  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.
