Effects of fractional diffraction on nonlinear PT phase transitions and stability of dark solitons and vortices

TL;DR

This paper investigates how fractional diffraction influences the existence, phase transitions, and stability of dark solitons and vortices in nonlinear PT-symmetric waveguides, revealing new nonlinear phase transition phenomena.

Contribution

It introduces the impact of fractional diffraction on PT phase transitions and stability of dark solitons and vortices in nonlinear optical waveguides.

Findings

Solution branches merge and disappear with increased gain-loss strength.

Fractional diffraction affects the boundaries of existence regions for DSs and vortices.

Stable dark solitons and vortices are confirmed through numerical simulations.

Abstract

The wave propagation under the action of fractional diffraction has recently drawn increasing attention in nonlinear optics. Here, we address the effect of fractional diffraction on the existence, phase transitions, and stability of dark solitons (DSs) and vortices in parity-time (PT) symmetric graded-index waveguide with self-defocusing nonlinearity. The DSs and vortices are produced by numerical solution of the corresponding one- and two-dimensional fractional nonlinear Schr\"odinger equations. We show that solution branches of fundamental and higher-order DSs collide pair-wise (merge) and disappear with the increase of the gain-loss strength, revealing nonlinear PT phase transitions in the waveguide. Numerically identifying the merger points, we demonstrate effects of the fractional diffraction on the phase transition.The phase transition points determine boundaries of existence regions for the DSs and vortices.The stability of the DSs and vortices is studied by means of the linearization with respect to small perturbations. Direct simulations of perturbed evolution corroborate their stability properties predicted by the analysis of small perturbations.