Optical Bloch oscillation and Zener tunneling in the fractional Schrodinger equation

We demonstrate optical Bloch oscillation (OBO) and optical Zener tunneling (OZT) in the fractional Schrodinger equation (FSE) with periodic and linear potentials, numerically and theoretically. We investigate in parallel the regular Schrodinger equation and the FSE, by adjusting the Levy index, and expound the differences between the two. We find that the spreading of the OBO decreases in the fractional case, due to the diminishing band width. Increasing the transverse force, due to the linear potential, leads to the appearance of OZT, but this process is suppressed in the FSE. Our results indicate that the adjustment of the Levy index can effectively control the emergence of OBO and OZT, which can inspire new ideas in the design of optical switches and interconnects.