On the existence of optical vortex solitons propagating in saturable nonlinear media

TL;DR

This paper establishes the existence of optical vortex solitons in saturable nonlinear media using variational methods, providing explicit estimates and numerical analysis of their properties.

Contribution

It introduces a new existence theory for ring-profiled optical vortex solitons in saturable nonlinear media, with explicit parameter estimates and numerical illustrations.

Findings

Existence of positive solutions for vortex solitons is proven.

Explicit estimates for wave propagation constant and energy flux are provided.

Numerical analysis illustrates soliton amplitude and propagation behavior.

Abstract

In this paper, an existence theory is established for ring-profiled optical vortex solitons. We consider such solitons in the context of an electromagnetic light wave propagating in a self-focusing nonlinear media and governed by a nonlinear Schr\"odinger type equation. A variational principle and constrained minimization approach is used to prove the existence of positive solutions for an undetermined wave propagation constant. We provide a series of explicit estimates related to the wave propagation constant, a prescribed energy flux, and vortex winding number. Further, on a Nehari manifold, the existence of positive solutions for a wide range of parameter values is proved. We also provide numerical analysis to illustrate the behavior of the soliton's amplitude and wave propagation constant with respect to a prescribed energy flux and vortex winding number.