Vortices and ring dark solitons in nonlinear amplifying waveguides

TL;DR

This paper explores the formation and stability of vortex structures and ring dark solitons in nonlinear amplifying waveguides, revealing their self-similar evolution and robustness against perturbations.

Contribution

It introduces the concept of stable, self-similar vortex and ring dark soliton structures in nonlinear amplifying waveguides, supported by analytical and numerical analysis.

Findings

Vortex tori and ring dark solitons are generated with specific initial conditions.

These structures exhibit exponential shrinking of vortex cores and notches.

The self-similar structures are stable against azimuthal perturbations.

Abstract

We consider the generation and propagation of (2+1)-dimensional beams in a nonlinear waveguide with the linear gain. Simple self-similar evolution of the beams is achieved at the asymptotic stage, if the input beams represent the fundamental mode. On the contrary, if they carry vorticity or amplitude nodes (or phase slips), vortex tori and ring dark solitons (RDSs) are generated, featuring another type of the self-similar evolution, with an exponentially shrinking vortex core or notch of the RDS. Numerical and analytical considerations reveal that these self-similar structures are robust entities in amplifying waveguides, being \emph{stable} against azimuthal perturbations.