Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction

We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrodinger equation, characterized by its Levy index, with self-tbcusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Levy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation. Different scenarios of bifurcations emerge with the change of stability: the branches of asymmetric solitons split off the branches of unstable symmetric solitons with the increase of soliton power and form a supercritical type bifurcation for self-focusing saturable nonlinearity; the branches of asymmetric solitons bifurcates from the branches of unstable antisymmetric solitons for self-defocusing saturable nonlinearity, featuring a convex shape of the bifurcation loops: an antisymmetric soliton loses its stability via a supercritical bifurcation, which is followed by a reverse bifurcation that restores the stability of the symmetric soliton. Furthermore, we found a scheme of restoration or destruction the symmetry of the antisymmetric solitons by controlling the fractional diffraction in the case of self-defocusing saturable nonlinearity. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Automated summary

This study investigates the existence, bifurcation, and stability of two-dimensional optical solitons in the context of the fractional nonlinear Schrodinger equation. Different scenarios of bifurcations are observed depending on the stability and type of nonlinearities, with asymmetric solitons emerging through symmetry breaking bifurcation. The restoration or destruction of symmetry in antisymmetric solitons can be controlled by adjusting the fractional diffraction in the case of self-defocusing saturable nonlinearity.