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.