We propose and demonstrate a type of multi-focus autofocusing beams, circular hyperbolic umbilic beams (CHUBs), based on the double-active variable caustics in catastrophe theory. The mathematical form is more general compared to circular Airy, Pearcey and swallowtail beams. The CHUBs can generate multi-focus at its optical axis, while the on-axis intensity fluctuates up to two orders of magnitude that of the maximum intensity in the initial plane. Using the concept of topographic prominence, we quantify the autofocusing ability. We construct the criteria for selecting the effective foci, and then explore the influence of related parameters. Our findings suggest that the CHUBs could be a suitable tool for multi-particle manipulation, optical tweezers, optical lattices and related applications.

We propose and demonstrate a new, to the best of our knowledge, kind of partially coherent vector beam called the partially coherent radially polarized circular Airy beam (PCRPCAB). The PCRPCAB inherits the autofocusing ability of the radially polarized circular Airy beam (RPCAB) and can create an optical potential well at the center of the beam, whose depth can be adjusted by changing the coherent width. We find that, as coherent width decreases, the intensity becomes higher in the dark notch caused by the polarization singularity, and the singularity of the degree of polarization (DOP) remains along propagation, with its waist controllable by the coherent width. Our results make the PCRPCAB a good candidate for optical micromanipulation, disordered optical lattices, etc.

In this paper, partially coherent radially polarized vortex circular Airy beams (PCRPVCABs) are theoretically and experimentally studied for the first time. Comparing with partially coherent radially polarized circular Airy beam, the autofocusing ability of PCRPVCAB can be controlled or even enhanced by the topological charge of the vortex phase. Besides, we show a unique distribution of the degree of polarization, vortex-phase induced polarization transition, and the phenomenon of beam spot rotation after the PCRPVCAB passing through a polarizer. Our results make the PCRPVCAB a good candidate for optical micro-manipulation, free-space communications, formation of disordered optical lattices, etc.