TRANSVERSE PATTERNS IN NONLINEAR OPTICAL RESONATORS
CONTENTS INTRODUCTION HISTORICAL SURVEY PATTERNS IN NONLINEAR OPTICAL RESONATORS LOCALIZED STRUCTURES: VORTICES AND SOLITONS EXTENDED PATTERNS OPTICAL PATTERNS IN OTHER CON?GURATIONS MIRRORLESS CON?GURATION SINGLE-FEEDBACK-MIRROR CON?GURATION OPTICAL FEEDBACK LOOPS THE CONTENTS OF THIS BOOK REFERENCES ORDER PARAMETER EQUATIONS FOR LASERS MODEL OF A LASER LINEAR STABILITY ANALYSIS DERIVATION OF THE LASER ORDER PARAMETER EQUATION ADIABATIC ELIMINATION MULTIPLE-SCALE EXPANSION ORDER PARAMETER EQUATIONS FOR OTHER NONLINEAR RESONATORS OPTICAL PARAMETRIC OSCILLATORS THE REAL SWIFT–HOHENBERG EQUATION FOR DOPOS SCALES DERIVATION OF THE OPE THE COMPLEX SWIFT–HOHENBERG EQUATION FOR OPOS THE ORDER PARAMETER EQUATION FOR PHOTOREFRACTIVE OSCILLATORS DESCRIPTION AND MODEL ADIABATIC ELIMINATION AND OPERATOR INVERSION PHENOMENOLOGICAL DERIVATION OF ORDER PARAMETER EQUATIONS ZERO DETUNING: LASER HYDRODYNAMICS AND OPTICAL VORTICES HYDRODYNAMIC FORM OPTICAL VORTICES STRONG DI?RACTION STRONG DI?USION INTERMEDIATE CASES VORTEX INTERACTIONS FINITE DETUNING: VORTEX SHEETS AND VORTEX LATTICES VORTICES “RIDING” ON TILTED WAVES DOMAINS OF TILTED WAVES SQUARE VORTEX LATTICES RESONATORS WITH CURVED MIRRORS WEAKLY CURVED MIRRORS MODE EXPANSION CIRCLING VORTICES LOCKING OF TRANSVERSE MODES DEGENERATE RESONATORS THE RESTLESS VORTEX THE MODEL SINGLE VORTEX VORTEX LATTICES “OPTICAL” OSCILLATION MODE PARALLEL TRANSLATION OF A VORTEX LATTICE EXPERIMENTAL DEMONSTRATION OF THE “RESTLESS” VORTEX PHASE-INSENSITIVE MODES PHASE-SENSITIVE MODES DOMAINS AND SPATIAL SOLITONS SUBCRITICAL VERSUS SUPERCRITICAL SYSTEMS MECHANISMS ALLOWING SOLITON FORMATION SUPERCRITICAL HOPF BIFURCATION SUBCRITICAL HOPF BIFURCATION AMPLITUDE AND PHASE DOMAINS AMPLITUDE AND PHASE SPATIAL SOLITONS SUBCRITICAL SOLITONS I: SATURABLE ABSORBER MODEL AND ORDER PARAMETER EQUATION AMPLITUDE DOMAINS AND SPATIAL SOLITONS NUMERICAL SIMULATIONS SOLITON FORMATION SOLITON MANIPULATION: POSITIONING, PROPAGATION, TRAPPING AND SWITCHING EXPERIMENTS SUBCRITICAL SOLITONS II: NONLINEAR RESONANCE 10 1 ANALYSIS OF THE HOMOGENEOUS STATE NONLINEAR RESONANCE 10 2 SPATIAL SOLITONS 10 2 1 ONE-DIMENSIONAL CASE 10 2 2 TWO-DIMENSIONAL CASE PHASE DOMAINS AND PHASE SOLITONS 11 1 PATTERNS IN SYSTEMS WITH A REAL-VALUED ORDER PARAMETER 11 2 PHASE DOMAINS 11 3 DYNAMICS OF DOMAIN BOUNDARIES 11 3 1 VARIATIONAL APPROACH 11 3 2 TWO-DIMENSIONAL DOMAINS 11 4 PHASE SOLITONS 11 5 NONMONOTONICALLY DECAYING FRONTS 11 6 EXPERIMENTAL REALIZATION OF PHASE DOMAINS AND SOLITONS 11 7 DOMAIN BOUNDARIES AND IMAGE PROCESSING TURING PATTERNS IN NONLINEAR OPTICS 12 1 THE TURING MECHANISM IN NONLINEAR OPTICS 12 2 LASER WITH DI?USING GAIN 12 2 1 GENERAL CASE 12 2 2 LASER WITH SATURABLE ABSORBER 12 2 3 STABILIZATION OF SPATIAL SOLITONS BY GAIN DI?USION 12 3 OPTICAL PARAMETRIC OSCILLATOR WITH DI?RACTING PUMP 12 3 1 TURING INSTABILITY IN A DOPO 12 3 2 STOCHASTIC PATTERNS 12 3 3 SPATIAL SOLITONS IN?UENCED BY PUMP DI?RACTION THREE-DIMENSIONAL PATTERNS 13 1 THE SYNCHRONOUSLY PUMPED DOPO 13 1 1 ORDER PARAMETER EQUATION 13 2 PATTERNS OBTAINED FROM THE 3D SWIFT–HOHENBERG EQUATION 13 3 THE NONDEGENERATE OPO 13 4 CONCLUSIONS 13 4 1 TUNABILITY OF A SYSTEM WITH A BROAD GAIN BAND 13 4 2 ANALOGY BETWEEN 2D AND 3D CASES PATTERNS AND NOISE 14 1 NOISE IN CONDENSATES 14 1 1 SPATIO-TEMPORAL NOISE SPECTRA 14 1 2 NUMERICAL RESULTS 14 1 3 CONSEQUENCES 14 2 NOISY STRIPES 14 2 1 SPATIO-TEMPORAL NOISE SPECTRA 14 2 2 STOCHASTIC DRIFTS 14 2 3 CONSEQUENCES