Diffraction of beams by infinite or finite amplitude-phase gratings

Abstract

In this paper a theory for the diffraction of beams by thin amplitude-phase gratings in the scalar diffraction regime is given. The grating can be strictly periodic and therefore of infinite spatial extent (infinite grating) or can be a grating with a finite number of periods (finite grating). The main result of this paper is that we can write down mathematical expressions for the diffraction of beams by these kinds of gratings. General expressions for the diffraction patterns at the far-field region are derived. As a numerical application of the theory presented in this paper the diffraction of Hermite-Gaussian and distorted beams by a Ronchi ruling (infinite and finite) is studied.