Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials

TL;DR

This paper demonstrates that optical-lattice potentials can stabilize various 2D solitons and vortices against supercritical collapse caused by cubic-quintic nonlinearity, expanding the understanding of stabilization mechanisms in nonlinear media.

Contribution

It shows that optical lattices can stabilize 2D solitons and vortices against supercritical collapse, using variational approximation and numerical solutions, for the first time in this context.

Findings

OLs stabilize solitons against super-critical collapse

Stability follows the Vakhitov-Kolokolov criterion

Applicable to optical media and BEC in pancake traps

Abstract

It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by the cubic attractive nonlinearity in the 2D geometry. We demonstrate OLs can also stabilize various species of fundamental and vortical solitons against the super-critical collapse, driven by the double-attractive cubic-quintic nonlinearity (however, solitons remain unstable in the case of the pure quintic nonlinearity). Two types of OLs are considered, producing similar results: the 2D Kronig-Penney "checkerboard", and the sinusoidal potential. Soliton families are obtained by means of a variational approximation, and as numerical solutions. The stability of the families, which include fundamental and multi-humped solitons, vortices of oblique and straight types, vortices built of quadrupoles, and supervortices, strictly obeys the Vakhitov-Kolokolov criterion. The model applies to optical media and BEC in "pancake" traps.