By decomposing a linearly polarized light field in terms of plane waves, the elliptic intensity distribution across the focal spot is shown to be determined by the E-vector's longitudinal component. Considering that the Poynting vector's projection onto the optical axis (power flux) is independent of the E-vector's longitudinal component, the power flux cross section has a circular form. Using a near-field scanning optical microscope (NSOM) with a small-aperture metal tip, we show that a glass zone plate (ZP) having a focal length of one wavelength focuses a linearly polarized Gaussian beam into a weak ellipse with the Cartesian axis diameters FWHM(x)=(0.44±0.02)λ and FWHM(y)=(0.52±0.02)λ and the (depth of focus) DOF=(0.75±0.02)λ, where λ is the incident wavelength. The comparison of the experimental and simulation results suggests that NSOM with a hollow pyramidal aluminum-coated tip (with 70° apex and 100 nm diameter aperture) measures the transverse intensity, rather than the power flux or the total intensity. The conclusion that the small-aperture metal tip measures the transverse intensity can be inferred from the Bethe-Bouwkamp theory.

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Using the Richards-Wolf formalism, we obtain general expressions for all components of the electric and magnetic strength vectors near the sharp focus of an optical vortex with the topological charge m and nth-order azimuthal polarization. From these equations, simple consequences are derived for different values of m and n. If m=n>1, there is a non-zero intensity on the optical axis, like the one observed when focusing a vortex-free circularly polarized light field. If n=m+2, there is a reverse flux of light energy near the optical axis in the focal plane. The derived expressions can be used both for simulating the sharp focusing of optical fields with the double singularity (phase and polarization) and for a theoretical analysis of focal distributions of the intensity and the Poynting vector, allowing one to reveal the presence of rotational symmetry or the on-axis reverse energy flux, as well as the focal spot shape (a circle or a doughnut).