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

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(-i2f)e(<^>)+ (i.e., the minus second-order vortex right circularly polarized beam) and e(i2f)e(<^>)- (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.

Automated summary

Using the Richards-Wolf diffraction integral, the longitudinal energy evolution of fractional order vector vortex (FOVV) beams on the focal plane was studied. The existence of backflow energy was revealed when the binary topological charges satisfied specific conditions. Component circularly polarized vortex beams played significant roles in generating reverse energy flux. The longitudinal energy on the focal plane exhibited axial symmetry for FOVV beams with integer sums and differences of binary topological charges, but was disrupted when the sums or differences were not integers.