Tight focusing of axially symmetric polarized vortex beams is studied numerically based on vector diffraction theory. The mathematical expressions for the focused fields are derived. Simulation results show that the focused fields and phase distributions at focus are largely influenced by both the polarization order and topological charge of the incident beams. Moreover, focal spots with flat-topped or tightly-focused patterns can be flexibly achieved by carefully choosing the polar- ization order and the topological charge, which confirms the potential of such beams in wide applications, such as optical tweezers, laser printing, lithography, and material processing.
