Intensity fluctuations and the degree of polarization in Gaussian random electromagnetic fields

For an electromagnetic beam described by Gaussian statistics the normalized intensity fluctuations are known to depend on the beam's degree of polarization. With general non-paraxial random electromagnetic waves, such as optical near fields, a complete characterization of the polarization state requires a 3 x 3 coherence matrix and a three-dimensional degree of polarization. We demonstrate that, under the assumption of Gaussian statistics, the normalized intensity fluctuations in the three-dimensional case are expressible in terms of the three-dimensional degree of polarization. Since such a general description can be employed even for beams with only a transverse electric field, several important physical results follow from comparison of the three-dimensional and usual two-dimensional formulations. The results are expected to be particularly important in intensity interferometry.