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

TL;DR

This paper predicts and analyzes the stability of new higher-order vortex solitons, multipoles, and supervortices in optical and Bose-Einstein condensate lattices, expanding understanding of complex vortex structures in nonlinear media.

Contribution

It introduces new types of vortex solitons and supervortices in optical lattices and BECs, with stability conditions and direct simulation validation.

Findings

Vortex ring solitons are stable if phase difference > π/2.

Supervortices are stable if phase difference < π/2.

Stability diagrams are provided based on simulations.

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 \Delta \phi between adjacent solitons in the ring is larger than \pi/2, while the supervortices are stable in the opposite case, \Delta \phi <\pi /2. A qualitative explanation to the stability is given.