Symmetry in the diffraction of beams carrying orbital angular momentum

Abstract

Diffraction of orbital-angular-momentum--carrying Laguerre-Gauss vortex (LGV) beams by $N$-fold rotationally symmetric regular polygons is studied analytically and experimentally. The structure, symmetry, and dependence of the diffraction pattern on the angular momentum index of the LGV beam and the number of sides in the polygon are systematically investigated, and features and trends are identified. The evolution of the diffraction pattern and its symmetry with the aperture position relative to the waist is also studied, leading to a generalized Friedel's law for diffraction of LGV beams.