Degree of polarization of statistically stationary electromagnetic fields

The analysis presented in this paper resolves an outstanding controversial issue of statistical optics, concerning the existence of the degree of polarization of any random, statistically stationary electromagnetic field. We show that the second-order electric spectral correlation matrix at any point in such a field may be uniquely expressed as the sum of three matrices, the first of which represents a completely polarized contribution. The ratio of the average intensity of the polarized part to the total average intensity provides a unique and unambiguous definition of the spectral degree of polarization of the electric field. It may be expressed by a simple formula in terms of the eigenvalues of the correlation matrix of the electric field and it reduces, for the two-dimensional case, to the usual well-known expression for the degree of polarization of beam-like fields. The results of this paper are of special interest for near-field optics.