Assanto / Residori / Clerc Localized States in Physics: Solitons and Patterns

1. Auflage 2011
ISBN: 978-3-642-16549-8
Verlag: Springer
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 286 Seiten

Systems driven far from thermodynamic equilibrium can create dissipative structures through the spontaneous breaking of symmetries. A particularly fascinating feature of these pattern-forming systems is their tendency to produce spatially confined states. These localized wave packets can exist as propagating entities through space and/or time. Various examples of such systems will be dealt with in this book, including localized states in fluids, chemical reactions on surfaces, neural networks, optical systems, granular systems, population models, and Bose-Einstein condensates.This book should appeal to all physicists, mathematicians and electrical engineers interested in localization in far-from-equilibrium systems. The authors - all recognized experts in their fields - strive to achieve a balance between theoretical and experimental considerations thereby giving an overview of fascinating physical principles, their manifestations in diverse systems, and the novel technical applications on the horizon.

Prof. Orazio Descalzi has edited in the last years the following books: Instabilities and Nonequilibrium Structures VII & VIII (Kluwer Academic Publishers, 2004)- Instabilities and Nonequilibrium Structures IX (Kluwer Academic Publishers, 2004) Nonequilibrium Statistical Mechanics and Nonlinear Physics (Elsevier, 2005)- Nonequilibrium Statistical Mechanics and Nonlinear Physics (American Institute of Physics, 2007

Autoren/Hrsg.

Assanto, Gaetano

Residori, Stefania

Clerc, Marcel

Descalzi, Orazio

Inhaltsverzeichnis

1;Localized States in Physics:Solitons and Patterns;3
1.1;Preface;5
1.2;Acknowledgements;7
1.3;Contents;9
1.4;List of Contributors;15
1.5;Part I Solitons, self-confined light and optical turbulence;19
1.5.1;Chapter 1 Light Self-trapping in Nematic Liquid Crystals;20
1.5.1.1;1.1 Introduction;20
1.5.1.2;1.2 Reorientational Self-focusing in Nematic Liquid Crystals;21
1.5.1.3;1.3 Spatial Optical Solitons in Purely Nematic Liquid Crystals;24
1.5.1.4;1.4 Spatial Optical Solitons in Chiral Nematic Liquid Crystals;28
1.5.1.5;1.5 Conclusions;31
1.5.1.6;References;32
1.5.2;Chapter 2 Photonic Plasma Instabilities and Soliton Turbulence in Spatially Incoherent Light;34
1.5.2.1;2.1 Introduction;35
1.5.2.2;2.2 Basic Theory and Formalism;36
1.5.2.2.1;2.2.1 Wigner Formalism;36
1.5.2.2.2;2.2.2 Initial Stages of Instability. Linear Perturbation Theory;38
1.5.2.2.3;2.2.3 Growth Rate and Conditions for Weak/Strong Turbulence;39
1.5.2.2.4;2.2.4 Debye Scaling;41
1.5.2.3;2.3 Quasi-Linear Approximation;42
1.5.2.3.1;2.3.1 General Derivation;43
1.5.2.3.2;2.3.2 Bump-on-Tail Dynamics;44
1.5.2.4;2.4 Numerical Analysis;45
1.5.2.4.1;2.4.1 Numerical Results for BOT Instability;45
1.5.2.4.2;2.4.2 Numerical Results for Multiple BOT Instability;46
1.5.2.5;2.5 Experimental Observation;47
1.5.2.5.1;2.5.1 Experimental Setup;47
1.5.2.5.2;2.5.2 Single Bump-on-Tail Instability;48
1.5.2.5.3;2.5.3 Holographic Readout of Dynamics;51
1.5.2.5.4;2.5.4 Multiple Bump-on-Tail Instability and Long-RangeTurbulence Spectra;52
1.5.2.6;2.6 Discussion and Conclusions;54
1.5.2.7;References;54
1.5.3;Chapter 3 Gap-Acoustic Solitons: Slowing and Stopping of Light;57
1.5.3.1;3.1 Introduction;58
1.5.3.2;3.2 Derivation of the Equations;61
1.5.3.2.1;3.2.1 Electromagnetic Field Equations with Phonon Perturbations;61
1.5.3.2.2;3.2.2 Acoustic Wave Equations with Electrostrictive Perturbations;64
1.5.3.2.2.1;3.2.2.1 Slowly-Varying Phonon Field;66
1.5.3.2.2.2;3.2.2.2 Brillouin Scattering—Phonon Fields at k ~ 2k0;66
1.5.3.2.3;3.2.3 The Bragg-Brillouin-Kerr System;67
1.5.3.3;3.3 Lagrangian, Hamiltonian, and Conserved Quantities;67
1.5.3.3.1;3.3.1 Dimensionless Variables;69
1.5.3.4;3.4 Gap-Acoustic Solitons;70
1.5.3.5;3.5 Soliton Stability and Instability;73
1.5.3.6;3.6 Summary and Conclusions;80
1.5.3.7;References;82
1.5.4;Chapter 4 Optical Wave Turbulence and Wave Condensation in a Nonlinear Optical Experiment;83
1.5.4.1;4.1 Introduction;84
1.5.4.2;4.2 Experimental setup;85
1.5.4.3;4.3 Theoretical Background;86
1.5.4.3.1;4.3.1 Evolution Equation;86
1.5.4.3.2;4.3.2 Long-Wave Model;87
1.5.4.3.3;4.3.3 The Fjørtoft Argument;88
1.5.4.3.4;4.3.4 Hamiltonian Formulation;90
1.5.4.3.5;4.3.5 Canonical Transformation;91
1.5.4.3.6;4.3.6 The Kinetic Wave Equation;92
1.5.4.3.7;4.3.7 Modulational Instability and the Creation of Solitons;95
1.5.4.4;4.4 Numerical Method;96
1.5.4.5;4.5 Experimental and Numerical Results;96
1.5.4.5.1;4.5.1 Direct cascade of energy;100
1.5.4.6;4.6 Conclusions;101
1.5.4.7;4.7 Acknowledgements;102
1.5.4.8;References;102
1.6;Part II Localized structures in pattern forming systems;104
1.6.1;Chapter 5 Localized Structures in the Liquid Crystal Light Valve Experiment;105
1.6.1.1;5.1 Introduction;106
1.6.1.2;5.2 The Liquid Crystal Light Valve Experiment;107
1.6.1.2.1;5.2.1 Description of the setup;107
1.6.1.2.2;5.2.2 The optical feedback: model equations;109
1.6.1.3;5.3 Experimental Observations of Optical Localized Structures;111
1.6.1.3.1;5.3.1 Round localized structures: interaction and dynamics;111
1.6.1.3.2;5.3.2 Triangular localized structures: bistability and phasesingularities;112
1.6.1.3.3;5.3.3 Bipatterns and localized peaks;114
1.6.1.3.4;5.3.4 1D spatially forced model;115
1.6.1.4;5.4 Control of Optical Localized Structures;116
1.6.1.4.1;5.4.1 Pinning range and localized structures;116
1.6.1.4.2;5.4.2 Controlled storage of localized structures matrices;117
1.6.1.5;5.5 Propagation Properties of Optical Localized Structures;119
1.6.1.6;5.6 Conclusions;121
1.6.1.7;References;121
1.6.2;Chapter 6 Convectons;123
1.6.2.1;6.1 Introduction;123
1.6.2.2;6.2 Convectons with periodic boundary conditions;126
1.6.2.3;6.3 Convectons with ICCBC;130
1.6.2.4;6.4 Multiconvectons;132
1.6.2.5;6.5 Localized traveling waves;133
1.6.2.6;6.6 Interpretation;134
1.6.2.7;6.7 Summary;137
1.6.2.8;References;138
1.6.3;Chapter 7 Morphological Characterization of Localized Hexagonal Patterns;140
1.6.3.1;7.1 Introduction;140
1.6.3.2;7.2 Prototypical Model for Hexagon Formation;142
1.6.3.3;7.3 Localized Hexagonal States: Geometrical Considerations and Morphological Characterizations;143
1.6.3.4;7.4 Heuristic Description of the Localization Process;146
1.6.3.5;7.5 The Case of a Localized Line of Cells;148
1.6.3.6;7.6 Conclusions and Perspective;150
1.6.3.7;References;151
1.7;Part III Localized structures for optical applications;152
1.7.1;Chapter 8 Cavity Solitons in Vertical Cavity Surface Emitting Lasers and their Applications;153
1.7.1.1;8.1 Introduction;154
1.7.1.2;8.2 CS motion;155
1.7.1.2.1;8.2.1 Numerical Analysis of CS motion in a constant phase gradient;156
1.7.1.2.2;8.2.2 Experimental Evidence of CS motion in a constant phase gradient;158
1.7.1.3;8.3 Applications of CS movement;162
1.7.1.3.1;8.3.1 CS drift in a constant gradient;162
1.7.1.3.2;8.3.2 Experimental realization of reconfigurable CS arrays;163
1.7.1.4;8.4 CS motion and device defects;167
1.7.1.4.1;8.4.1 CS force microscope;168
1.7.1.4.2;8.4.2 Modeling of an inhomogeneous device;169
1.7.1.4.3;8.4.3 Interaction between phase gradient and defects: the CS tap;170
1.7.1.4.3.1;8.4.3.1 Experiment;171
1.7.1.4.3.2;8.4.3.2 Numerical Simulations;173
1.7.1.5;8.5 Conclusions;177
1.7.1.6;References;178
1.7.2;Chapter 9 Cavity Soliton Laser based on coupledmicro-resonators;180
1.7.2.1;9.1 Introduction;181
1.7.2.2;9.2 Experimental Setup;182
1.7.2.3;9.3 Bistability regime;184
1.7.2.3.1;9.3.1 Multistable Regime;186
1.7.2.3.2;9.3.2 Local bifurcation diagram;187
1.7.2.3.3;9.3.3 Towards the whole bifurcation diagram;189
1.7.2.4;9.4 Coherence properties of laser solitons;192
1.7.2.4.1;9.4.1 Modal properties;193
1.7.2.5;9.5 Conclusions and Perspectives;195
1.7.2.6;References;196
1.7.3;Chapter 10 Cavity soliton laser based on a VCSEL with saturable absorber;198
1.7.3.1;10.1 Introduction;199
1.7.3.2;10.2 The model;201
1.7.3.2.1;10.2.1 Bistability;202
1.7.3.2.2;10.2.2 Plane wave instabilities;204
1.7.3.2.3;10.2.3 Pattern forming instabilities;204
1.7.3.3;10.3 CS switching techniques;205
1.7.3.3.1;10.3.1 Switching dynamics;207
1.7.3.3.1.1;10.3.1.1 Incoherent injection;208
1.7.3.3.1.2;10.3.1.2 Injection at the cavity frequency;210
1.7.3.3.1.3;10.3.1.3 Injection at the CS frequency;211
1.7.3.3.2;10.3.2 Switching energy;212
1.7.3.3.2.1;10.3.2.1 Injection at the cavity frequency;212
1.7.3.3.2.2;10.3.2.2 Injection at the CS frequency;214
1.7.3.4;10.4 Stability of the CS;214
1.7.3.5;10.5 Motion of the CS in a finite device;217
1.7.3.5.1;10.5.1 Circular pump;217
1.7.3.6;10.6 Conclusions;219
1.7.3.7;References;221
1.7.4;Chapter 11 Dynamic Control of Localized Structures in a Nonlinear Feedback Experiment;223
1.7.4.1;11.1 Introduction;224
1.7.4.2;11.2 Self-organized localized structures in feedback systems;225
1.7.4.3;11.3 Localized structures in a single-feedback system using a liquid crystal light valve as a nonlinearity;229
1.7.4.3.1;11.3.1 Formation of localized structures;231
1.7.4.4;11.4 Boundary-induced localized structures in LCLV;233
1.7.4.5;11.5 Dynamic and static position control of feedback localized states;237
1.7.4.6;11.6 Gradient induced motion control of feedback localized structures;241
1.7.4.7;11.7 Summary;246
1.7.4.8;References;246
1.8;Part IV Excitability and localized states;249
1.8.1;Chapter 12 Interaction of oscillatory and excitable localized states in a nonlinear optical cavity;250
1.8.1.1;12.1 Introduction;250
1.8.1.2;12.2 Model;251
1.8.1.3;12.3 Overview of the behavior of localized states;252
1.8.1.3.1;12.3.1 Hopf bifurcation;253
1.8.1.3.2;12.3.2 Saddle-loop bifurcation;253
1.8.1.3.3;12.3.3 Excitability;255
1.8.1.4;12.4 Interaction of two oscillating localized states;255
1.8.1.4.1;12.4.1 Full system;256
1.8.1.4.2;12.4.2 Simple model: two coupled Landau-Stuart oscillators;260
1.8.1.4.2.1;12.4.2.1 Estimation of parameters I;263
1.8.1.4.2.2;12.4.2.2 Estimation of parameters II: quenching experiments;263
1.8.1.4.2.3;12.4.2.3 Estimation of d;264
1.8.1.4.2.4;12.4.2.4 Results and dynamical regimes of the simple model;265
1.8.1.5;12.5 Interaction of excitable localized states: logical gates;268
1.8.1.6;12.6 Summary;272
1.8.1.7;References;272
1.8.2;Chapter 13 Lurching waves in thalamic neuronal networks;274
1.8.2.1;13.1 Introduction;274
1.8.2.2;13.2 The model;276
1.8.2.2.1;13.2.1 Smooth and Lurching waves;279
1.8.2.3;13.3 Exploration of parameter space and continuation;281
1.8.2.3.1;13.3.1 Direct time integration;281
1.8.2.3.2;13.3.2 Continuation using Newton method;283
1.8.2.3.3;13.3.3 Pseudo-arclength continuation;287
1.8.2.4;13.4 Discussion;288
1.8.2.5;References;289
1.9;Index;291