Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic Nonlinear Medium

TL;DR

This paper proves the existence of coupled optical vortex solitons in quadratic nonlinear media, revealing unique properties like the absence of semi-trivial solutions and the positivity of the second harmonic.

Contribution

It introduces a rigorous mathematical proof for the existence of ring-profiled vortex solitons in a coupled nonlinear Schrödinger system with quadratic nonlinearity, highlighting novel properties.

Findings

Existence of ring-profiled vortex solitons proven mathematically

Solutions are positive with undetermined wave propagation constants

System does not admit semi-trivial solutions, second harmonic remains positive

Abstract

We consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of ring-profiled optical vortex solitons appearing as solutions to a constrained minimization problem and as solutions to a min-max problem. In the case of the constrained minimization problem solutions are shown to be positive with undetermined wave propagation constants, but in the min-max approach the wave propagation constants can be prescribed. The quadratic nonlinearity introduces some interesting properties not commonly observed in other coupled systems in the context of nonlinear optics, such as the system not accepting any semi-trivial solutions, meaning, that optical solitons cannot be observed when, say, one of the beams are off. Additionally, the second harmonic always remains positive.