Improper statistics of the radiation from a randomly rotating source

In a previous study [ J. Opt. 19 , 0905603 ( 2017 ) JOOPDB 0150-536X 10.1088/2040-8986/aa7cac ], we revealed that the complete second-order statistics of narrowband polarized waves are characterized by 13 parameters, in contrast to the four parameters of the traditional Stokes vector description of the statistics of partially polarized light. In this study, we analyzed the second-order statistics of the field of a randomly rotating source of electromagnetic radiation and showed that it includes covariance of the right- and left-circular polarizations that are not captured by the Stokes vector formalism. We illustrate this finding using simple examples of rotating quadrupoles and dipole pairs.