Diffraction of a Gaussian beam by a four-sector binary grating with a shift between adjacent sectors

In this article as a diffractive optical element we consider a composed four-sector binary grating under Gaussian laser beam illumination. The angular sectors are bounded by the directions y=x and y=−x, and consist of parts of a binary rectilinear grating; thereby, two neighboring parts are shifted by a half spatial rectilinear grating period. The diffracted wave field amplitude is calculated, showing that the straight-through, zeroth-diffraction-order beam is an amplitude-reduced Gaussian beam, and the higher-diffraction-order beams, deviated with respect to the propagation axis, are non-vortex beams described by modified Bessel functions. The transverse intensity profiles of the higher-diffraction-order beams, numerically and experimentally obtained, have form of a four-leaf clover; they are similar to the Laguerre-Gaussian LG(0,2) beam (with radial mode number n=0 and azimuthal mode number l=2) described by circular cosine function, in a paraxial, far-field approximation.