Fractional Schrödinger equation in optics

Abstract

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

© 2015 Optical Society of America

Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice

Changming Huang and Liangwei Dong
Opt. Lett. 41(24) 5636-5639 (2016)

Dissipative surface solitons in a nonlinear fractional Schrödinger equation

Changming Huang and Liangwei Dong
Opt. Lett. 44(22) 5438-5441 (2019)

One-dimensional solitons in fractional Schrödinger equation with a spatially periodical modulated nonlinearity: nonlinear lattice

Liangwei Zeng and Jianhua Zeng
Opt. Lett. 44(11) 2661-2664 (2019)

Surface gap solitons in a nonlinear fractional Schrödinger equation

Jing Xiao, Zhaoxia Tian, Changming Huang, and Liangwei Dong
Opt. Express 26(3) 2650-2658 (2018)

Anomalous interaction of Airy beams in the fractional nonlinear Schrödinger equation

Lifu Zhang, Xiang Zhang, Haozhe Wu, Chuxin Li, Davide Pierangeli, Yanxia Gao, and Dianyuan Fan
Opt. Express 27(20) 27936-27945 (2019)