Multi-focus autofocusing circular hyperbolic umbilic beams

Abstract

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.