Diffraction of Bessel beams on 2D amplitude gratings -- a new branch in the Talbot effect study

TL;DR

This paper develops an analytical theory for the diffraction of Bessel beams on 2D amplitude gratings, revealing a lattice of annular microbeams in the Talbot planes, supported by experiments and simulations, and applicable to Laguerre-Gaussian beams.

Contribution

The paper introduces a new analytical framework for understanding Bessel beam diffraction on 2D gratings within the Talbot effect, extending to Laguerre-Gaussian beams.

Findings

Diffraction pattern forms a lattice of annular microbeams.

Pattern diameters depend on grating period, beam size, Talbot plane, and topological charge.

Experimental results with free electron laser support the theory.

Abstract

In this paper, an analytical theory for the diffraction of a Bessel beam of arbitrary order $J_l(\kappa r)$ on a 2D amplitude grating is presented. The diffraction pattern in the main and fractional Talbot planes under certain conditions is a lattice of annular microbeams, the diameters of which depend on the grating period, the illuminating beam diameter, the number of the Talbot plane, and the topological charge $l$. For the rings near the optical axis, the latter reproduces $l$ of the illuminating beam. Experiments carried out on the Novosibirsk free electron laser at a wavelength $\lambda = 141$$\mu$m using gratings with hole diameters of down to $d \approx 2\lambda $, as well as, the numerical simulations, well support the theory. Since the Laguerre-Gaussian beams can be represented as a superposition of Bessel beams, results of this paper can be applied to the analysis of the Talbot effect with the Laguerre-Gaussian beams.