Tightly focusing vector circular airy beam through a hard aperture

We investigate the tightly focusing property of radially polarized circular Airy beams through a hard aperture, and find that, in the longitudinal component of focal field, there are several spots arranging along the propagation axis. And the spot number is determined by the number of rings of input intensity pattern, as a result of the vectorial interference effect. When the aperture is fixed, the ring number can be controlled by tuning the initial radius of main ring of the input beam rc. The intensity ratio between the middle and first/last spots varies with the decay factor of the input beam a. Taking advantage of these focusing properties, we can generate sphere- and cylinder-shape optical cages, 41λ-length optical needle, and 80λ-length optical dark channel.