Fractional Schrodinger equation in optics

In quantum mechanics, the space-fractional Schrodinger equation provides a natural extension of the standard Schrodinger equation when the Brownian trajectories in Feynman path integrals are replaced by Levy flights. Here an optical realization of the fractional Schrodinger equation, based on transverse light dynamics in aspherical optical cavities, is proposed. As an example, a laser implementation of the fractional quantum harmonic oscillator is presented in which dual Airy beams can be selectively generated under off-axis longitudinal pumping. (C) 2015 Optical Society of America