Tight focusing of high-order polarized anomalous vortex beam

Based on the vector Debye theory, the tight focusing properties of a high-order polarized anomalous vortex (HPAV) beam are studied. The corresponding mathematical expressions of the HPAV beam are derived theoretically. We accomplish the inner and outer gear shapes of the focusing intensity where the number of the gear tooth can be modulated by polarization order. The results show that the focusing gear intensity can be flexibly modulated by initial polarization azimuth which may determine the trapping effects. Various charming focusing field patterns can be used to capture two kinds of different refractive indices particles simultaneously. The compactness of the intensity distribution can be freely adjusted by the HPAV beam topological charges and polarization order. The focal spot size, which is far beyond the Rayleigh diffraction limitation can be achieved. It may be expected to have potential applications in optical microscopy, imaging, optical telecommunication and other fields.