We present an exact calculation of the cross-spectral density tensor of the near field thermally emitted into free space by an opaque planar surface. The approach, based on fluctuational electrodynamics and the fluctuation-dissipation theorem, yields novel near-field correlation properties. We show that the spatial coherence length of the field close to the surface at a given wavelength $\lambda$ may be much smaller than the well-known $\lambda /2$ of blackbody radiation. We also show that a long-range correlation may exist, when resonant surface waves, such as surface-plasmon or surface-phonon polaritons, are excited. These results should have important consequences in the study of coherence in thermal emission and in the modeling of nanometer scale radiative transfer.

• Received 16 October 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.1660