Interpretation of the recipe for synthesizing genuine cross-spectral density matrices

A physical interpretation of the recipe for synthesizing genuine 2 × 2 cross-spectral density matrices that characterize stochastic electromagnetic sources and beams is described. In this interpretation, the synthesized field is regarded as an incoherent superposition of spatially coherent fields originating from a partially polarized, spatially incoherent virtual source. The coherence and the polarization properties of the synthesized field are also examined in view of this interpretation. As a result, we found that the spectral degree of coherence and that of polarization of the synthesized field are generally different from those of the virtual source by the effect of the superposition. We also found, however, that there are some situations in which the spectral degree of polarization of the synthesized field remains unchanged even though the superposition takes place.