Anomalous interaction of Airy beams in the fractional nonlinear Schrödinger equation

Abstract

We investigate the mutual interaction of two spatially-separated Airy beams in the nonlinear Schrödinger equation with the fractional Laplacian. Depending on the beam separation (<i>d</i>), relative phase and Lévy index (<i>α</i>), we observed an anomalous attraction or repulsion between the Airy beams. Anomalous attraction leads to a single breather soliton with a period that grows exponentially as <i>α</i> increases. In this region of the parameter space, we identify a crossover between two asymmetric regimes: as the Lévy index exceeds a critical value <i>α</i> _c, the period of breather soliton for <i>d</i>>0 is orders of magnitude larger than for <i>d</i><0, while the opposite occurs as <i>α</i><<i>α</i> _c. Our results reveal a novel scenario for Airy beams interaction in the framework of fractional nonlinear Schrödinger equation and provide an alternative mechanism to control breather soliton generation.