A sectorial arrangement of spatially-shifted grating for composite Laguerre-Gaussian OAM beam generation

The first diffraction order of a planar 1D grating has a plane wavefront for a plane wave incidence. We propose an algorithm to tailor the shape of this wavefront to the desired propagation mode. The algorithm works by segmenting the 1D grating into sectors and shifting gratings in each sector along the grating vector by some fraction of the grating period. The algorithm determines the fractional shift required in each sector to impart a desired shape to the wavefront. Through simulations and experiments, we show the applicability of the design process by demonstrating the coaxial generation of one or multiple Laguerre-Gaussian orbital angular momentum beams. In addition, we demonstrate the independent regulation of relative intensities and phases of components in the generated beam.