# Existence of Optical Vortex Solitons in Photorefractive Media

## TL;DR

This paper proves the existence of optical vortex solitons in photorefractive media, providing theoretical constraints and numerical methods to analyze their properties in nonlinear optical physics.

## Contribution

It introduces an existence theory for vortex solitons in photorefractive media, using constrained minimization and finite element methods.

## Key findings

- Existence of positive exponentially decaying vortex solutions.
- Constraints on propagation constants for vortex stability.
- Numerical computation methods for vortex profiles.

## Abstract

Optical propagation and vortices in nonlinear media have been intensively studied in modern optical physics. In this paper, we establish constraints regarding the propagation constant and provide an existence theory and numerical computations for positive exponentially decaying solutions for a class of ring-profiled solitons in a type of nonlinear media known as a photorefractive nonlinearity. Our methods include constrained minimization and finite element formalism, and we study the vortex profile and its propagation by fixing the energy flux.