Interpretation of the coherency matrix for three-dimensional polarization states

From an appropriate parameterization of the three-dimensional (3D) coherency matrix R, that characterizes the second-order, classical states of polarization, the coherency matrices are classified and interpreted in terms of incoherent decompositions. The relevant physical quantities derived from R, as the intensity, the degree of polarimetric purity, the indices of polarimetric purity, the angular momentum, the degree of directionality and the degree of linear polarization are identified and interpreted on the light of the case study performed. The information provided by R about the direction of propagation is clarified and it is found that coherency matrices with, does not always represent states with a well-defined direction of propagation. Moreover, it is demonstrated the existence of 3D mixed states that cannot be decomposed into a superposition of a pure state, a 2D unpolarized state, and a 3D unpolarized state. Appropriate representation and interpretation for all the different types of 3D coherency matrices is provided through physical consistent criteria. Under the approach proposed, the conventional two-dimensional model arises naturally.