Hermite-Gaussian–like soliton in the nonlocal nonlinear fractional Schrödinger equation

Abstract

The propagation of an optical beam in the nonlocal nonlinear fractional Schrödinger equation (NNFSE) was numerically investigated. The results reveal that the stability of beam propagation decreases as the Lévy index decreases in the local fractional case. However, the nonlocal response can effectively enhance the stability of beam propagation and leads to a completely stable solitons formation in the NNFSE. In addition, the shapes of fundamental mode solitons are determined by the Lévy indexes and nonlocalities. For the high-order solitons case, the shapes slightly vary with the change of nonlocality, but are strongly dependent on the Lévy index. Furthermore, the critical power of the stable soliton decreases as the Lévy index decreases since the decrease of the Lévy index will weaken the diffraction effect.