Interpretation of three-dimensional polarization states through the smart decomposition of the polarization matrix

A complete description of a three-dimensional (3D) polarization state is provided by the two most significant eigenstates of the polarization matrix, together with the two indices of polarimetric purity. By means of the so-called smart decomposition, such information can be arranged to represent the state as a combination of two components, one partially polarized (active component) and one unpolarized. Contrary to what happens for two-dimensional (2D) polarization states (with the electric field fluctuating within a fixed plane), whose active component is constituted by a single totally polarized state, in the general case of 3D polarization states the active component is given by a weighted incoherent composition of the two above-mentioned eigenstates. We show that a detailed description of the intensity and spin anisotropies is encompassed by the active component of the state, which admits a simple interpretation and geometric representation. In addition, it is found that the degree of nonregularity can be viewed as a distance of the state to a regular state.