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Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic Nonlinear Medium
  • Luciano Medina
Luciano Medina
New York University

Corresponding Author:lmedina@nyu.edu

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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 but the wave propagation constants undetermined, 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.
21 Oct 2022Submitted to Mathematical Methods in the Applied Sciences
21 Oct 2022Submission Checks Completed
21 Oct 2022Assigned to Editor
01 Nov 2022Review(s) Completed, Editorial Evaluation Pending
03 Nov 2022Reviewer(s) Assigned
18 Apr 2023Editorial Decision: Revise Minor
28 Apr 20231st Revision Received
16 May 2023Submission Checks Completed
16 May 2023Assigned to Editor
16 May 2023Review(s) Completed, Editorial Evaluation Pending
17 May 2023Reviewer(s) Assigned
06 Jul 2023Editorial Decision: Accept