Generation of periodic evolution patterns by the interaction of pearcey-gaussian beams carrying sidelobe in parabolic potential

Abstract

Based on the fractional Schrödinger equation, the propagation properties of the Pearcey-Gaussian beam with the sidelobe in the parabolic potential are studied by using the split-step Fourier numerical simulation method. The focusing phenomenon appears without the parabolic potential when Pearcey-Gaussian beam carries the sidelobe. In the case of the parabolic potential, the beam forms the bound state in the propagation process. The period of the bound state decreases as the parabolic potential coefficient increases. In addition, the interaction of two Pearcey-Gaussian beams with the sidelobe in the potential is investigated. The effect of Lévy index, interval parameter, initial phase factor and parabolic potential coefficient on the interaction of two Pearcey-Gaussian beams with sidelobe is considered.