Optical helicity, chirality, and spin of 3D-structured Laguerre-Gaussian optical vortices

Optical fields possess energy, momentum, and helicity. For the plane waves and paraxial fields of standard, classical optics, the spin angular momentum and optical helicity are well understood, both being proportional to the degree of circular polarization. In contrast, 3D non-paraxial optical fields generated by spatial confinement, such as tight focusing and evanescent waves, may possess spin angular momentum and optical helicity when the degree of 2D-circular polarization is zero. In this work using quantum electrodynamics we highlight two novel properties of non-paraxial optical vortices 1) a non-zero optical helicity (chirality) density for 2D-unpolarized (and 2D-linearly polarized) 3D optical vortices and 2) a longitudinal spin angular momentum density for 2D-linearly polarized 3D optical vortices