Generation of Talbot-like fields

TL;DR

This paper introduces a diffraction integral using eigenfunctions of the Laplacian to generate self-reproducing Talbot-like fields, including Bessel and Airy beam superpositions, with applications in self-focusing.

Contribution

It presents a novel integral approach for propagating specific optical fields and demonstrates how to produce Talbot-like self-imaging and self-focusing effects.

Findings

Successfully propagates Bessel and Airy beams using the new integral

Constructs fields that reproduce periodically in propagation (Talbot effect)

Shows superposition of Airy beams induces self-focusing

Abstract

We present an integral of diffraction based on particular eigenfunctions of the Laplacian in two dimensions. We show how to propagate some fields, in particular a Bessel field, a superposition of Airy beams, both over the square root of the radial coordinate, and show how to construct a field that reproduces itself periodically in propagation, i.e., a field that renders the Talbot effect. Additionally, it is shown that the superposition of Airy beams produces self-focusing.