Families of Vortex Solitons in Periodic Media

Abstract

Various families of charge-one vortex solitons in two-dimensional periodic media are reported. These vortices reside either in the semi-infinite gap or higher band gaps of the media. For both Kerr and saturable nonlinearities (either focusing or defocusing), infinite vortex families are found. All these families do not bifurcate from Bloch bands; rather, they turn around before reaching edges of Bloch bands. It is further revealed that vortices with drastically different topological shapes can belong to the same vortex family, which is quite surprising.

arXiv commentTo appear in Phys. Rev. A (with higher resolution figures)

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• Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials
• Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials
• Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media
• Dynamics of gap solitons in a dipolar Bose-Einstein condensate on a three-dimensional optical lattice
• Dipolar bright solitons and solitary vortices in a radial lattice
• Stable structures with high topological charge in nonlinear photonic quasicrystals
• Geometric stabilization of extended S=2 vortices in two-dimensional photonic lattices: theoretical analysis, numerical computation and experimental results
• Beam steering and topological transformations driven by interactions between discrete vortex and fundamental solitons
• Lattice vortices induced by noncommutativity
• Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential
• Half-vortex soliton lattices in spin-orbit-coupled Bose-Einstein condensates with a quasi-flat band