On solutions of Maxwell's equations with dipole sources over a thin conducting film (Q2804977)

The authors deduce solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole located near a thin film lying between two unbounded isotropic and non-magnetic media. If both the dipole and the observation point lie on the layer, then the authors show that the fields can be expressed in terms of geometrically convergent series and known transcendental functions. Considerable simplifications of the formulas are achieved when the film surface resistivity is much larger in magnitude than the intrinsic impedance of the ambient space. In this case, a few terms are retained in the series expansions for the fields yielding simple approximate formulas for all distances from the source.