Optical solitons and vortices in fractional media: A mini-review of recent results

TL;DR

This mini-review summarizes recent numerical and analytical findings on stable optical solitons and vortices in fractional media, highlighting models with fractional diffraction, nonlinearities, and linear potentials, and their potential experimental realizations.

Contribution

It provides a concise overview of recent advances in understanding stable solitons and vortices in fractional nonlinear Schrödinger models, including analytical approaches and potential optical implementations.

Findings

Numerical results demonstrate stable propagation of solitons and vortices in fractional media.

Analytical findings include variational approximations and solutions for fast-moving solitons.

Brief discussion of dissipative solitons governed by fractional complex Ginzburg-Landau equation.

Abstract

The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schroedinger equation including fractional one- or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination of mirrors, lenses, and phase masks. The results presented in the article were chiefly obtained in a numerical form. Some analytical findings are included too -- in particular, for fast moving solitons, and results produced by the variational approximation. Also briefly considered are dissipative solitons which are governed by the fractional complex Ginzburg-Landau equation.