Contrary to monographs on non-linear optics this book concentrates on problems of self-organization in various important contexts. The reader learns how patterns in non-linear optical systems are created and what theoretical methods can be applied to describe them. Next, various aspects of pattern formation such as associative memory, information processing, spatio-temporal instability, photo refraction, and so on are treated.
The book addresses graduate students and researchers in physics and optical engineering.

Inhalt

Self-Organization in Nonlinear Optics - Kaleidoscope of Patterns.- 1 What Is This Book About?.- 2 Nonlinear Optics: The Good Old Times.- 3 The First Model - Kerr-Slice/Feedback Mirror System.- 4 Diffusion, Diffraction, and Spatial Scales.- 5 One More Scheme: The First Step Toward Optical Synergetics.- 6 Nonlocal Interactions; Optical Kaleidoscope of Patterns.- 7 OK-Equation and "Dry Hydrodynamics".- 8 One More Nonlinear Element: Two-Component Optical Reaction-Diffusion Systems.- 9 Diffraction at Last; Rolls and Hexagons.- 10 diffraction and Diffraction.- 11 Far Away from Hexagons: Delay in Time and Space.- 12 Diffusion + Diffraction + (Interference) + Nonlocal Interactions = Akhseals.- References.- 1 Information Processing and Nonlinear Physics: From Video Pulses to Waves and Structures.- 1 Information Encoding by Carrier Modulation and the Physics of Nonlinear Oscillations and Waves.- 2 Modulation of Light Waves and Information Encoding in Digital Optical Computers. Optical Triggers.- 3 Strong Optical Nonlinearities. Nonlinear Materials.- 4 Generation and Transformation of Femtosecond Light Pulses.- 5 Control of Transverse Interactions in Nonlinear Optical Resonators: Generation, Hysteresis, and Interaction of Nonlinear Structures.- 6 Conclusion. Nonlinear Optics and Molecular Electronics.- References.- 2 Optical Design Kit of Nonlinear Spatial Dynamics.- 1 Elementary Optical Synergetic Blocks.- 1.1 Characteristics of a Synergetic Block.- 1.2 Optical Synergetic Block Based on LCLV.- 1.3 Main Mathematical Models.- 1.4 Optical Multistability and Switching Waves.- 2 Integral Transverse Interactions.- 2.1 The Synergetic Optical Block with an Electronic Feedback Circuit.- 3 Optical Counterparts of Two-Component Reaction-Diffusion Systems.- 3.1 Linear Stability Analysis and Bifurcation of Uniform States.- 4 Conclusion.- References.- 3 Pattern Formation in Passive Nonlinear Optical Systems.- 1 Induced and Spontaneous Patterns.- 1.1 Materials and Geometries.- 2 Mirror Feedback Systems.- 2.1 Kerr Slice with Feedback Mirror.- 2.2 Basic Model and Stability Analysis.- 2.3 Liquid Crystal Light Valve Systems.- 3 Pattern Formation in Optical Cavities.- 3.1 Vector Kerr Model and Equations.- 3.2 Spatial Stability of Symmetric Solutions.- 3.3 Pattern Formation in a Two-Level Optical Cavity.- 4 Conclusion.- References.- 4 Spatio-Temporal Instability Threshold Characteristics in Two-Level Atom Devices.- 1 Linear Stability Analysis of Stationary Solutions.- 2 Feedback Mirror Experiment.- 2.1 Experimental Results.- 2.2 Linear Analysis.- 2.3 Static and Dynamical Thresholds.- 2.4 Role of the Longitudinal Grating.- 2.5 Discussion of the Phase Conjugation Effects.- 2.6 Role of the Homogeneous Dephasing Time.- 2.7 Role of the Time Delay.- 3 The Ségard and Macke Experiment.- 3.1 Experiment.- 3.2 Linear Analysis.- 3.3 Physics of the Coupling.- 3.4 No Rabi Gain at Threshold.- 4 Rayleigh Self-Oscillation in an Intrinsic System.- 4.1 Characteristics of the Self-Oscillation in the No-Pump Depletion Model.- 4.2 Threshold Characteristics for Depleted Pump Fields.- 4.3 Doppler Effect.- 5 Conclusion.- References.- 5 Transverse Traveling-Wave Patterns and Instabilities in Lasers.- 1 Basic Equations and Transverse Traveling-Wave Solution.- 2 Instabilities: Direct Stability Analysis and Phase Equations.- 3 Pattern Transition and Selection.- 4 Conclusion.- References.- 6 Laser-Based Optical Associative Memories.- 1 Nonlinear Dynamic Equations and Steady-State Equations.- 2 Single- and Multimode Stationary Solutions. Spatial Multistability.- 3 Operation with Injected Signal.- 4 General Description of the System.- References.- 7 Pattern and Vortex Dynamics in Photorefractive Oscillators.- 1 Pattern Formation and Complexity.- 1.1 The Multimode Optical Oscillator: 1-, 2-, 3-Dimensional Optics.- 1.2 The Photorefractive Ring Oscillator. How to Control the Fresnel Number.- 1.3 Periodic (PA) and Chaotic (CA) Alternation and Space-Time Chaos.- 2 Phase Singularities, Topological Defects, and Turbulence.- 2.1 Phase Singularities in Linear Waves. Speckle Experiments.- 2.2 Phase Singularities in Nonlinear Optics: Scaling Laws.- 2.3 Comparison of Vortex Statistics in Speckle and Photorefractive Patterns.- 2.4 Transition from Boundary- to Bulk-Controlled Regimes.- 3 Theory of Pattern Formation and Pattern Competition.- 3.1 Equations of Photorefractive Oscillator.- 3.2 Truncation to a Small Number of Modes: Numerical Evidence of PA, CA, and STC.- 3.3 Symmetry Breaking at the Onset of Pattern Competition.- References.- 8 Prom the Hamiltonian Mechanics to a Continuous Media. Dissipative Structures. Criteria of Self-Organization.- 1 The Transition from Reversible Equations of Mechanics to Irreversible Equations of the Statistical Theory.- 1.1 Physical Definition of Continuous Medium.- 1.2 The Gibbs Ensemble for Nonequilibrium Processes.- 1.3 The Unified Definition of "Continuous Medium" Averaging over Physically Infinitesimal Volume.- 1.4 The Constructive Role of the Dynamic Instability of the Motion of Atoms.- 2 The Unified Description of Kinetic and Hydrodynamic Motion.- 2.1 The Generalized Kinetic Equation.- 3 The Equation of Entropy Balance. The Heat Flow.- 4 Equations of Hydrodynamics with Self-Diffusion.- 5 Effect of Self-Diffusion on the Spectra of Hydrodynamic Fluctuations.- 6 The Kinetic Approach in the Theory of Self-Organization - Synergetics. Basic Mathematical Models.- 7 Kinetic and Hydrodynamic Description of the Heat Transfer in Active Medium.- 8 Kinetic Equation for Active Medium of Bistable Elements.- 9 Kinetic Fluctuations in Active Media.- 9.1 The Langevin Source in the Kinetic Equation.- 9.2 Spatial Diffusion. "Tails" in the Time Correlations.- 9.3 The Langevin Source in the Reaction Diffusion (FKPP) Equation.- 10 Natural Flicker Noise ("1/f Noise").- 10.1 Natural Flicker Noise for Diffusion Processes.- 10.2 Natural Flicker Noise for Reaction-Diffusion Processes.- 11 Criteria of Self-Organization.- 11.1 Evolution in the Space of Controlling Parameters. S-Theorem.- 11.2 The Comparison of the Relative Degree of Order of States on the Basis of the S-Theorem Using Experimental Data.- 12 Conclusion. Associative Memory and Pattern Recognition.- References.