On the existence of optical vortex solitons propagating in saturable nonlinear media
arXiv:1505.06157 · doi:10.1063/1.4974316
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 Schrödinger 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.
arXiv commentErrors have been corrected from a previous version
References in corpus (7)
- Solitons in nonlinear lattices
- Observation of discrete vortex solitons in optically-induced photonic lattices
- Rotary solitons in Bessel photonic lattices
- Stable ring vortex solitons in Bessel optical lattices
- Paraxial Light Beams with Angular Momentum
- Stable multiple-charged localized optical vortices in cubic-quintic nonlinear media
- Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice