Far-field diffraction of vortex grating

In this paper, we study theoretically and experimentally the far-field diffraction of amplitude vortex grating. The analytic expression of the diffraction intensity distribution is deduced according to Bessel function and its recursion formula, and the dependence relation of the diffraction on the parameters of grating is exhibited. The numerical simulations indicate the diffraction patterns consist of two characteristic components, namely, the inner spot and the periphery turbine-like fringes. The number of grating lines and their rotation direction determine the structure of the periphery turbine-like fringes. The density of the grating lines influences the radial size of the turbine-like fringe structure, and the hard-edged aperture controls the compaction of the fringes besides limiting the diffraction intensity. The practical experimental results verify these conclusions. The study of this paper will be helpful for the understanding the diffraction characteristics of vortex grating and regulating artificially the intensity distribution of the beam.