Electromagnetic degree of coherence in space-time and space-frequency domains

In this work, we apply a recently introduced electromagnetic degree of coherence to address the coherence properties of random, stationary electromagnetic fields. In particular, we consider the limit of complete coherence in space-frequency and space-time domains. We show that in both domains the (electric) coherence tensor is analogous, in its spatial and temporal structure, to the coherence function of fully coherent scalar fields. The results are important in the rigorous electromagnetic theory of optical coherence, as encountered, e.g., in non-paraxial near fields and diffractive optics.