Nonparaxial, quasihomogeneous electromagnetic sources and their wide-angle far fields

We consider random, three-component, planar, quasihomogeneous electromagnetic sources and the nonparaxial far fields which they produce. We show that by measuring the far-field spectral polarization matrix on a spherical surface throughout a half-space enables to reconstruct the low spatial-frequency parts of the degrees of correlation between the parallel source field components. Further, detecting, in addition, the far-zone angular cross-spectral density matrix for all pairs of directions with significant intensity allows to deduce the low spatial-frequency contributions to the spectral densities of the source field components as well as the degrees of correlation between the orthogonal components. The validity of the formalism is demonstrated by considering a three-component, electromagnetic Gaussian Schell-model source. The results are important for the research on electromagnetic wide-angle radiators such as many thermal and fluorescent sources and light-emitting diodes.