Orbital angular momentum of vector light fields at the tight focus

Abstract

We introduce here new physical quantities. By analogy with the conventional orbital angular momentum (OAM), they are called polarization OAM and hybrid OAM. It is known that the conventional OAM indicates the presence of an optical vortex in the light field and is equal to the topological charge. The same way, the polarization OAM indicates the presence of a "vortex of the linear polarization direction" in the vector field and is equal to the singularity index of the vector field. Thus, it shows how many full turnovers makes the linear polarization vector along a closed contour around the optical axis. The hybrid OAM demonstrates that along a closed contour around the optical axis, the vector field changes not only by the direction of major axis of the polarization ellipse, but also by the ratio between the major and minor ellipse axes. The hybrid OAM is equal to the number of full turnovers of the polarization ellipse. These new OAMs are derived for several typical initial vector fields to demonstrate their functionality. The initial electric field has only two transverse components, which determine the longitudinal component of the OAM vector. However, at the tight focus, all three components of the E-vector arise, and therefore, longitudinal component of the OAM vector is defined by all three electric field components. Thus, if one of these three OAMs is zero in the initial field, then at the focus, this OAM can become nonzero due to appearing longitudinal field component, contributing to this OAM. We believe that these newly introduced OAMs can be applicable to other vector fields, allowing more complete description of their properties.