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Nonlinear Optical Cavity Dynamics

From Microresonators to Fiber Lasers
1. Aufl.

von: Philippe Grelu
151,99 €
Verlag:	Wiley-VCH
Format:	PDF
Veröffentl.:	23.12.2015
ISBN/EAN:	9783527685813
Sprache:	englisch
Anzahl Seiten:	456

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Beschreibungen

Titelbeschreibung

By recirculating light in a nonlinear propagation medium, the nonlinear optical cavity allows for countless options of light transformation and manipulation. In passive media, optical bistability and frequency conversion are central figures. In active media, laser light can be generated with versatile underlying dynamics. Emphasizing on ultrafast dynamics, the vital arena for the information technology, the soliton is a common conceptual keyword, thriving into its modern developments with the closely related denominations of dissipative solitons and cavity solitons. Recent technological breakthroughs in optical cavities, from micro-resonators to ultra-long fiber cavities, have entitled the exploration of nonlinear optical dynamics over unprecedented spatial and temporal orders of magnitude. By gathering key contributions by renowned experts, this book aims at bridging the gap between recent research topics with a view to foster cross-fertilization between research areas and stimulating creative optical engineering design.

Inhaltsverzeichnis

List of Contributors XIII Foreword XXIII 1 Introduction 1 Philippe Grelu References 8 2 Temporal Cavity Solitons in Kerr Media 11 Stéphane Coen andMiro Erkintalo 2.1 Introduction 11 2.2 Mean-Field Equation of Coherently Driven Passive Kerr Resonators 13 2.3 Steady-State Solutions of the Mean-Field Equation 15 2.4 Existence and Characteristics of One-Dimensional Kerr Cavity Solitons 18 2.5 Original Experimental Observation of Temporal Kerr Cavity Solitons 21 2.6 Interactions of Temporal CSs 25 2.7 Breathing Temporal CSs 29 2.8 Emission of DispersiveWaves by Temporal CSs 31 2.9 Conclusion 34 References 34 3 Dynamics and Interaction of Laser Cavity Solitons in Broad-Area Semiconductor Lasers 41 Thorsten Ackemann, Jesus Jimenez, Yoann Noblet, Neal Radwell, Guangyu Ren, Pavel V. Paulau, Craig McIntyre, Gian-Luca Oppo, Joshua P. Toomey, and Deborah M. Kane 3.1 Introduction 41 3.2 Devices and Setup 43 3.2.1 Devices 43 3.2.2 Experimental Setup 44 3.3 Basic Observations and Dispersive Optical Bistability 45 3.3.1 Basic Observation of Spatial Solitons 45 3.3.2 Interpretation as Dispersive Optical Bistability 47 3.3.3 Comparison to Absorptive Case 49 3.4 Modelling of LS and Theoretical Expectations in Homogenous System 50 3.4.1 Model Equations 50 3.4.2 Interaction of Laser Solitons in a Homogenous System 52 3.5 Phase and Frequency Locking of Trapped Laser Cavity Solitons 54 3.5.1 Basic Observation 54 3.5.2 Experiments on Locking Phase 55 3.5.3 Adler Locking: Theory 59 3.6 Dynamics of Single Solitons 60 3.6.1 Transient Dynamics 62 3.6.2 Outlook on Asymptotic Dynamics 65 3.7 Summary and Outlook 68 Acknowledgments 70 References 70 4 Localized States in SemiconductorMicrocavities, from Transverse to Longitudinal Structures and Delayed Systems 77 Stéphane Barland, Massimo Guidici, Julien Javaloyes, and Giovanna Tissoni 4.1 Introduction 77 4.2 Lasing Localized States 80 4.2.1 Transverse Localized States in Coupled Microcavities 80 4.2.2 Time-Localized Structures in Passive Mode-Locked Semiconductor Laser 82 4.3 Localized States in Nonlinear Element with Delayed Retroaction 87 4.3.1 Front Pinning in Bistable System with Delay 88 4.3.2 Topological Dissipative Solitons in Excitable System with Delay 92 4.4 Conclusion and Outlook 98 Acknowledgements 99 References 99 5 Dynamics of Dissipative Solitons in Presence of Inhomogeneities and Drift 107 Pedro Parra-Rivas, Damià Gomila, Lendert Gelens, Manuel A. Matías, and Pere Colet 5.1 Introduction 107 5.2 General Theory: Swift–Hohenberg Equation with Inhomogeneities and Drift 108 5.3 Excitability Regimes 113 5.4 Fiber Cavities and Microresonators:The Lugiato–Lefever model 116 5.5 Periodically Pumped Ring Cavities 119 5.6 Effects of Drift in a Periodically Pumped Ring Cavity 120 5.7 Summary 125 Acknowledgments 125 References 125 6 Dissipative Kerr Solitons in Optical Microresonators 129 Tobias Herr, Michael L. Gorodetsky, and Tobias J. Kippenberg 6.1 Introduction to Optical Microresonator Kerr-Frequency Combs 129 6.2 Resonator Platforms 131 6.2.1 Ultra High-Q (MgF2) Crystalline Microresonators 131 6.2.2 Integrated Photonic Chip Microring Resonators 132 6.3 Physics of the Kerr-comb Formation Process 132 6.3.1 Nonlinear Coupled Mode Equations 135 6.3.2 Degenerate Hyperparametric Oscillations 138 6.3.3 Primary Sidebands 140 6.4 Dissipative Kerr Solitons in Optical Microresonators 141 6.4.1 AnalyticalTheory of Dissipative Kerr Solitons 141 6.5 Signatures of Dissipative Kerr Soliton Formation in Crystalline Resonators 145 6.6 Laser Tuning into the Dissipative Kerr Soliton States 147 6.7 Simulating Soliton Formation in Microresonators 148 6.8 Characterization of Temporal Dissipative Solitons in Crystalline Microresonators 149 6.9 Resonator Mode Structure and Soliton Formation 151 6.10 Using Dissipative Kerr solitons to Count the Cycles of Light 152 6.11 Temporal Solitons and Soliton-Induced Cherenkov Radiation in an Si3N4 Photonic Chip 155 6.12 Summary 157 References 158 7 Dynamical Regimes in Kerr Optical Frequency Combs: Theory and Experiments 163 Aurélien Coillet, Nan Yu, Curtis R. Menyuk, and Yanne K. Chembo 7.1 Introduction 163 7.2 The System 164 7.3 The Models 166 7.3.1 Modal Expansion Model 166 7.3.2 Spatiotemporal Model 167 7.3.3 Stability Analysis 168 7.4 Dynamical States 171 7.4.1 Primary Combs 171 7.4.2 Solitons 176 7.4.3 Chaos 179 7.5 Conclusion 183 7.6 Acknowledgments 184 References 184 8 Nonlinear Effects in Microfibers and Microcoil Resonators 189 Muhammad I.M. Abdul Khudus, Rand Ismaeel, Gilberto Brambilla, Neil G. R. Broderick, and Timothy Lee 8.1 Introduction 189 8.2 Linear Optical Properties of Optical Microfibers 191 8.3 Linear Properties of Optical Microcoil Resonators 193 8.4 Bistability in Nonlinear Optical Microcoil Resonators 195 8.4.1 Broken Microcoil Resonators 197 8.4.2 Polarization Effects in Nonlinear Optical Microcoil Resonators 198 8.4.3 Possible Experimental Verification 199 8.5 Harmonic Generation in Optical Microfibers and Microloop Resonators 200 8.5.1 Mathematical Modeling and Efficiency ofThird Harmonic Generation 201 8.5.2 Third Harmonic Generation in Microloop Resonators 204 8.5.3 Second-Harmonic Generation 208 8.6 Conclusions and Outlook 209 References 209 9 Harmonic Laser Mode-Locking Based on Nonlinear Microresonators 213 Alessia Pasquazi, Marco Peccianti, David J. Moss, Sai Tac Chu, Brent E. Little, and Roberto Morandotti 9.1 Introduction 213 9.2 Modeling 215 9.3 Experiments 219 9.3.1 Short Cavity, Unstable Laser Oscillation 223 9.3.2 Short Cavity, Stable Laser Oscillation 224 9.3.3 Short Cavity, Dual-Line Laser Oscillation 226 9.4 Conclusions 228 References 229 10 Collective Dissipative Soliton Dynamics in Passively Mode-Locked Fiber Lasers 231 François Sanchez, Andrey Komarov, Philippe Grelu, Mohamed Salhi, Konstantin Komarov, and Hervé Leblond 10.1 Introduction 231 10.1.1 Dissipative Solitons and Mode-Locked Lasers 231 10.1.2 Multiple Pulses and Their Interactions 232 10.2 Multistability and Hysteresis Phenomena 234 10.2.1 Multiple Pulsing 234 10.2.2 Multistability Observations 235 10.2.3 Modeling Multiple Pulsing and Hysteresis 236 10.3 Soliton Crystals 238 10.3.1 From Soliton Molecules to Soliton Crystals 238 10.3.2 Soliton Crystal Experiments 239 10.3.3 Modeling Soliton Crystal Formations 240 10.3.4 Soliton Crystal Instability 243 10.4 Toward the Control of Harmonic Mode-Locking by Optical Injection 244 10.5 Complex Soliton Dynamics 247 10.5.1 Unfolding Complexity 247 10.5.2 Analogy Between Soliton Patterns and the States of Matter 247 10.5.3 Soliton Rain Dynamics 250 10.5.4 Chaotic Pulse Bunches 252 10.6 Summary 256 Acknowledgments 257 References 257 11 Exploding Solitons and RogueWaves in Optical Cavities 263 Wonkeun Chang and Nail Akhmediev 11.1 Introduction 263 11.2 Passively Mode-Locked Laser Model 266 11.3 The Results of Numerical Simulations 268 11.4 Probability Density Function 270 11.5 Conclusions 272 11.6 Acknowledgements 272 References 273 12 SRS-Driven Evolution of Dissipative Solitons in Fiber Lasers 277 Sergey A. Babin, Evgeniy V. Podivilov, Denis S. Kharenko, Anastasia E. Bednyakova, Mikhail P. Fedoruk, Olga V. Shtyrina, Vladimir L. Kalashnikov, and Alexander A. Apolonski 12.1 Introduction 277 12.2 Generation of Highly Chirped Dissipative Solitons in Fiber Laser Cavity 279 12.2.1 Modeling 279 12.2.1.1 Analytical Solution of CQGLE in the High Chirp Limit 281 12.2.1.2 Comparison of Analytics with Numerics 284 12.2.2 Experiment and its Comparison with Simulation 286 12.2.3 NPE Overdriving and its Influence on Dissipative Solitons 288 12.3 Scaling of Dissipative Solitons in All-Fiber Configuration 290 12.3.1 DifferentWays to Increase Pulse Energy, Limiting Factors 290 12.3.2 SRS Threshold for Dissipative Solitons at Cavity Lengthening 292 12.4 SRS-Driven Evolution of Dissipative Solitons in Fiber Laser Cavity 297 12.4.1 NSE-Based Model in Presence of SRS 297 12.4.1.1 Model Details 298 12.4.1.2 Simulation, Comparison with Experiment 299 12.4.2 Generation of Stokes-Shifted Raman Dissipative Solitons 302 12.4.2.1 Proof-of-Principle Experiment 304 12.4.3 Characteristics of Raman dissipative Solitons 306 12.4.3.1 Variation of the Soliton Spectra with Filter Parameters 306 12.4.3.2 Variation of the Soliton Spectra with the Raman Feedback Parameters 307 12.4.4 Generation of Multicolor Soliton Complexes and Their Characteristics 307 12.5 Conclusions and Future Developments 310 References 312 13 Synchronization in Vectorial Solid-State Lasers 317 Marc Brunel, Marco Romanelli, and Marc Vallet 13.1 Introduction 317 13.2 Self-Locking in Dual-Polarization Lasers 318 13.2.1 Vectorial Description of the Cavity 318 13.2.2 Self-Pulsing in Lasers with Crossed Loss and Phase Anisotropies 319 13.2.3 Polarization Self-Modulated Lasers 321 13.2.4 Mode-Locked Dual-Polarization Lasers 323 13.2.4.1 Phase Locking at c/4L 325 13.3 Dynamics of Solid-State Lasers Submitted to a Frequency-Shifted Feedback 327 13.3.1 Description of the System 327 13.3.1.1 Experimental Setup 328 13.3.2 Lang–Kobayashi Rate Equations 330 13.3.2.1 Phase Dynamics 331 13.3.2.2 Time-Scaled Rate Equations 331 13.3.3 Phase Locking 332 13.3.3.1 Continuous-Wave Case 332 13.3.3.2 Passive Q-Switching Case 333 13.3.4 Bounded Phase Dynamics 334 13.3.4.1 Intensity Bifurcation Diagram 334 13.3.4.2 Phase Bifurcation Diagram 336 13.3.4.3 Phasors 337 13.3.4.4 Role of the Coupling in the Active Medium 338 13.3.5 Measure of the Synchronization in the Bounded Phase Regime 339 13.4 Conclusion 341 Acknowledgments 341 References 341 14 Vector Patterns and Dynamics in Fiber Laser Cavities 347 StefanWabnitz, Caroline Lecaplain, and Philippe Grelu 14.1 Introduction 347 14.1.1 Pulsed Vector Dynamics with a Saturable Absorber 347 14.1.2 Vector DynamicsWithout a Saturable Absorber 348 14.2 Fiber Laser Models 349 14.2.1 The Scalar Cubic Ginzburg–Landau Equation 350 14.2.2 Vector Ginzburg–Landau Equations 352 14.2.3 Vector Nonlinear Schrödinger Equation 355 14.2.4 Numerical Simulations 357 14.3 Experiments of Vector Dynamics 357 14.3.1 The Anomalous GVD: From Chaos to Antiphase Dissipative Dynamics 359 14.3.2 The Normal GVD: Polarization-DomainWalls 362 14.4 Summary 364 Acknowledgments 364 References 364 15 Cavity Polariton Solitons 369 Oleg A. Egorov and Falk Lederer 15.1 Introduction 369 15.2 Mathematical Model 371 15.3 One-Dimensional Bright Cavity Polariton Solitons 373 15.3.1 Amplitude Equation in the Polaritonic Basis 374 15.3.2 CPSs Beyond the “Magic Angle” and Their Stability 376 15.3.3 Multi-Hump Cavity Polariton Solitons 378 15.4 Two-Dimensional Parametric Polariton Solitons 380 15.4.1 Amplitude Equations for the ParticipatingWaves 380 15.4.2 Families of Parametric Polariton Solitons 382 15.4.3 Excitation and Dynamics of PPSs 385 15.5 Two-Dimensional Moving Bright CPSs 387 15.6 Summary 389 Acknowledgments 389 References 390 16 Data Methods and Computational Tools for Characterizing Complex Cavity Dynamics 395 J. Nathan Kutz, Steven L. Brunton, and Xing Fu 16.1 Introduction 395 16.2 Data Methods 396 16.2.1 Dimensionality-Reduction: Principal Components Analysis 397 16.2.2 Search Algorithms and Library Building 398 16.2.3 Sparse Measurements and Compressive Sensing 400 16.2.4 Sparse Representation and Classification 401 16.3 Adaptive, Equation-Free Control Architecture 402 16.4 Prototypical Example: Self-Tuning Mode-Locked Fiber Lasers 403 16.4.1 Governing Equations 404 16.4.2 Jones Matrices forWaveplates and Polarizers 404 16.4.3 Performance Monitoring and Objective Function 405 16.4.4 Sparse Representation for Birefringence Classification 405 16.4.5 Self-Tuning Laser 406 16.5 Broader Applications of Self-Tuning Complex Systems 409 16.5.1 Phased Array Antennas 409 16.5.2 Coherent Laser Beam Combining 411 16.5.3 Neuronal Stimulation 412 16.6 Conclusions and Technological Outlook 413 Acknowledgments 415 References 415 17 Conclusion and Outlook 419 Philippe Grelu References 421 Index 423

Autorenportrait

Philippe Grelu has been Professor of Physics at Université de Bourgogne, in Dijon, France, since 2005. After receiving his PhD at University of Orsay (Paris XI) in quantum optics (1996), his interest moved to ultrafast nonlinear optics and mode-locked fiber lasers. His research includes spatio-temporal soliton dynamics and nonlinear microfiber optics. He developed a key expertise in nonlinear optical cavity dynamics, with major contributions in the fast developing field of dissipative solitons. He has delivered numerous invited talks at international conferences and has authored over 150 scientific publications.