Phase singularity points in tight focus of linearly polarized optical vortices near the region of reverse energy flow

Abstract

In this paper, we investigated the behavior of the phase and local wavevector of a tightly focused optical vortex with linear polarization. It was shown that in contrast to a scalar optical vortex, there are some centers of phase singularity points of optical vortices under tight focusing condition. If the topological charge of the focused vortex is equal to one, then the center of the focused vortex is located on the optical axis. If the topological charge is equal to two, then two optical vortices with unit topological charges are observed in the focal plane. These singularity points are shifted from the optical axis and bounded the area of energy backflow. If the topological charge exceeds two, then three optical vortices are formed in the focal plane, two of them have a unit topological charge and are shifted from the optical axis. It was analytically shown that with increasing of topological charge the centers of shifted optical vortices move away from the optical axis.