Super-resolution focusing of higher polarization order axially symmetric polarized beams

We propose the concept of axially symmetric polarized beams as an extension of radially and azimuthally polarized beams, and study the focusing properties and applications of higher polarization order axially-symmetric polarized beams. We present the mathematical expressions of the focusing field in an aplanatic focusing system and numerically calculate the focusing field distributions near focus, and find out some unique focusing properties, especially multiple-focus-spot super-resolution focusing, which will lead to some applications in super-resolution, multiple particles manipulation, near-field microscopy and so on.