Stable two-dimensional solitons in nonlinear lattices

Abstract

We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with self-focusing nonlinearity, embedded into a linear material. We show that such lattices can stabilize two-dimensional solitons against collapse. We also found that stable multipoles and vortex solitons are also supported by the nonlinear lattices, provided that the nonlinearity exhibits saturation.

12 pages, 3 figures, to appear in Optics Letters

References in corpus (13)

• Fundamental and vortex solitons in a two-dimensional optical lattice
• Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
• Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices
• Rotary solitons in Bessel photonic lattices
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity
• Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
• Matter-wave solitons in radially periodic potentials
• Mean-field analysis of collapsing and exploding Bose-Einstein condensates
• Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
• Reduced-symmetry two-dimensional solitons in photonic lattices
• Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity
• Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index

Cited by in corpus (32)

• Solitons in nonlinear lattices
• Solitons in combined linear and nonlinear lattice potentials
• Bright solitons from defocusing nonlinearities
• Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
• Algebraic bright and vortex solitons in defocusing media
• Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension
• Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling
• Solitons supported by localized nonlinearities in periodic media
• Three-dimensional hybrid vortex solitons
• Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity
• Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices
• A two-dimensional paradigm for symmetry breaking: the nonlinear Schrodinger equation with a four-well potential
• Quadratic fractional solitons
• Stabilization of multi-beam necklace solitons in circular arrays with spatially modulated nonlinearity
• Stable and oscillating solitons of $\mathcal{P}\mathcal{T}$-symmetric couplers with gain and loss in fractional dimension
• Localized modes and dark solitons sustained by nonlinear defects
• Stabilization of two-dimensional solitons in cubic-saturable nonlinear lattices
• Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity
• Bubbles and W-shaped solitons in Kerr media with fractional diffraction
• Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices
• Flat-floor bubbles, dark solitons, and vortices stabilized by inhomogeneous nonlinear media
• Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity
• Solitons and vortices in nonlinear potential wells
• Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices
• A magic tilt angle for stabilizing two-dimensional solitons by dipole-dipole interactions
• Asymmetric solitons and domain walls supported by inhomogeneous defocusing nonlinearity
• Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials
• Asymmetric localized states in periodic potentials with a domain wall-like Kerr nonlinearity
• Transfer and scattering of wave packets by a nonlinear trap
• Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component
• Observation of Light Localization at the Edges of Quasicrystal Waveguide Arrays
• Low-energy effective quantum field theoretic description of excitations about soliton configurations