Measurement of the vortex and orbital angular momentum spectra with a single cylindrical lens

A new technique for measuring the degenerate spectra of optical vortices and orbital angular momentum (OAM) of singular beams is theoretically studied and experimentally verified. The technique is based on measuring the intensity moments of higher orders of a beam containing vortices with both positive and negative topological charges. The appropriate choice of the vortex mode amplitudes of the combined beam forms anomalous regions in the form of resonant dips and bursts in the OAM spectrum. Since the intensity moments for vortices with positive and negative topological charges are the same (degenerate) for an axially symmetric beam, it was necessary to break the symmetry of the beam, so measurements were taken at the plane of the double focus of a cylindrical lens. The calibration measurements showed that the experimental error is not higher than 3.5%. The technique was implemented for measuring and analyzing combined beams with OAM anomalies. It was found that the dips and bursts in the OAM spectrum are caused by the vortex avalanche induced by weak perturbations of the holographic grating responsible for shaping the beam. The OAM dips or bursts are controlled by the ratio between the energy fluxes of the vortex avalanche with positive or negative topological charges.