Potential barrier-induced dynamics of finite energy Airy beams in fractional Schrödinger equation

Abstract

The dynamics of Airy beams modeled by the fractional Schrodinger equation (FSE) with the potential barrier are numerically investigated. Adjusting the Levy index provides a convenient way to control the diffraction of Airy beams which presents the non-diffraction and splitting property. It has been found that the total reflection of beams occurs when the depth of the single potential barrier exceeds the threshold, and that the number of reflected waves is influenced by the Levy index and the location of potential barrier. However, the periodic self-imaging phenomenon of Airy beams is shown under a symmetric potential barrier when the Levy index is equal to one, and the self-imaging period of the asymmetric Airy beams is analytically demonstrated and is as twice as that of symmetric Gaussian beams, moreover, the chaoticon of light field is formed during propagation as the Levy index increases. All the properties of Airy beams modeled by FSE confirm the potential application in optical manipulation.