Multidimensional Solitons

Written by the preeminent researcher in this field, Multidimensional Solitons provides a comprehensive survey of self-trapped modes in two- and three-dimensional nonlinear media. It reviews studies covering fundamentals and recently reported theoretical and experimental results in diverse areas, such as nonlinear optics and Bose-Einstein condensates. This vital work explores fundamental solitons, topologically organized ones, such as solitary vortices and hopfions, and a broad spectrum of other soliton species, including those in lattice and dissipative media. Multidimensional Solitons: Offers a general introduction to the modern “soliton science” Provides context on the fundamentals of solitons in nonlinear optics and Bose-Einstein condensates Instructs how the stabilization of two- and three-dimensional solitons is possible, which is a crucially important problem for multidimensional setups Presents theoretical (analytical and numerical) and experimental results on optical and matter-wave solitons in diverse settings Researchers – both theorists and experimentalists – working in optics and photonics, low-temperature and atomic physics, mathematical physics, and applied mathematics will all find this an instrumental reference. Graduate students in these disciplines will also find it as a valuable resource. Cover Half Title Title Page Copyright Page Acronyms Preface Table of Contents Chapter 1: Introduction 1.1 ONE-DIMENSIONAL SOLITONS 1.2 EXIT TO THE MULTIDIMENSIONAL WORLD REFERENCES Chapter 2: Basic Theoretical Models 2.1 MODELS WITH COMPETING AND SATURABLE NONLINEARITIES 2.2 STABILIZATION OF MULTIDIMENSIONAL SOLITONS BY LINEAR OR NONLINEAR POTENTIALS 2.3 THE GROSS–PITAEVSKII (GP) EQUATIONS WITH LEE–HUANG–YANG (LHY) CORRECTIONS FOR QUANTUM DROPLETS (QDs) 2.4 TWO-COMPONENT SYSTEMS WITH SPIN–ORBIT COUPLING (SOC) REFERENCES Chapter 3: The Use of Higher-Order Nonlinearities: Theory 3.1 THE SHAPE AND STABILITY OF 2D FUNDAMENTAL SOLITONS SUPPORTED BY THE COMPETING CUBIC–QUINTIC (CQ) NONLINEAR TERMS 3.2 STABILITY OF 2D VORTEX SOLITONS UNDER THE ACTION OF COMPETING NONLINEARITIES 3.3 STABLE 3D SOLITONS WITH EMBEDDED VORTICITY S =1 3.4 STABLE 2D AND 3D VORTEX SOLITONS IN SYSTEMS OF COUPLED EQUATIONS 3.5 SPATIOTEMPORAL OPTICAL VORTICES (STOVs) AND SPONTANEOUS SYMMETRY BREAKING (SSB) IN A DUAL-CORE PLANAR WAVEGUIDE 3.6 THE EFFECTIVE POTENTIAL OF AN INTERACTION BETWEEN FAR SEPARATED 2D AND 3D SOLITONS REFERENCES Chapter 4: The Use of Higher-Order Nonlinearities: Experiments in Optical Media 4.1 FUNDAMENTAL (2+1)D SOLITONS 4.2 QUASI-STABLE (2+1)D VORTEX SOLITONS 4.3 QUASI-STABLE ANNULAR SOLITON CLUSTERS (NECKLACE PATTERNS) 4.4 ROTATING “PROPELLER” PATTERNS REFERENCES Chapter 5: Linear Trapping Potentials 5.1 STABILIZATION OF 3D AND 2D FUNDAMENTAL SOLITONS AND VORTICES BY THE TRAPPING POTENTIAL 5.2 STABLE 2D TWO-COMPONENT SOLITONS WITH HIDDEN VORTICITY 5.3 TRAPPING TWO-COMPONENT SOLITONS AND VORTICES IN A SET OF CONFINING AND EXPULSIVE POTENTIALS BY MEANS OF LINEAR COUPLING REFERENCES Chapter 6: Nonlinear Trapping Potentials and Nonlinearity Management 6.1 THE BASIC SETTING 6.2 EXACT, APPROXIMATE, AND NUMERICAL RESULTS FOR THE ANTI-GAUSSIAN SPATIAL-MODULATION PROFILE 6.3 GYROSCOPE SOLITONS (VORTEX TORI) IN 3D 6.4 HOPFIONS: 3D SOLITONS WITH TWO INDEPENDENT TOPOLOGICAL CHARGES 6.5 VORTEX–ANTIVORTEX HYBRIDS IN THE PEANUT-SHAPED MODULATION PROFILE 6.6 LOCALIZED DARK VORTICES 6.7 NONLINEARITY MANAGEMENT (NM) REFERENCES Chapter 7: Spatially Periodic Potentials (Lattices): Theory 7.1 BASIC EQUATIONS 7.2 SOLITONS AND SOLITARY VORTICES STABILIZED BY THE LATTICE POTENTIAL 7.3 2D COMPOUND STATES IN THE FORM OF HIGHER-ORDER VORTICES AND SUPERVORTICES 7.4 TWO-DIMENSIONAL GAP SOLITONS (GSs) AND GAP VORTICES 7.5 2D SOLITONS IN A RADIAL POTENTIAL 7.6 GAP SOLITONS IN A 2D QUASI-PERIODIC LATTICE POTENTIAL (PENROSE TILING) 7.7 STABILIZATION OF VORTICES IN THE SECOND-HARMONICGENERATING MEDIUM BY A LATTICE POTENTIAL REFERENCES Chapter 8: Spatially Periodic Potentials (Lattices): Experiments 8.1 2D VORTEX SOLITONS STABILIZED BY VIRTUAL PHOTONIC LATTICES IN PHOTOREFRACTIVE (PhR) MEDIA 8.2 SPATIAL SOLITONS AND SPATIOTEMPORAL LIGHT BULLETS (LBs) IN MULTI-CORE BULK WAVEGUIDES REFERENCES Chapter 9: Stabilization of Multidimensional Solitons by Spin–Orbit Coupling (SOC) 9.1 INTRODUCTION TO THE TOPIC: INTERPLAY OF THE SOC AND NONLINEARITY 9.2 THE TWO-COMPONENT SOC MODEL 9.3 2D SOLITONS WITH THE RASHBA COUPLING 9.4 EFFECT OF COMBINED RASHBA AND DRESSELHAUS SPIN–ORBIT COUPLINGS ON THE SV AND MM SOLITONS IN 2D 9.5 2D SOLITONS UNDER THE ACTION OF THE ZEEMAN SPLITTING (ZS) 9.6 SV GAP SOLITONS IN THE DIFFRACTIONLESS LIMIT 9.7 METASTABLE 3D SOLITONS IN THE SOC SYSTEM REFERENCES Chapter 10: Emulation of the Spin—Orbit Coupling (SOC) in Optical Systems 10.1 SPATIOTEMPORAL SOLITONS IN DISPERSIVE DUAL-CORE COUPLERS 10.2 SPATIOTEMPORAL SOLITONS IN THE SOC-EMULATING (PARITY-TIME)-SYMMETRIC DUAL-CORE COUPLER REFERENCES Chapter 11: Quantum Droplets (QDs): Theory 11.1 THEORETICAL MODELS OF QDS IN THREE, TWO, AND ONE DIMENSIONS 11.2 STABLE QDs WITH EMBEDDED VORTICITY 11.3 TWO-DIMENSIONAL VORTEX MODES TRAPPED IN A SINGULAR POTENTIAL REFERENCES Chapter 12: Experiments: Quantum Droplets (QDs) in the BEC with Contact and Dipole–Dipole Interactions (DDIs) 12.1 OBLATE (QUASI-2D ALIAS “PANCAKE-SHAPED”) DROPLETS 12.2 THREE-DIMENSIONAL (ISOTROPIC) DROPLETS 12.3 COLLISIONS BETWEEN ISOTROPIC QDs 12.4 DROPLETS IN A HETERONUCLEAR BOSONIC MIXTURE 12.5 DROPLETS IN THE DIPOLAR CONDENSATE OF DYSPROSIUM 12.6 DROPLETS IN THE DIPOLAR CONDENSATE OF ERBIUM REFERENCES Chapter 13: Multidimensional Solitons in Nonlocal Media 13.1 INTRODUCTION TO THE TOPIC 13.2 ANISOTROPIC QUASI-2D SOLITONS BUILT BY DIPOLE–DIPOLE INTERACTIONS (DDIs) IN BOSE–EINSTEIN CONDENSATE OF MAGNETIC ATOMS 13.3 GIANT VORTEX RINGS (VRs) IN MICROWAVE-COUPLED BINARY BEC REFERENCES Chapter 14: Multidimensional Dissipative Solitons and Solitary Vortices 14.1 SPIRAL SOLITONS (VORTEX RINGS) PRODUCED BY THE 2D COMPLEX GINZBURG–LANDAU (CGL) EQUATION WITH THE CUBIC–QUINTIC (CQ) NONLIN 14.2 DISSIPATIVE VORTEX SOLITONS STABILIZED BY THE FREQUENCY-SELECTIVE FEEDBACK 14.3 WEAKLY LOCALIZED MODES IN MEDIA WITH NONLINEAR LOSSES (MULTI-PHOTON ABSORPTION) 14.4 LOCALIZED STATES IN 2D NONLINEAR DISSIPATIVE MEDIA WITH SPATIALLY MODULATED GAIN OR LOSS 14.5 TWO-DIMENSIONAL DSs (DISSIPATIVE SOLITONS) IN THE HO (HARMONIC-OSCILLATOR) TRAPPING POTENTIAL 14.6 DISSIPATIVE VORTEX SOLITONS STABILIZED BY SPATIALLY PERIODIC (LATTICE) POTENTIALS 14.7 TWO-COMPONENT DISSIPATIVE SOLITONS OF THE VORTEX–ANTIVORTEX (VAV) TYPE STABILIZED BY SOC (SPIN–ORBIT COUPLING) 14.8 THREE-DIMENSIONAL DISSIPATIVE SOLITONS REFERENCES Chapter 15: Conclusion REFERENCES Index