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.

中文翻译：

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贝塞尔光束在二维振幅光栅上的衍射——塔尔博特效应研究的一个新分支

在本文中，提出了二维振幅光栅上任意阶贝塞尔光束 $J_l(\kappa r)$ 的衍射解析理论。在一定条件下，主、分 Talbot 平面上的衍射图案是环形微束的晶格，其直径取决于光栅周期、照射光束直径、Talbot 平面的数量和拓扑电荷 $l$。对于靠近光轴的环，后者再现了照明光束的 $l$。在新西伯利亚自由电子激光器上进行的实验，波长为 $\lambda = 141 $$\mu$m，使用孔径低至 $d \approx 2\lambda $ 的光栅，以及数值模拟，很好的支持理论。由于拉盖尔-高斯光束可以表示为贝塞尔光束的叠加，