Focal shift in focused radially polarized ultrashort pulsed laser beams

Beginning with a beam coherence polarization (BCP) matrix, we obtain an analytical intensity expression for radially polarized ultrashort pulsed laser beams that pass through an apertureless aplanatic lens. We also investigate the intensity distribution of radially polarized beams in the vicinity of the focus. The focal shift of these beams is studied in detail. The focal shift depends strongly on Z(F) that coincides with pi times the Fresnel number.