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

Lj. Janicijevic, S. Topuzoski, L. Stoyanov, A. Dreischuh

**Abstract.**

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.

*Keywords: **Diffraction,
Diffractive optical element, Gaussian laser beam, Four-sector binary grating.*