Diffraction of a Laguerre-Gaussian beam in Raman interaction with a spatially periodic pump field

Abstract

We studied Fresnel diffraction of a Laguerre-Gaussian beam ${\text{LG}}_{p,l}$ with arbitrary azimuthal $l$ and radial $p$ indices on a grating induced during its Raman interaction with a spatially periodic pump field in an atomic medium. The diffraction pattern turned out to be more complex than the classical Talbot effect observed when a plane wave illuminates a two-dimensional grating. The simulation results show that, under certain conditions, at distances corresponding to the classical Talbot planes (integer and fractional), periodic amplitude-phase distributions appear. The diffraction patterns are not a probe-field image in the induced grating plane, but a regular array of vortex annular-shaped microbeams with an inhomogeneous intensity distribution depending on the $l$ and $p$ indices and with a topological charge equal to that of the initial probe beam. The intensity and spatial distribution of diffraction patterns can be controlled by Raman amplification in the induced grating by varying the pump-field intensity or the Raman detuning.