Topological Charge of Propagation-Invariant Laser Beams

Abstract

If a vortex propagation-invariant beam is given by all its intensity nulls, then its topological charge (TC) can be defined easily: its TC is equal to the sum of topological charges of all optical vortices in these intensity nulls. If, however, a propagation-invariant beam is given as a superposition of several light fields, then determining its TC is a complicated task. Here, we derive the topological charges of four different types of propagation-invariant beams, represented as axial superpositions of Hermite–Gaussian beams with different amplitudes and different phase delays. In particular, topological charges are obtained for such beam families as the Hermite–Laguerre–Gaussian (HLG) beams and two-parametric vortex Hermite beams. We show that the TC is a quantity resistant to changing certain beam parameters. For instance, when the parameters θ and α of the HLG beams are altered, the beam intensity also changes significantly, but the TC remains unchanged.