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

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 Schrodinger 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 Levy 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 Levy 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.

Automated summary

We investigate the existence, stability, and propagation dynamics of one- and two-dimensional defect solitons in an optical lattice with saturable nonlinearity in the fractional Schrodinger equation. The stability of solitons strongly depends on the Levy index, defect strength, and different bandgaps. In one dimension, solitons can exist stably in limited regions in the bandgap with high and low power for both negative and positive defect lattice. In two dimensions, defect solitons can exist stably at high and moderate power regions in the bandgap and all regions in the first bandgap with a negative defect lattice.