Toroidal and reverse flux of light in the sharp focus

Abstract

We obtain a set of explicit analytical expressions that completely describe a light field with a double higher-order singularity (phase and polarization), as well as distributions of its intensity and energy flux near the focus.There is a reverse energy flux on the optical axis near the focus, which is comparable in magnitude with the forward flux. There is a toroidal energy flux in the focal area near the dark rings in the distribution of the longitudinal component of the Poynting vector.