Generation of on-axis energy backflow via superoscillation focusing

On-axis energy backflow has recently been discovered in the focal fields of various light beams with phase or polarization singularities. However, although an azimuthally polarized beam superimposed with the first-order vortex phase satisfies the general conditions for achieving on-axis energy backflow, it is found to be difficult to induce this phenomenon under conventional focusing conditions. In this paper, we numerically demonstrate that the on-axis energy backflow can be achieved near the focus of azimuthally polarized first-order vortex beams via superoscillation focusing. To this end, the Laguerre-Gaussian (LG)-type complex amplitude is adopted, and the inherent superoscillation focusing capability of an azimuthally polarized LG first-order vortex beam is demonstrated by controlling the incident beam size appropriately. More remarkably, the on-axis energy backflow is observed in some superoscillation focusing fields under the specific incident beam size. Furthermore, we show that the generation of on-axis energy backflow is closely associated with the transverse vortex pairs near the optical axis in the superoscillation focusing field. Additionally, more simulation results indicate that these phenomena can be achieved for LG beams with different radial indices. The results provide a crucial approach for generating on-axis energy backflow in the focal region of light beams for which this phenomenon would otherwise be difficult to achieve.