Stable vortex solitons sustained by a localized gain in the cubic medium

TL;DR

This paper introduces a simple dissipative cubic medium system that supports stable high-charge vortex solitons through localized gain and defocusing nonlinearity, revealing new stability mechanisms and dynamical behaviors.

Contribution

It demonstrates the formation of stable vortex solitons with high topological charges in a purely cubic defocusing medium using localized linear gain, without competing nonlinearities.

Findings

Stable high-charge vortex solitons are supported by localized gain.

Increasing gain amplitude enhances stability and causes soliton expansion.

Unusual dynamics include transformation into lower or higher charge vortex states.

Abstract

We propose a simple dissipative system with purely cubic defocusing nonlinearity and nonuniform linear gain that can support stable localized dissipative vortex solitons with high topological charges without the utilization of competing nonlinearities and nonlinear gain or losses. Localization of such solitons is achieved due to an intriguing mechanism when defocusing nonlinearity stimulates energy flow from the ring-like region with linear gain to the periphery of the medium where energy is absorbed due to linear background losses. Vortex solitons bifurcate from linear gain-guided vortical modes with eigenvalues depending on topological charges that become purely real only at specific gain amplitudes. Increasing gain amplitude leads to transverse expansion of vortex solitons, but simultaneously it usually also leads to stability enhancement. Increasing background losses allows creation of stable vortex solitons with high topological charges that are usually prone to instabilities in conservative and dissipative systems. Propagation of the perturbed unstable vortex solitons in this system reveals unusual dynamical regimes, when instead of decay or breakup, the initial state transforms into stable vortex soliton with lower or sometimes even with higher topological charge. Our results suggest an efficient mechanism for the formation of nonlinear excited vortex-carrying states with suppressed destructive azimuthal modulational instabilities in a simple setting relevant to a wide class of systems, including polaritonic systems, structured microcavities, and lasers.