Information structure of a polarization state: the concept of metaspin

A complete description of the polarization properties of a random, stationary, generally three-dimensional (3D) optical field in a point is provided by the 3×3 polarization matrix. We show that its nine degrees of freedom can be represented by nine independent and decoupled parameters with simple and significant physical meanings. These cover the three orientation angles determining the intrinsic reference frame with respect to an arbitrary one, the three principal intensities representing the strengths of the components of the electric field along the respective intrinsic reference axes, and a real-valued vector, which we term metaspin, whose three components are given by the intrinsic correlations of the field components. Consequently, any given polarization state has an associated intensity-isotropic state, called the metaspin state, whose spin vector is fully determined by the metaspin vector. We also show that the concept of metaspin provides an illustrative synthesis procedure for 3D polarization states. The results can straightforwardly be applied to any 3×3 density matrix.