Spatial coherence of the thermal electromagnetic field in the vicinity of a dielectric slab

We present the analytic calculation of the cross-spectral density tensor of a thermally radiative planar dielectric slab in extreme near-field, intermediate near-field, and far-field zones. We show that the spatial coherence of the thermal field exhibits distinct features in these zones. At a given wavelength λ, the coherence length is many orders of magnitude smaller than λ in the extreme near-field zone, and is roughly λ2 in the far-field zone. In the intermediate near-field zone, the coherence length can be much longer than λ2 if the loss is small. The physical origin of the short-ranged spatial coherence in the extreme near-field zone is the spatially fluctuating surface charges at the air-dielectric interface. We also demonstrate that in the intermediate near-field zone, the long-ranged spatial coherence is induced by the waveguide modes of the dielectric slab. When the loss is small, the long-ranged coherence falls off approximately as 1 x, in contrast to 1 x for a blackbody radiator, where x refers to displacement parallel to the slab surface.