A full characterization of the polarization of vector light beams

We present an approach to fully characterize the polarization of general vector light beams. When attempting to generalize the notion of Stokes parameters to nonparaxial light beams in momentum space, we find that the Jones function that determines the Stokes parameters through the Pauli matrices is defined over a natural coordinate system that is fixed by a constant unit vector, called the Stratton vector. We further show that the Pauli matrices represent the intrinsic degree of freedom of the polarization with respect to the natural coordinate system so that the Stratton vector acts as an additional degree of freedom that complements the intrinsic degree of freedom to fully characterize the polarization. As a consequence of the new degree of freedom, the Stratton vector, in helicity states, a phase factor that has observable physical effects is identified. Examples of its application to characterizing the state of polarization are also given.