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In this work, using the Richards-Wolf formalism, we consider the sharp focusing of optical vortices with hybrid polarization, which combines the properties of azimuthal and circular polarizations. It is shown that these beams have a number of unique properties: the intensity pattern in such beams is rotating with distance from the focal spot and the longitudinal component of the spin angular momentum is asymmetrically shaped.

In this paper, using the Richards-Wolf equations, we analyze focusing circularly polarized light with flat diffractive lenses. It is shown that as the numerical aperture of the lens increases, the size of the focal spot first decreases and then begins to grow. The minimum focal spot is observed at NA=0.96 (FWHM=0.55λ). With a further increase in the numerical aperture of the lens, the growth of the longitudinal component leads to an increase in the size of the focal spot. When the flat diffractive lens is replaced by an aplanatic lens, the size of the focal spot decreases monotonically as the numerical aperture of the lens increases.