Spin angular momentum and optical chirality of Poincaré vector vortex beams

Abstract: The optical chirality and spin angular momentum of structured scalar vortex beams has been intensively studied in recent years. The pseudoscalar topological charge $\ell$ of these beams is responsible for their unique properties. Constructed from a superposition of scalar vortex beams with topological charges $\ell_\text{A}$ and $\ell_\text{B}$, cylindrical vector vortex beams are higher-order Poincar\'e modes which possess a spatially inhomogeneous polarization distribution. Here we highlight the highly tailorable and exotic spatial distributions of the optical spin and chirality densities of these higher-order structured beams under both paraxial (weak focusing) and non-paraxial (tight focusing) conditions. Our analytical theory can yield the spin angular momentum and optical chirality of each point on any higher-order or hybrid-order Poincar\'e sphere. It is shown that the tunable Pancharatnam topological charge $\ell_{\text{P}} = (\ell_\text{A} + \ell_\text{B})/2$ and polarization index $m = (\ell_\text{B} -\ell_\text{A})/2$ of the vector vortex beam plays a decisive role in customizing their spin and chirality spatial distributions. We also provide the correct analytical equations to describe a focused, non-paraxial scalar Bessel beam.