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 lambda , the coherence length is many orders of magnitude smaller than lambda in the extreme near-field zone, and is roughly lambda/2 in the far-field zone. In the intermediate near-field zone, the coherence length can be much longer than lambda/2 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/square root x , in contrast to 1/x for a blackbody radiator, where x refers to displacement parallel to the slab surface.
Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA. and Ginzton Laboratory, Stanford University, Stanford, California 94305, USA.
Wah Tung
WT
Lau
Jung-Tsung
JT
Shen
Georgios
G
Veronis
Shanhui
S
Fan