List of Contributors XVII

Part I Nanostructured Devices 1

1 Modeling Quantum-Dot-Based Devices 3
Kathy Lüdge

1.1 Introduction 3

1.2 Microscopic Coulomb Scattering Rates 4

1.2.1 Carrier–Carrier Scattering 5

1.2.2 Detailed Balance 8

1.3 Laser Model with Ground and Excited States in the QDs 9

1.3.1 Temperature Effects 14

1.3.2 Impact of Energy Confinement 15

1.3.3 Eliminating the Excited State Population Dynamics 17

1.4 Quantum Dot Switching Dynamics and Modulation Response 18

1.4.1 Inhomogeneous Broadening 19

1.4.2 Temperature-Dependent Losses in the Reservoir 20

1.4.3 Comparison to Experimental Results 20

1.5 Asymptotic Analysis 21

1.5.1 Consequences of Optimizing Device Performance 25

1.6 QD Laser with Doped Carrier Reservoir 26

1.7 Model Reduction 28

1.8 Comparison to Quantum Well Lasers 29

1.9 Summary 30

Acknowledgment 30

References 30

2 Exploiting Noise and Polarization Bistability in Vertical-Cavity Surface-Emitting Lasers for Fast Pulse Generation and Logic Operations 35
Jordi Zamora-Munt and Cristina Masoller

2.1 Introduction 35

2.2 Spin-Flip Model 39

2.3 Polarization Switching 40

2.4 Pulse Generation Via Asymmetric Triangular Current Modulation 44

2.5 Influence of the Noise Strength 48

2.6 Logic Stochastic Resonance in Polarization-Bistable VCSELs 49

2.7 Reliability of the VCSEL-Based Stochastic Logic Gate 52

2.8 Conclusions 53

Acknowledgment 54

References 54

3 Mode Competition Driving Laser Nonlinear Dynamics 57
Marc Sciamanna

3.1 Introduction 57

3.2 Mode Competition in Semiconductor Lasers 58

3.3 Low-Frequency Fluctuations in Multimode Lasers 61

3.4 External-Cavity Mode Beating and Bifurcation Bridges 64

3.5 Multimode Dynamics in Lasers with Short External Cavity 65

3.6 Polarization Mode Hopping in VCSEL with Time Delay 67

3.6.1 Polarization Switching Induced by Optical Feedback 67

3.6.2 Polarization Mode Hopping with Time-Delay Dynamics 69

3.6.3 Coherence Resonance in a Bistable System with Time Delay 71

3.7 Polarization Injection Locking Properties of VCSELs 73

3.7.1 Optical Injection Dynamics 74

3.7.2 Polarization and Transverse Mode Switching and Locking: Experiment 76

3.7.3 Bifurcation Picture of a Two-Mode Laser 81

3.8 Dynamics of a Two-Mode Quantum Dot Laser with Optical Injection 83

3.9 Conclusions 85

Acknowledgments 86

References 86

4 Quantum Cascade Laser: An Emerging Technology 91
Andreas Wacker

4.1 The Essence of QCLs 92

4.1.1 Semiconductor Heterostructures 92

4.1.2 Electric Pumping 94

4.1.3 Cascading 94

4.2 Different Designs 96

4.2.1 Optical Transition and Lifetime of the Upper State 96

4.2.2 Effective Extraction from the Lower Laser Level 96

4.2.3 Injection 97

4.3 Reducing the Number of Levels Involved 98

4.4 Modeling 100

4.5 Outlook 103

Acknowledgments 104

4.6 Appendix: Derivation of Eq. (4.1) 104

References 105

5 Controlling Charge Domain Dynamics in Superlattices 111
Mark T. Greenaway, Alexander G. Balanov, and T. Mark Fromhold

5.1 Model of Charge Domain Dynamics 112

5.2 Results 117

5.2.1 Drift Velocity Characteristics for ? = 0?, 25?, and 40? 118

5.2.2 Current–Voltage Characteristics for ? = 0?, 25?, and 40? 119

5.2.3 I(t) Curves for ? = 0?, 25?, and 40? 120

5.2.4 Charge Dynamics for ? = 0?, 25?, and 40? 122

5.2.5 Stability and Power of I(t) Oscillations for 0? < ? <</i>90? 128

5.2.6 Frequency of I(t) for 0? < ? <</i>90? 130

5.3 Conclusion 132

Acknowledgment 132

References 132

Part II Coupled Laser Device 137

6 Quantum Dot Laser Tolerance to Optical Feedback 139
Christian Otto, Kathy L¨udge, Evgeniy Viktorov, and Thomas Erneux

6.1 Introduction 139

6.2 QD Laser Model with One Carrier Type 141

6.3 Electron-Hole Model for QD Laser 142

6.3.1 Similar Scattering Times te and th 143

6.3.2 Different Scattering Times te and th 144

6.3.3 Small Scattering Lifetime of the Holes a = O(1) 144

6.3.4 Very Small Scattering Lifetime of the Holes a = O(? -1/2) 144

6.4 Summary 145

Acknowledgment 146

6.5 Appendix A: Rate Equations for Quantum Well Lasers 146

6.6 Appendix B: Asymptotic Analysis for a QD Laser Model with One Carrier Type 148

6.7 Appendix C: Asymptotic Analysis for a QD Laser Model with Two Carrier Types 153

References 158

7 Bifurcation Study of a Semiconductor Laser with Saturable Absorber and Delayed Optical Feedback 161
Bernd Krauskopf and Jamie J. Walker

7.1 Introduction 161

7.2 Bifurcation Analysis of the SLSA 164

7.3 Equilibria of the DDE and Their Stability 168

7.4 Bifurcation Study for Excitable SLSA 171

7.5 Bifurcation Study for Nonexcitable SLSA 173

7.6 Dependence of the Bifurcation Diagram on the Gain Pump Parameter 176

7.7 Conclusions 178

References 179

8 Modeling of Passively Mode-Locked Semiconductor Lasers 183
Andrei G. Vladimirov, Dmitrii Rachinskii, and Matthias Wolfrum

8.1 Introduction 183

8.2 Derivation of the Model Equations 184

8.3 Numerical Results 189

8.4 Stability Analysis for the ML Regime in the Limit of Infinite Bandwidth 197

8.4.1 New’s Stability Criterion 197

8.4.2 Slow Stage 199

8.4.3 Fast Stage 199

8.4.4 Laser Without Spectral Filtering 200

8.5 The Q-Switching Instability of the ML Regime 203

8.5.1 Laser Without Spectral Filtering 204

8.5.2 Weak Saturation Limit 207

8.5.3 Variational Approach 209

8.6 Conclusion 212

Acknowledgments 213

References 213

9 Dynamical and Synchronization Properties of Delay-Coupled Lasers 217
Cristina M. Gonzalez, Miguel C. Soriano, M. Carme Torrent, Jordi Garcia-Ojalvo, and Ingo Fischer

9.1 Motivation: Why Coupling Lasers? 217

9.2 Dynamics of Two Mutually Delay-Coupled Lasers 218

9.2.1 Dynamical Instability 218

9.2.2 Instability of Isochronous Solution 220

9.3 Properties of Leader–Laggard Synchronization 224

9.3.1 Emergence of Leader–Laggard Synchronization 224

9.3.2 Control of Lag Synchronization 226

9.4 Dynamical Relaying as Stabilization Mechanism for Zero-Lag Synchronization 228

9.4.1 Laser Relay 228

9.4.2 Mirror Relay 230

9.5 Modulation Characteristics of Delay-Coupled Lasers 231

9.5.1 Periodic Modulation 231

9.5.2 Noise Modulation 235

9.5.3 Application: Key Exchange Protocol 238

9.6 Conclusion 240

Acknowledgments 240

References 241

10 Complex Networks Based on Coupled Two-Mode Lasers 245
Andreas Amann

10.1 Introduction 245

10.2 Complex Networks on the Basis of Two-Mode Lasers 246

10.3 The Design Principles of Two-Mode Lasers 248

10.4 The Dynamics of Two-Mode Lasers Under Optical Injection 253

10.4.1 The Model Equations 253

10.4.2 The = 0 Case 254

10.4.3 The Finite Case 257

10.5 Conclusions 264

Acknowledgments 265

References 265

Part III Synchronization and Cryptography 269

11 Noise Synchronization and Stochastic Bifurcations in Lasers 271
Sebastian M. Wieczorek

11.1 Introduction 271

11.2 Class-B Laser Model and Landau–Stuart Model 272

11.3 The Linewidth Enhancement Factor and Shear 274

11.4 Detection of Noise Synchronization 275

11.5 Definition of Noise Synchronization 278

11.6 Synchronization Transitions via Stochastic d-Bifurcation 280

11.6.1 Class-B Laser Model Versus Landau–Stuart Equations 282

11.7 Noise-Induced Strange Attractors 285

11.8 Conclusions 289

References 290

12 Emergence of One- and Two-Cluster States in Populations of Globally Pulse-Coupled Oscillators 293
Leonhard L¨ucken and Serhiy Yanchuk

12.1 Introduction 293

12.1.1 Pulse-Coupled Oscillators 294

12.1.2 Phase-Response Curve as a Parameter 295

12.1.3 System Description 298

12.2 Numerical Results 300

12.3 Appearance and Stability Properties of One-Cluster State 302

12.3.1 Inadequacy of the Linear Stability Analysis 302

12.3.2 One-Cluster State is a Saddle Point 302

12.3.2.1 Existence of a Local Unstable Direction 302

12.3.2.2 Existence of a Local Stable Direction 303

12.3.2.3 Other Stable and Unstable Local Directions 304

12.3.3 Stable Homoclinic Orbit to One-Cluster State 305

12.4 Two-Cluster States 306

12.4.1 Stability of Two-Cluster States 308

12.5 Intermediate State for Symmetric PRC with ß = 0.5 309

12.6 Conclusions 310

12.7 Appendix: Existence of a Homoclinic Orbit 310

References 315

13 Broadband Chaos 317
Kristine E. Callan, Lucas Illing, and Daniel J. Gauthier

13.1 Introduction 317

13.2 Optoelectronic Oscillators 318

13.3 Instability Threshold 323

13.4 Transition to Broadband Chaos 325

13.5 Asymptotic Analysis 327

13.6 Summary and Outlook 330

Acknowledgments 331

References 331

14 Synchronization of Chaotic Networks and Secure Communication 333
Ido Kanter and Wolfgang Kinzel

14.1 Introduction 333

14.2 Unidirectional Coupling 334

14.3 Transmission of Information 335

14.4 Bidirectional Coupling 336

14.5 Mutual Chaos Pass Filter 339

14.5.1 Protocol 342

14.6 Private Filters 345

14.7 Networks 346

14.8 Outlook 350

References 350

15 Desultory Dynamics in Diode-Lasers: Drift, Diffusion, and Delay 355
K. Alan Shore

15.1 Introduction 355

15.2 Carrier Diffusion in Diode Lasers 357

15.3 Intersubband Laser Dynamics 359

15.4 Carrier Diffusion Effects in VCSELs 362

15.4.1 Transverse Mode Competition and Secondary Pulsations 362

15.4.2 VCSEL Polarization Selection 363

15.4.3 Nanospin VCSELs 363

15.5 Delayed Feedback and Control of VCSEL Polarization 364

15.6 VCSEL Chaos and Synchronization and Message Transmission 365

15.7 Delay Deletion: Nullified Time of Flight 369

15.8 Chaos Communications: Optimization and Robustness 371

15.9 Conclusion 372

Acknowledgments 373

References 373

Further Reading 380

Index 381