Helical reverse flux of light of a focused optical vortex

Using the Richards–Wolf formalism, we show that if an optical vortex with a topological charge of 3 and with left (opposite) circular polarization is sharply focused by an aplanatic system, then in the focal plane there is a reversed flux of light energy near the optical axis (on the axis itself it is zero), which is only 2–3 times less than the forward energy flux in the focus. It is also shown that near the optical axis the reverse flux propagates along a counterclockwise helix (spiral) around the optical axis. The reverse flux near the optical axis is also demonstrated by the FDTD-simulation of diffraction of a circularly polarized plane wave by a third-order spiral zone plate with a numerical aperture of about 1. A Rayleigh microparticle trapped in the area of such a focus should move in the opposite direction with respect to the direction of beam propagation. (paper)