Topology and Polarization of Optical Vortex Fields from Atomic Phased Arrays

We developed a theoretical formalism for the generation of optical vortices by phased arrays of atoms. Using the Jacobi-Anger expansion, we demonstrated the resulting field topology and determined the least number of individual atoms necessary for the generation of vortices with a given topological charge. Vector vortices were considered, taking into account both the spin and orbital angular momenta of electromagnetic fields. It was found for the vortex field that, in the far field limit, the spatial variation in spin-density matrix parameters-orientation and alignment-is independent of the distance to the radiation source.