Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice

Abstract
We predict new generic types of vorticity-carrying soliton complexes in a class of physical systems including an attractive Bose-Einstein condensate in a square optical lattice (OL) and photonic lattices in photorefractive media. The patterns include ring-shaped higher-order vortex solitons and supervortices. Stability diagrams for these patterns, based on direct simulations, are presented. The vortex ring solitons are stable if the phase difference Δ between adjacent solitons in the ring is larger than π/2, while the supervortices are stable in the opposite case, Δ < π/2. A qualitative explanation to the stability is given.
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