Propagation of Gaussian beam based on two-dimensional fractional Schrödinger equation

Abstract

In this paper, the dynamic evolution of Gaussian beam governed by the two-dimensional fractional Schrödinger equation with variable coefficient is studied. The influences of the longitudinal modulation, the Lévy index and the chirp parameters on the evolution of the Gaussian beam are discussed in detail. The results show that in the absence of the beam chirp, the unchirped Gaussian beam is axisymmetric and exhibits a ring-shaped structure, but due to the longitudinal modulation, the size of the ring will change. In the presence of the beam chirp, the axisymmetry is broken and optical beam in propagation exhibits a crescent structure. In the longitudinal periodic modulation, the chirped Gaussian beam oscillates periodically along a certain direction. The influence of the Lévy index on the evolution of the Gaussian beam is also studied, and the result shows that the increasing of the Lévy index will enhance the diffraction of the optical beam in propagation.