Transformation of higher-order optical vortices upon focusing by an astigmatic lens

Abstract

A circular Laguerre–Gaussian mode transformation by an astigmatic lens is considered theoretically as an example of the higher-order optical vortex symmetry breakdown. Behind the lens, an m-charged optical vortex converts into ∣m∣ secondary first-order vortices whose evolution upon the beam propagation has been studied. In the beam cross section, they are positioned on a straight line crossing the beam axis. Orientation of this straight line is determined by the direction of the energy circulation within the incident beam. Depending on the parameters of the beam and the lens, in certain cross-sections all the secondary vortices can invert their signs; and in these sections (inversion planes) ∣m∣ edge dislocations (transverse vortices) appear. The morphology of secondary vortices is analyzed and the local orbital angular momentum of the nearest vicinity of an optical vortex core is shown to characterize the vortex anisotropy.