Tight focusing properties of anomalous vortex beams

Tight focusing properties of an anomalous vortex beam (AVB) passing through a high numerical aperture (NA) lens system are investigated, based on vector Debye integral. The numerical examples show that intensity distribution for the AVBs in focal region depend on the beam parameters including the topological charge m, the order of the AVBs n. Furthermore, the phase distribution and the intensity distribution at the different propagation distance z are discussed in detail. Our results will be useful to find the potential applications of AVBs.