Some consequences of the van Cittert-Zernike theorem for partially polarized stochastic electromagnetic fields

Coherence and polarization properties of the field generated by a partially polarized incoherent source are examined in terms of the 2x2 cross-spectral density matrix, with a view to deriving an electromagnetic counterpart of the van Cittert-Zernike theorem. Emphasis is placed on the polarization properties of the field. As some consequences of the extended theorem, we found that the spectral degree of polarization of the resultant field is generally different from that of the source and that both are the same in a special case. A different somewhat unconventional view of the extended theorem is also discussed in brief.