LAUSR

Abstract Based on fractional Schrodinger equation (FSE), we have emphatically investigated the evolution of Airy-Gaussian (AiG) beams under Gaussian potential by split-step Fourier method. Only when beam is incident vertically can splitting occur. When taking Gaussian potentials into account, periodic evolution can be achieved by assigning appropriate values to barrier parameters, avoiding the transmission phenomenon. Transmission and reflection (TR) ratio varies with values of barrier width and height, and period changes accordingly. Critical barrier height increases with the larger Levy index as a whole, while it eventually tends to be stable with the larger barrier width. In addition, compared with Gaussian wells, it is easier to achieve total reflection in Gaussian barriers.