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, such as the intensity, degree of polarimetric purity, the indices of polarimetric purity, angular momentum, degree of directionality, and degree of linear polarization, are identified and interpreted in 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 rank R = 2 do not always represent states with a well-defined direction of propagation. Moreover, the existence of 3D mixed states that cannot be decomposed into a superposition of a pure state, a two-dimensional (2D) unpolarized state, and a 3D unpolarized state is demonstrated. Appropriate representation and interpretation for all the different types of 3D coherency matrices are provided through physically consistent criteria. Under the approach proposed, the conventional 2D model arises naturally.