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.

我们提出了一种通过使用具有多涡旋相位的混合偏振贝塞尔-高斯（HPBG）光束来实现各种中心对称形状的方法，该光束是通过将一些一阶偏轴拓扑电荷嵌入到以等长弧长隔开的涡旋中而获得的。圆圈。根据Debye-Wolf电磁衍射公式（通常用于描述高数值孔径光学系统的聚焦），我们研究了具有多涡旋相位（矢量电场）的HPBG光束紧密聚焦的强度分布的演变。通过调整嵌入涡旋相的位置矢量，涡旋相的数量以及混合极化的径向与方位角之比，可以确定径向极化角和方位极化角。仿真结果表明，涡旋相的数量等于空心多边形的顶点数量，极性矢量幅度的增大会导致空心多边形变形，并且径向极化角与方位极化角的比值会影响边缘的清晰度。焦平面中的空心多边形的角分别。我们可以通过控制多涡旋相位奇点的数量和位置来产生三角形，正方形，五边形，六边形和中空区域的内部十字架，以及外部十字架，嵌入的星星和雪花。聚焦结构对于噪声是鲁棒的，并且沿光轴保持有限的厚度。这些特定的强度分布图对于潜在的应用具有重要意义，包括捕获多个微米级粒子，非线性光学，光束整形，