Sharper focal spot generated by 4π tight focusing of higher-order Laguerre-Gaussian radially polarized beam.

The focal electric fields for a 4π high numerical aperture (NA) focusing system with both the doughnut and higher-order Laguerre-Gaussian (LG) radially polarized (RP) beams are investigated in the case of NA=1, and the full width at half-maximum values of the focal spots are calculated. Compared with the single-lens high NA focusing configuration, a sharper spot, whose size is reduced efficiently in the transverse as well as the axial direction, can be formed. Such size reduction is attributed to not only the destruction interference of the longitudinal component caused by the π phase shift between any two adjacent rings of the incident higher-order LG RP beam coming from one particular direction but also the perfect destruction interference of the radial component formed by the two counter-propagating incident beams.