 1

INTRODUCTION ' 1

Chapter 2

BASIC LASER CHA RAC TERISTICS 5

2.1 Double heterostructure characteristics 5

2.2 Direct and indirect semiconductors 7

2.2.1 En ergy -and mom entum conservation 7

2.2.2 Sem iconductor materials for direct and indirect semi-

conductors 8

2.3 Emission and absorption 10

2.3.1 Density of photon oscillation states 11

2.3.2 Principal mechanisms of radiative transitions 12

2.3.3 Carrier lifetime and lifetime of spontaneous emission 15

2.3.4 Gain and stimulated emission 18

2.4 Lasing characteristics of Fabry Perot-type lasers 25

2.4.1 Lasing conditions 25

2.4.2 Dynamic characteristics of laser operation 28

2.4.3 Light current characteristics, threshold current and

quantum efficiency 32

2.4.4 Basic laser structures 36

2.4.5 Modifications for the spontaneous emission term 41

2.5 Dynamic single-mode laser structures 44

2.5.1 DFB laser characteristics 47

References 52

Chapter 3

LONGITUDINAL M OD E SPECTRUM OF LASING EMISSION 59


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vi Contents

3.1 Multimode rate equations 59

3.2 Spectral envelope for Fabry Perot-type lasers (lineargain 61

3.3 Influence of nonlinear gain on the spectral characteristics 65

3.3.1 Symm etric nonlinear gain 65

3.3.2 Asymmetric nonlinear gain 69

3.3.3 Nonlinear gain, conclusions 75

References 76

Chapter 4

INTENSITY-MODULATION CHARACTERISTICS OF

LASER DIODES 78

4.1 Modulation characteristics by studying single-mode rate

equations 78

4.1.1 Turn-on delay 81

4.1.2 Rate equations, small signal analysis 83

4.1.3 Relaxation oscillation damping 86

4.1.4 Upper limits for the modulation bandwidth of laser

diodes 88

4.2 Influence of lateral carrier diffusion on relaxation oscillation

damping 91

4.3 Modulation bandw idth limits due to parasitic elements 93

4.4 Examples for high speed modulation of laser diodes 95

4.5 Modulation and longitudinal mode spectrum 97

4.5.1 Transient spectra of laser diodes 98

4.5.2 Lasing spectra under high speed modulation 100

4.5.3 Dynamic single-mode condition 105

4.6 Modulation with binary signals 106

4.7 Harmonic and intermodulation distortions (without fibre

interaction) 108

4.7.1 Harmonic and intermodulation distortions for low

modulation frequencies 109

4.7.2 Harmonic and intermodulation distortions for high

modulation frequencies 113

References 114

Chapter 5

FREQUENCY-MODULATION CHARACTERISTICS OF

LASER DIOD ES 119

5.1 Relation between intensity-modulation and frequency modu-

lation 119

5.2 Current/frequency-modulation characteristics 122

5.3 Ch irp effects in directly modulated laser diodes 125


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Contents vii

5.3.1 Spectral line broadening due to laser chirping 125

5.3.2 Chirp-reduction by proper pulse shaping 127

5.3.3 Time-bandw idth product of chirped pulses 128

5.3.4 Transmission of chirped pulses over single-mode fibres 131

5.4 Possibilities of modifying the chirp param eter

a

135

5.4.1 Dispersion ofthechirp parameter a 135

5.4.2 Chirp of laser diodes, coupled to optical cavities 136

References 141

Chapter 6

INSTABILITIES AN D BISTABILITY IN LAS ER DIOD ES 145

6.1 Repetitive self-pulsations due to lateral instabilities 146

6.2 Instability and bistability in laser diodes with segmented

contacts 147

References 150

Chapter 7

NOISE CHAR ACTERISTICS O F SOLITARY LASER DIOD ES 15 2

7.1 Relative intensity noise RIN) 152

7.1.1 Basic proper ties of noise signals 152

7.1.2 Definition and measurement of

R IN

154

7.1.3 Requirement ofRIN for intensity modulated systems 155

7.2 Introduction ofthespontaneous emission noise 157

7.3 Intensity noise of laser diodes 160

7.3.1 Intensity noise of laser diodes by studying single-

mode rate equations 160

7.3.2 Mode partition noise 163

7.3.3 Mode par tition noise analysis for nearly single-mode

lasers 166

7.3.4 Mode-hopping noise 170

7.3.5

1// intensity

noise 172

7.4 Statistics of intensity noise 173

7.4.1 Statistics of amplified spontaneous emission 176

7.4.2 Probability density distribution for the total laser light

output 180

7.4.3 Statistics of mode partition noise 181

7.4.4 Turn-on jitter in laser diodes 184

7.5 Mode partition noise for the transmission of pulse-code

modulated (PCM)-signals 186

7.5.1 Multimode lasers 186

7.5.2 The mode partition coefficient A: 192

7.5.3 Nearly single-mode lasers 194


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viii Contents

7.6 Phase and frequency noise 196

7.6.1 Phase and frequency noise characterization in general 196

7.6.2 Spectral line shape for white frequency noise 198

7.6.3 Spectral line shape for

1// frequency

noise 200

7.6.4 Frequency noise and spectral linewidth for single-

mode laser diodes 202

7.6.5 Power-independent contribution to the linewidth of

laser diodes 205

7.6.6 Correlation between FM-noise and AM -noise 207

References 208

Chapter 8

NOISE IN INTERFEROMETERS INCLUDING MODAL

NOISE AN D DISTORTIONS 214

8.1 Noise in interferometers 215

8.1.1 Complex degree of coherence

s

215

8.1.2 Interferom etric noise analysis for single-mode lasers 216

8.1.3 Interferometric set-ups for measuring the linewidth

and the degree of coherence 224

8.1.4 Interferometric noise analysis for multimode lasers 227

8.2 Modal noise 232

8.2.1 Modal noise for monochromatic light sources 233

8.2.2 Modal noise for single-mode lasers with finite spectral

linewidth 238

8.2.3 Modal noise for multimode laser diodes 242

8.2.4 Modal distortions 243

8.3 M odal noise and distortions in single-mode fibres 243

References 246

Chapter 9

SEMICONDUCTOR LASERS WITH OPTICAL FEEDBACK 250

9.1 Amplitude and phase conditions for laser diodes with

external cavities 251

9.1.1 Short external reflectors for longitudinal mode stabili-

zation 256

9.1.2 Emission frequency shifts due to optical feedback 258

9.1.3 Single external cavity mode condition 259

9.1.4 Spectral linewidth for laser diodes with external

optical feedback 261

9.2 Dynamics of laser diodes with external reflections 267

9.2.1 Derivation ofthetime-dependent electric field 267

9.2.2 Modulation characteristics of external-cavity lasers 269

9.3 Laser diodes with distant reflections 271


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Contents ix

9.3.1 Classification of feedback regimes 27 3

9.3.2 Phase and frequency noise of laser diodes with distant

reflectors 275

9.3.3 Intensity noise in laser diodes with distant reflectors 276

9.3.4 Coherence collapse 279

9.3.5 Tolerab le feedback levels 282

References 285

Chapter 1

LASER DIODES WITH NEGATIVE ELECTRONIC

FEEDBACK 291

10.1 Modulation characteristics of laser diodes with negative

electronic feedback 291

10.2 Linewidth narrowing and phase noise reduction with nega-

tive electronic feedback 294

References . 296

Chapter 11

CIRCUITRY FOR DRIVING TH E LASER DIOD E 298

11.1 Schemes for stabilizing the bias current 298

11.2 Laser drivers with optoelectron ic integration 302

References 305

APPENDIX 306

INDEX 308

noise in laser

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