Local wavevector near energy backflow zones of optical vortices

In this paper, we consider the behavior of the phase and local wave vector of a tightly focused optical vortex with linear polarization. It is shown that the regions of phase singularity correspond to giant values of the local wave vector. In contrast to the scalar approximation, when the theory predicts that when focusing an optical vortex with a large topological charge at the focus, the optical vortex is preserved with the same topological charge, the non--paraxial vector approximation shows that a vortex with a large topological charge at the focus always splits into several vortices. That is, several points of phase singularity arise (and, as a consequence, several regions with a giant wave vector). In particular, if the topological charge is equal to two, then two optical vortices with unit topological charges shifted from the optical axis are observed in the focal plane. If the topological charge exceeds two (i.e. three or more), then three optical vortices are always formed in the focal plane, two of which have a single topological charge and are shifted from the optical axis, and the third vortex remains on the optical axis and has a topological charge two less than the initial topological charge of the focused optical vortex. In this case, the centers of the vortices shifted from the optical axis approximately correspond to the boundaries of the zones of reverse energy flow.