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2015

Fractional Schr\"{o}dinger equation in optics

Longhi, Stefano

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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.

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