Singularity index and orbital angular momentum of a beam with a hybrid polarization singularity

Alongside scalar optical vortex beams, which have a topological charge (TC), a spiral wave front and carry an orbital angular momentum (OAM) that can be transferred to microparticles and rotate them along circular trajectories, polarization optical vortices are also known, in which the polarization state in the beam cross section changes with a change in the azimuthal angle. Such vortices have points of polarization singularity, which are described by indices similar to TZ. However, polarization OAMs for polarization vortices have not yet been considered. Meanwhile, laser beams with inhomogeneous polarization can perform spiral transfer of matter in polarization-sensitive media. In this paper, two possible definitions of polarization OAMs are considered. One OAM is proportional to the azimuthal rate of change of the linear polarization vector direction, and the second (hybrid OAM) is proportional to the azimuthal rate of change of the degree of ellipticity of the polarization ellipse. For example, the normalized polarization OAM is equal to the order of a cylindrical vector beam and is also equal to the order of a Poincaré beam.