Sharper Focal Spot for a Radially Polarized Beam Using Ring Aperture with Phase Jump

We study analytically and numerically in which way the width of ring aperture containing a phase jump affects the size and intensity of the focal spot generated with a radially polarized beam. It is shown that by means of destructive interference of beams coming from the different-phase rings it becomes possible to overcome the scalar diffraction limit corresponding to the first zero of the zero-order Bessel function. The minimal focal spot size (FWHM=0.33λ) is found to be attained when the annular aperture width amounts to 20% of the full-aperture radius. In this case, the side-lobe intensity is not larger than 30% of the central peak. A wider annular aperture with the phase jump introduced is also shown to form a focal spot not exceeding the diffraction limit for a narrow annular aperture, simultaneously providing a nearly six times higher intensity. In this case, the side lobes amount to 35% of the central peak.