Effects of aberrations in vortex-beams generated with amplitude diffraction gratings

Abstract

We present a mathematical model for the generation of vortex-beams by using a square profile amplitude fork diffraction grating with arbitrary topological charge. The mathematical framework of aberrations in the forkedshape diffraction grating is analysed, and the resulting diffracted pattern is simulated. Three cases of desired distortions (aberrations) in the diffraction grating are considered, obtaining phase modulation from the amplitude grating. Experimental optical vortices are generated by using a transmission spatial light modulator, which is used as a dynamic diffraction grating, allowing us to aberrate it. We show the effect of aberrations in the experimental diffracted vortex-beams and compare it with the numerical simulation.

Optical vortex generated with an asymmetric forked grating

“…Forked gratings exploited for optical-vortex beams generation are simple and widely used laboratory tools. Being optical elements in general, they can possess some imperfections (aberrations) like defocusing or coma [19]. In the present study, we concentrate our attention on geometrical stretching (compression) of the forked grating scale.…”

“…where φ 0 is the azimuth angle, 0 is a normalized radius, 0 = ρ 0 /w(z) and γ = arctan(z/z R ) is the Gouy phase. The system (19) can be resolved with respect to γ:…”