Self-Fourier transform and self-Fourier beams due to parabolic potential

TL;DR

This paper explores how certain light beams in a parabolic potential undergo oscillations and automatic Fourier transforms during propagation, introducing a new class of self-Fourier beams with potential optical applications.

Contribution

The study reveals that beams in a parabolic potential can perform automatic Fourier transforms and introduces a new class of self-Fourier beams based on this property.

Findings

Beams oscillate and perform automatic Fourier transforms during propagation.

Parity asymmetry affects the oscillation period.

Finite-energy Airy beams exhibit periodic inversion.

Abstract

We investigate the propagation of light beams including Hermite-Gauss, Bessel-Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams -- that is, the beams whose Fourier transforms are the beams themselves.