Propagation characteristics of ring Airy beams modeled by fractional Schrödinger equation

Abstract

We have numerically investigated the propagation properties of ring Airy beams modeled by a fractional Schrödinger equation (FSE). Beam splitting is exhibited and clarified from the view of group delay. Compared with the case of the condition in free space, the focal intensity is greatly enhanced and presents a trend from increasing to decreasing with the decrement of the Lévy index, while the focal length largely increases; in addition, the parabolic trajectory is distorted with the Bessel pattern gradually disappearing. However, both the focal intensity and its length get decreased due to the absence of the initial phase of ring Airy beams; simultaneously, the size of the focal spot decreases for a larger Lévy index. The changes of focusing properties are clearly clarified. Moreover, without initial phase, the ratio of focal intensity under the Lévy index to the condition in free space is given to show the faster growth of focal intensity when the Lévy index is lower than 1.25; otherwise, the trend gets reversed. The autofocusing properties of ring Airy beams modeled by FSE can find applications in optical trapping and manipulation.