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.

5 pages, 3 figures

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Fractional Quantum Mechanics
• Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well

Cited by in corpus (61)

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