Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity

Abstract

We address the issue of mobility of localized modes in two-dimensional nonlinear Schrödinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals. We discuss numerically obtained exact stationary solutions and their stability, focussing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility, and a well defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.

19 pages, 4 figures

References in corpus (9)

• Spatial Solitons in Optically-Induced Gratings
• Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
• Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation
• Reduced-symmetry two-dimensional solitons in photonic lattices
• Stability of vortex solitons in a photorefractive optical lattice
• Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays
• Controlled switching of discrete solitons in waveguide arrays
• Nonlinear photonic lattices in anisotropic nonlocal self-focusing media
• All-optical switching and amplification of discrete vector solitons in nonlinear cubic birefringent waveguide arrays

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