  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.
