Diffracted optical vortices by an angular aperture

Abstract

The measurement of the topological charge of laser beams with orbital angular momentum (OAM) is key to many applications like deciphering information encoded in several channels. Current techniques useful for that purpose are interferometry, diffraction through different poligonal apertures like triangular or pentagonal and, azimuthal and radial decomposition. A less explored issue is the diffraction of OAM beams through circular sectors. Jack et al. studied the angular diffraction of Gaussian beams (whose OAM is null) through a circular sector. By means of a Fourier transform of the truncated Gaussian beam they showed that the orbital angular momentum spectrum of the transmitted beam has a sinc-shaped envelope centered at zero orbital angular momentum, the width of which increases as the central angle of the circular sector decreases. We analyze here the spectrum of a laser beam with integer OAM that has been diffracted by a circular sector. We present results for circular sectors of different central angles. For circular π-sector, we also study the influence of the transmittance in the OAM spectra of the transmitted beam, using straight borders of nanometric thin films of titanium oxide with different thicknesses. We use a spatial light modulator with a fork hologram placed on to generate the incoming OAM beam and measure the evolution of the intensity profile of the diffracted beam as it propagates away from the circular sector. The spectra of the diffracted OAM beams are shown numerically and experimentally to have a sinc shaped envelope centered at the OAM value of the incoming OAM wave.