Tightly focused laser light with azimuthal polarization and singular phase

Using simplified Richards-Wolf formulas we show that laser light with azimuthal polarization and singular phase can produce a smaller focal spot than that from a laser beam with radial polarization, other conditions remaining the same. It is numerically shown that when focusing an azimuthally polarized laser beam with phase singularity using a zone plate a 1.3 times smaller focal spot can be attained than when an aplanatic lens is used. A spiral phase plate can be replaced with a phase step with a $\pi$-phase shift. In this case the subwavelength focal spot from a laser beam with azimuthal polarization, which is formed near the zone plate surface, loses circular symmetry, while becoming smaller and acquiring an elliptical form with radiuses of $0.273\lambda$ and $0.314\lambda$ ($NA = 1$).