Optical vortex beams with the infinite topological charge

Abstract

Up to now, Gaussian optical vortices (OVs) were investigated with the finite topological charge (TC). Here, we study an OV with the infinite TC. Such OVs have a countable number of phase singularities (isolated intensity nulls), which typically have the unitary TC and are located either equidistantly or not equidistantly on a straight line in the beam transverse cross section. Such OVs are structurally stable (form-invariant) and their transverse intensity is conserved on propagation, changing only in scale and rotation. Orbital angular momentum (OAM) of such OVs is finite, since only a finite number of screw dislocations are within the Gaussian beam in the area of notable intensity, whereas the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to the parabolic growth of the OAM of such beams. A unique feature of these beams is that their normalized OAM can be adjusted (both increased and decreased) by simple change of the waist radius of the Gaussian beam. In addition to the two form-invariant beams, we studied a Gaussian beam with a countable number of edge dislocations (zero-intensity lines), which is not form-invariant, but, after an astigmatic transform by a cylindrical lens, also becomes an infinite-topological-charge beam.