Energy Backflow in Tightly Focused Fractional Order Vector Vortex Beams with Binary Topological Charges

Abstract

Using the Richards–Wolf diffraction integral, the longitudinal energy evolution on the focal plane of the fractional order vector vortex (FOVV) beams was studied. These beams possessed a vortex topological charge n and a polarization topological charge m, and were subjected to tight focusing through a larger numerical aperture. Our investigation revealed the existence of backflow energy when the binary topological charges n and m satisfied the conditions of n + m = 2 or n − m = −2. The component circularly polarized vortex beams of e−i2ϕe^+ (i.e., the minus second-order vortex right circularly polarized beam) and ei2ϕe^− (i.e., the second-order vortex left circularly polarized beam) played significant roles in the generation of reverse energy flux at the focal region. For FOVV beams with binary topological charges n and m, whose sum and difference were integers, the longitudinal energy on the focal plane exhibited axial symmetry. If the sum or the difference of the topological charges n and m was not an integer, the axisymmetric longitudinal energy on the focal plane was disrupted.