Toroidal Vortices of Energy in Tightly Focused Second-Order Cylindrical Vector Beams

In this paper, we simulate the focusing of a cylindrical vector beam (CVB) second order, using Richards–Wolf formula. Many papers have been published on CVB, but they did not report forming toroidal vortices energy (TVE) near focus. TVE are fluxes light in longitudinal planes along closed paths around some critical points at which flux is zero. 3D case, such form surface, and rotates circle lying transverse plane. formed pairs with different directions rotation (similar to optical topological charges signs). We show that when wavelength 532 nm focused by lens numerical aperture NA = 0.95, periodically appear distance about 0.45 ?m (0.85 ?) from axis (with period z-axis 0.8 (1.5 ?)). The arise pairs: vortex nearest focal plane twisted clockwise, next counterclockwise. These accompanied saddle points. At higher distances z-axis, pattern repeated, 0.7 (1.3 ?), region repeated observed. When limited narrow annular aperture, these