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 linear potential or not, is influenced by Lévy index. When the linear potential is considered, the periodic evolution of the Pearcey Gaussian beams is given, and results show that transmission period is inversely proportional to the linear potential coefficient. And the direction of beam propagation can be controlled by the symbol of linear potential parameters. The propagation of incident beam with transverse wave velocity have been studied. Moreover, the chirp does not influence the evolution period of the Pearcey Gaussian beam but the intensity distribution. These properties can be well implemented to the promising applications of Pearcey Gaussian beam in optical manipulation and optical switch.

Abrupt focus and bright spot formation in fractional system with PT-symmetric nonlocal nonlinearity

“…Bai et al and Zang et al explored the adjustable splitting and collision of Airy beam [20] and Gaussian beam [21], respectively. The dynamics of other beams, such as super-Gaussian beam [22], Lommel Gaussian beam [23], Pearcey-Gaussian beam [24] in linear and nonlinear fractional systems have also been investigated. Meanwhile, the existence and robustness of diverse soliton states, such as ghost states [25], double gray solitons [26], asymmetric localized states [27] in fractional nonlinear system, are extensively discussed.…”