Focus shaping by tightly focusing locally linear polarized vortex beams with Pancharatnam-Berry tailored

Based on vector diffraction theory, we demonstrated that the three-dimensional spatial separation of the two foci can be achieved by modulating the polarization distribution of the input vector light field. The Pancharatnam-Berry tailored vector light field combined with a vortex phase can realize both foci possess vortices of arbitrary topological charges. The simulation results show that the tightly focused vector vortex beam can generate two vortices with independent topological charges, and the spatial distance between the two vortex foci can be adjusted. Moreover, the focal field distribution with optical cage or flat-topped profile can be easily obtained by appropriately choosing the polarized structure and vortex phase of the input beams. We generate a perfect optical cage that is almost surrounded by uniform light intensity. The flat-topped focus can be formed by focusing of a single vortex, as well as the superposition focusing of the two vortices. These engineered focus profiles may find potential applications in optical imaging, laser micromachining, particle trapping and manipulations.