Abruptly autofocusing beams exhibit a sudden and significant increase in intensity at the focal point, with enhancements reaching several orders of magnitude. This effect is achieved without relying on conventional lenses or nonlinear effects, while the beam maintains a low-intensity profile prior to focus. This unique property has demonstrated significant potential for diverse applications ranging from optical manipulation to optical trapping and biomedical therapy. In recent years, regulating and optimizing the autofocusing characteristics of beams through light field design has attracted extensive attention. While traditional Airy beams have been extensively studied for their exceptional self-accelerating, self-bending, and self-healing properties, butterfly beams have emerged as a novel research focus due to their controllable parametric properties and stable higher-order focal dispersion structures. The propagation dynamics of the new beam combining these two autofocusing beams with additional vortex-phase modulation are highly anticipated. In this paper, we propose a novel circular butterfly Airy vortex beam (CBAVB) and systematically investigate its autofocusing properties in free-space propagation. The results are expected to provide a reference for the application of CBAVB in optical communication, optical trapping, and biomedical therapy.

Initially, we utilize the split-step Fourier algorithm to numerically simulate the propagation of CBAVB in free space. Subsequently, the influence of different parameters on the autofocusing characteristics of the beam is investigated. Furthermore, the energy flow of the beam and the influence of optical vortices are analyzed using the Poynting vector and angular momentum density vector, respectively. Finally, we analyze the autofocusing performance of CBAVB through a comparative study.

Through numerical simulations of the beam propagation dynamics, the superior autofocusing characteristics of CBAVB are demonstrated. The incorporation of optical vortices can significantly improve the focusing performance coefficient of CBAVB (Fig. 2). By adjusting the position of the optical vortex and the size of the topological charge, the autofocusing behavior can be flexibly controlled while maintaining the position of maximum intensity (Fig. 3). Simultaneously altering the transverse scale factor and spatial offset factor can enhance the beam’s focusing performance coefficient while effectively regulating the focus position (Fig. 4). The autofocusing mechanism of CBAVB (Fig. 5) and the influence of optical vortices on the beam (Fig. 6) are analyzed based on the beam’s Poynting vector and angular momentum density vector. In addition, compared with CAVB and CBVB, CBAVB demonstrates superior autofocusing performance (Fig. 7).

In this paper, we propose a novel autofocusing circular butterfly Airy vortex beam (CBAVB), whose propagation in free space is numerically simulated using the split-step Fourier algorithm. The effects of topological charge, optical vortex position, transverse scale factor, and spatial offset factor on the autofocusing characteristics of the beam are investigated. Furthermore, the propagation dynamics of CBAVB are further analyzed through the Poynting vector and angular momentum density vector. The research results show that the incorporation of optical vortices significantly promotes the maximum focusing performance coefficient of CBAVB. By adjusting the position of the optical vortex and the size of its topological charge, the transverse intensity distribution of CBAVB can be flexibly regulated, and the beam’s focusing performance coefficient can be improved. Altering the transverse scale factor and spatial offset factor can also regulate the focusing position and effectively enhance the beam’s autofocusing performance. Compared with the CAVB and CBVB, CBAVB demonstrates superior autofocusing performance. These results suggest the promising potential of CBAVB for applications in free-space optical communications, biomedical imaging, optical manipulation, and related fields.