Fractional Schrödinger equation in optics

Optics Letters
Stefano Longhi

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.

References

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Citations

Apr 22, 2016·Scientific Reports·Yiqi ZhangMin Xiao
Dec 16, 2016·Optics Letters·Changming Huang, Liangwei Dong
Dec 21, 2017·Scientific Reports·Yiqi ZhangYanpeng Zhang
Jul 16, 2017·Scientific Reports·Changming Huang, Liangwei Dong
Aug 31, 2016·Physical Review. E·Wei-Ping ZhongTingwen Huang
Nov 14, 2015·Physical Review Letters·Yiqi ZhangMin Xiao
Jul 1, 2015·Optics Letters·Stefano Longhi
Feb 7, 2018·Optics Express·Jing XiaoLiangwei Dong
Dec 1, 2018·Optics Letters·Xiankun Yao, Xueming Liu
Oct 16, 2019·Optics Letters·Liangwei DongWei Qi
Dec 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A P Riascos, José L Mateos
Apr 16, 2016·Optics Letters·Stefano Longhi, Shane M Eaton
Nov 16, 2019·Optics Letters·Changming Huang, Liangwei Dong
Nov 12, 2020·Scientific Reports·Mahboubeh Ghalandari, M Solaimani
May 13, 2021·Scientific Reports·Mario I Molina

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