Tight focusing of the centrosymmetric shape of hybrid polarized beams by adjustable multi-vortex phases

We propose an approach for achieving various centrosymmetric shapes by employing hybrid polarized Bessel–Gaussian (HPBG) beams with multi-vortex phases, which are obtained by embedding a few first-order off-axis topological charges into vortices separated by equal arc lengths of a circle. According to the Debye–Wolf electromagnetic diffraction formula (which is routinely used to describe focusing by high numerical aperture optical systems), we investigate the evolution of tightly focused intensity profiles of the HPBG beams with multi-vortex phases (which are the vectorial electric field of radial and azimuthal polarization), by tuning the positional vectors of the embedded vortex phases, the number of vortex phases and the ratio of radial to azimuthal polarization of the hybrid polarization. The simulation results show that the number of vortex phases is equal to the number of vertices of hollow polygons, increasing the magnitude of polar vector leads to deformation of the hollow polygons, and that the ratio of the radial and azimuthal polarization magnitudes affects the edge sharpness of the hollow polygon in the focal plane, respectively. We can produce triangles, squares, pentagons, hexagons, and inner crosses in the central hollow region, and outer crosses, embedded stars and snowflakes by manipulating the numbers and sites of multi-vortex phase singularities. The focusing structures are robust to noise and maintain a limited thickness along the optical axis. These specific intensity profiles are significant for potential applications including the trapping of multiple micro-sized particles, nonlinear optics, optical beam shaping, and optical telecommunication applications. (paper)