Periodic evolution of the Pearcey Gaussian beam under fractional effect

Abstract

In this paper, the propagation dynamics of the Pearcey Gaussian beam modeled by the fractional Schrödinger equation in linear potential have been investigated. Different from the propagation properties of the Pearcey Gaussian beam described by the standard Schrödinger equation, the diffraction-free phenomenon which is presented under the fractional Schrödinger equation with or without linear potential, is influenced by the Lévy index. When the linear potential is considered, the periodic evolution of the Pearcey Gaussian beams is given, and results show that the transmission period is inversely proportional to the linear potential coefficient. The direction of beam propagation can also be controlled by the symbol of linear potential parameters. The propagation of incident beam with transverse wave velocity has been studied. Moreover, the chirp does not influence the evolution period of the Pearcey Gaussian beam but does influence the intensity distribution. These properties can be well implemented for promising applications of Pearcey Gaussian beams in optical manipulation and optical switches.