Defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation

Abstract

We address the existence, stability, and propagation dynamics of both one- and two-dimensional defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation. Under the influence of fractional effect, in one dimension, solitons exist stably in limited regions in the semi-infinite bandgap with high and low power both for a negative and positive defect lattice. In the first bandgap, solitons are stable for negative defect lattice, while unstable for positive defect lattice. In the second bandgap, only stable solitons can propagate in small regions for the positive defect lattice. With increasing the Lévy index from 1 to 2, the power of the defect solitons decreases in the semi-infinite bandgap and increases in the first bandgap. Linear stability analyses show that, the domains of stability for defect solitons strongly depend on the Lévy index, defect strength and different bandgaps. In two dimension, defect solitons can exist stably at high and moderate power regions in the semi-infinite bandgap and all regions in the first bandgap with negative defect lattice, while they are stable at high, moderate and low power regions in the semi-infinite bandgap and unstable in the first bandgap with positive defect lattice.