Generalized van Cittert-Zernike theorem for the crossspectral density matrix of quasi-homogeneous planar electromagnetic sources

We present a generalized van Cittert-Zernike theorem for the cross-spectral density matrix of quasi-homogeneous planar electromagnetic sources. An example of the generation of a beam with interesting polarization and spatial coherence properties is discussed. This example was obtained by choosing the appropriate spectral density distribution of the source. We found that, under certain conditions, a quasi-homogeneous, polarized source may produce a beam in the farfield that is unpolarized in the typical one-point sense but polarized in the two-point mutual polarization sense.