Li P, Li R, Dai C. Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction.
OPTICS EXPRESS 2021;
29:3193-3210. [PMID:
33770923 DOI:
10.1364/oe.415028]
[Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2020] [Accepted: 12/25/2020] [Indexed: 06/12/2023]
Abstract
We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy 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.
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