Two-dimensional electromagnetic fluctuations in arbitrary geometries

A general-purpose formulae for the nonretarded two-dimensional Green function in the case of arbitrary geometrical shapes of lossy dielectrics is derived by the method of complex variables. Spectral power densities of fluctuating electromagnetic fields are determined by real and imaginary parts of the Green function. Spectral properties of fluctuating fields in given geometrical domains may be obtained by appropriate conformal mappings. The applicability of the method is illustrated by in comparison with some exact solutions, in particular, related to a cylinder, to an arbitrary wedge, and to a plane slit. The impact of curved surfaces upon spectral characteristics is analyzed by numerical calculations of fields inside the "open" parabolic domain and inside or outside of "close" cylindrical domains as compare with a plane case. The controllability of spectral properties by a local curvature of surface is demonstrated.