Focusing property of a double-ring-shaped radially polarized beam

The intensity distributions of a tightly focused radially polarized beam that has a double-ring-shaped transverse mode pattern were calculated based on vector diffraction theory. The distribution of the longitudinal component near the focus varied drastically with the degree of truncation of the incident beam by a pupil. When the ratio of the pupil radius to the beam radius was approximately 1.3, the longitudinal component disappeared at the focal point, owing to destructive interference. This dark area surrounded by an intense light field was of the order of the wavelength, with excellent intensity symmetry.