LASER DIODE MODULATION AND NOISE

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> 5' O ft I o Vi LASER DIODE MODULATION AND NOISE K. Petermann lnstitutfiir Hochfrequenztechnik, Technische Universitdt Berlin Kluwer Academic Publishers i Dordrecht / Boston / London KTK Scientific Publishers / Tokyo

CONTENTS PREFACE xi Chapter 1 INTRODUCTION ' 1 Chapter 2 BASIC LASER CHARACTERISTICS 5 2.1 Double heterostructure characteristics 5 2.2 Direct and indirect semiconductors 7 2.2.1 Energy-and momentum conservation 7 2.2.2 Semiconductor materials for direct and indirect semiconductors 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 MODE SPECTRUM OF LASING EMISSION 59

vi Contents 3.1 Multimode rate equations 59 3.2 Spectral envelope for Fabry Perot-type lasers (linear gain) 61 3.3 Influence of nonlinear gain on the spectral characteristics 65 3.3.1 Symmetric 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 bandwidth 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 DIODES 119 5.1 Relation between intensity-modulation and frequency modulation 119 5.2 Current/frequency-modulation characteristics 122 5.3 Chirp effects in directly modulated laser diodes 125

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-bandwidth product of chirped pulses 128 5.3.4 Transmission of chirped pulses over single-mode fibres 131 5.4 Possibilities of modifying the chirp parameter a 135 5.4.1 Dispersion of the chirp parameter a 135 5.4.2 Chirp of laser diodes, coupled to optical cavities 136 References 141 Chapter 6 INSTABILITIES AND BISTABILITY IN LASER DIODES 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 CHARACTERISTICS OF SOLITARY LASER DIODES 15 2 7.1 Relative intensity noise (RIN) 152 7.1.1 Basic properties of noise signals 152 7.1.2 Definition and measurement of RIN 154 7.1.3 Requirement of RIN for intensity modulated systems 155 7.2 Introduction of the spontaneous emission noise 157 7.3 Intensity noise of laser diodes 160 7.3.1 Intensity noise of laser diodes by studying singlemode rate equations 160 7.3.2 Mode partition noise 163 7.3.3 Mode partition 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

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 singlemode 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 AND DISTORTIONS 214 8.1 Noise in interferometers 215 8.1.1 Complex degree of coherence s " 215 8.1.2 Interferometric 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 Modal 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 stabilization 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 of the time-dependent electric field 267 9.2.2 Modulation characteristics of external-cavity lasers 269 9.3 Laser diodes with distant reflections 271

Contents ix 9.3.1 Classification of feedback regimes 273 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 Tolerable feedback levels 282 References 285 Chapter 10 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 negative electronic feedback 294 References. 296 Chapter 11 CIRCUITRY FOR DRIVING THE LASER DIODE 298 11.1 Schemes for stabilizing the bias current 298 11.2 Laser drivers with optoelectronic integration 302 References 305 APPENDIX 306 INDEX 308

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