n-Fold Polarization Measures and Associated Thermodynamic Entropy of N Partially Coherent Pencils of Radiation

An n-fold (n=2,…,N) measure of the degree of polarization associated with an N×N coherency matrix characterizing N pencils of radiation is discussed. The measure is cast in terms of the N possible scalar invariants of the coherency matrix and automatically takes into account possible rank deficiency. When N = 2, the single polarization measure reduces to the usual expression for polarization as the fraction of the intensity contained in the polarized component. The N = 3 case is discussed as an illustrative example, with special reference to the rank deficiency of a plane wave arbitrarily oriented with respect to the given coordinate system. Finally, these results are used to redevelop von Laue's theory of the thermodynamic entropy of partially coherent pencils of radiation.