Topology and Polarization of Optical Vortex Fields from Atomic Phased Arrays

We developed theoretical formalism for generation of optical vortices by phased arrays of atoms. Using Jacobi-Anger expansion, we demonstrate the resulting field topology and determine the least number of array elements necessary for generation of vortices with a given topological charge. Vector vortices were considered, taking into account both spin and orbital angular momenta of electromagnetic fields. It was found that for the vortex field near the phase singularity, the transverse-position dependence of 3D polarization parameters is independent of the distance to the radiation source.