Fractional Schr\"{o}dinger equation in optics

TL;DR

This paper proposes an optical implementation of the fractional Schrödinger equation using transverse light dynamics in aspherical optical cavities, demonstrating the generation of dual Airy beams in a laser-based fractional quantum harmonic oscillator.

Contribution

It introduces a novel optical realization of the fractional Schrödinger equation and demonstrates its application in generating dual Airy beams.

Findings

Successful laser implementation of fractional quantum harmonic oscillator

Generation of dual Airy beams via off-axis longitudinal pumping

Extension of quantum mechanics concepts to optical systems

Abstract

In quantum mechanics, the space-fractional Schr\"{o}dinger equation provides a natural extension of the standard Schr\"{o}dinger equation when the Brownian trajectories in Feynman path integrals are replaced by Levy flights. Here an optical realization of the fractional Schr\"{o}dinger 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.