Shaping and processing the vortex spectra of singular beams with anomalous orbital angular momentum

The article examines physical mechanisms responsible for shaping the vortex avalanche induced by a weak perturbation of the holographic lattice of a combined vortex beam. For this, we have developed a new technique for measuring the degenerate spectra of optical vortices and orbital angular momentum of combined singular beams. 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 mode amplitudes in the combined beam enables us to form orbital angular momentum anomalous spectral regions in the form of resonance dips and bursts. Since the intensity moments of a vortex mode with positive and negative topological charges are the same (the moments are degenerate) for an axially symmetric beam, the measurements are carried out in the plane of the double focus of a cylindrical lens. The calibration measurements show that the experimental error is not higher than 4.5 %. We also reveal that the dips and bursts in the orbital angular momentum spectrum are caused by the vortex avalanche induced by weak perturbations of the holographic grating relief responsible for the beam shaping. The appearance of the orbital angular momentum dips or bursts is controlled by the relation between the energy fluxes in the vortex avalanche with positive or negative topological charges.