Spectral properties of fluctuating electromagnetic fields in a plane cavity: implication for nanoscale physics

Spectral power densities of fluctuating electromagnetic fields and their spatial derivatives of all orders in any point of a transparent plane gap between two media described by different complex permittivities and by different temperatures were derived on a basis of generalized Kirchhoff's law. Electromagnetic losses into the two absorbing media induced by a field of a point dipole or of point multipolelike origins situated in any place of interest at the transparent gap were determined. The corresponding electrodynamical regular Green problem for a point dipole and for point multipoles of any orders constituted by the point dipole was solved. We demonstrate ways to obtain different asymptotic cases following from our general solution including the problem for a half space, Planck's formula for black body radiation, the van der Waals forces for solids kept at different temperatures, and contributions from propagating and evanescent waves. Expressions for electromagnetic loss of a point multipole of any order in selected geometry of the problem were derived and, as an important limiting case related to problems of near field microscopy, when the multipole is situated over a half space.