Polarization Singularity Index and Orbital Angular Momentum of Vector Light Fields

Abstract

Besides scalar optical vortices that have a topological charge (TC), helical wave front, and carry an orbital angular momentum (OAM) that can be transferred to particles and rotate them along circular trajectories, polarization optical vortices are also known, whose polarization state in the beam section changes with the azimuthal angle. Such vortices are polarization singularities that are described by indices, similar to the TC. However, polarization OAM for polarization vortices still has not been considered, although laser beams with inhomogeneous polarization can perform spiral mass transport in polarization-sensitive media. In this work, we consider two possible definitions of the polarization OAM. One OAM is proportional to the azimuthal velocity of changing direction of linear polarization vector, whereas the other (hybrid OAM) is proportional to the azimuthal velocity of changing ellipticity degree of the polarization ellipse. For instance, the normalized polarization OAM is equal to the order of a cylindrical vector beam and also equals the order of Poincaré beam.