Classical, Polarization, and Hybrid Orbital Angular Momentum of Vector Fields with Polarization Singularities

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 introduce and consider two analogues of the OAM for vector fields. One polarization OAM analogue is the polarization orientation azimuthally changing velocity, or polarization OAM (pOAM), whereas the hybrid OAM analogue is the polarization ellipticity azimuthally changing velocity, or hybrid OAM (hOAM). For instance, we demonstrate that the normalized pOAM is equal to the order of a cylindrical vector beam and also equals the order of Poincaré beam. In optical material processing, the considered OAM analogues describe how light fields with different polarization affect polarization-sensitive media. In optical data transmission, these OAM analogues allow distinguishing different light fields that are indistinguishable by their conventional OAM.