Energy flows in tight focus of optical vortices

In this paper we investigated tight focusing of optical vortex with topological charge m = 2 and left circular polarization. The simulation was based on Richards-Wolf equation. Light with wavelength 532 nm was focused by aplanatic lens with numerical aperture NA=0.95. It was shown that the longitudinal component of Poynting vector has negative values on the optical axis. The reason of the energy backflow is due to the fact that the projection of the spin flow onto the optical axis is negative and exceeds in absolute value the projection of the orbital energy flow, which is always positive.