Generalized revival and splitting of an arbitrary optical field in GRIN media

TL;DR

This paper investigates the non-paraxial propagation of arbitrary optical fields in quadratic GRIN media, revealing conditions for field revival and splitting, with applications to Bessel and Airy functions and validation through numerical comparisons.

Contribution

It introduces a non-paraxial analysis showing revival and splitting phenomena in arbitrary fields within GRIN media, extending understanding beyond paraxial approximations.

Findings

Field revival occurs at specific wavelengths and distances.

Propagation results in splitting into generalized Bessel functions and Airy functions.

Numerical simulations confirm analytical predictions.

Abstract

Assuming a non-paraxial propagation operator, we study the propagation of an electromagnetic field with an arbitrary initial condition in a quadratic GRIN medium. We show that at certain specific periodic distances, the propagated field is given by the fractional Fourier transform of a superposition of the initial field and of a reflected version of it. We also prove that for particular wavelengths, there is a revival and a splitting of the initial field. We apply this results, first to an initial field given by a Bessel function and show that it splits into two generalized Bessel functions, and second, to an Airy function. In both cases our results are compared with the exact numerical ones.