Polarization dynamics of random 3D light fields

We study the time evolution of the instantaneous polarization state, i.e., the polarization dynamics of random, statistically stationary three-dimensional electromagnetic fields. Two intensity-normalized polarization correlation functions which characterize the similarity of the polarization state at two times are presented. One of them is based on the generalized instantaneous Poincaré vectors and the other on the Jones vectors. We discuss the basic properties of the correlation functions and define a polarization time as a time interval over which the state of polarization does not significantly change. If the field obeys Gaussian statistics the polarization correlation functions are expressible in terms of certain second-order, measurable parameters characterizing the partial polarization and partial coherence of the field. We exemplify the formalism with a uniformly partially polarized, temporally Gaussian correlated field, and with the field at the intersection of three orthogonally propagating, linearly polarized and mutually correlated beams. The results are expected to find use in applications where the polarization fluctuations of a three-dimensional field play an important role.