Interaction of Airy beams modeled by the fractional nonlinear cubic-quintic Schrödinger equation

Abstract

We investigate theoretically and numerically the interaction of Airy beams modeled by fractional nonlinear cubic-quintic Schrödinger equation. By considering fractional diffraction effect, when the initial beam interval between the two Airy beams is large enough, it is found that two in-phase Airy beams attract and repel each other, and two out-of-phase beams repel each other. This is different from the interaction of two Airy beams with large interval in standard nonlinear Schrödinger equation, where the two beams display a weak interaction. For smaller interval, single breathing soliton and symmetric breathing soliton pairs are formed in the in-phase and out-of-phase cases, respectively. As the Lévy index decreases, for the single breathing soliton, the oscillation becomes stronger, the mean peak intensity increases, and the soliton width decreases, for the symmetric breathing soliton pair, the width becomes narrower, and the repulsion between the two Airy components becomes stronger. Besides, the quintic defocusing strength will modulate the interaction of Airy beams. When the strength coefficient increases, the width of the breathing soliton formed in the in-phase case becomes wider, the repulsion between the two beams in the out-of-phase case increases, as well as the width of the soliton pair becomes wider. The work may provide new control methods on the interaction of Airy beams.