Nonlinear Optical Cavity Dynamics

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.

Auteur
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.

Contenu

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: SwiftHohenberg Equation with Inhomogeneities and Drift 108

5.3 Excitability Regimes 113

5.4 Fiber Cavities and Microresonators:The LugiatoLefever 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 AnalyticalTh...