  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.
