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.

A single acoustic metamaterial with multifunctional use is highly needed for various applications. Herein, a bifunctional acoustic metamaterial for beam switching between the focusing beam and bottle beam is demonstrated, which consists of a groove structure for binary phases and a partitioned piezoelectric transducer (p-PZT) for incident wavefront modulation. The p-PZT is divided into inner and outer regions for selective excitation, and the focusing beam and bottle beam can be switched in real-time by applying different exciting signals on the p-PZT. Theoretical calculation, numerical simulation, and experimental measurement are conducted to verify the effectiveness of the proposed bifunctional acoustic metamaterial for beam switching. Furthermore, the focal plane of both the focusing beam and bottle beam can be linearly tuned by the operating frequency. This work may find potential applications in medical ultrasonic therapy, sound printing, and biological particle manipulation.

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.

In this work, we propose and demonstrate the ring-arrayed Pearcey Gaussian chirp beams (RAPGCBs) synthesized by multiple two-dimensional Pearcey beams. The general analytical formula for the propagation of RAPGCBs is presented. We find that, depending on synthesized number n, the profiles of the beams present different polygonal shapes, and the autofocusing properties can be controlled by chirp factor β. Furthermore, we study the properties of the RAPGCBs carrying optical vortices (OVs). It shows that a single OV or two positive OVs form an autofocusing hollow field, and opposite OVs will annihilate, which results in greatly increased autofocusing ability. Our experimental results agree with the simulations. Such beams have potential applications in particle trapping and biology medical fields.

In this paper, one kind of multi-focusing electric and magnetic field which is sourced from an azimuthally polarized vortex circular hyperbolic umbilic beam (APVCHUB) is presented. After passing through a high NA objective, both the electric and magnetic fields of the APVCHUBs will focus multiple times, and a high-purity longitudinal magnetic field (p q =80%) will be generated. Besides, the mutual induction of the vortex phase and azimuthal polarization changes the electric and magnetic fields’ vibration state and intensity distribution, making the longitudinal magnetic field carry an m-order concentric vortex. Our findings suggest that the APVCHUB could have potential applications in magnetic particle manipulation, extremely weak magnetic detection, data storage, semiconductor quantum dot excitation, etc.