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An expressio n for t he fi eld of an elect ric dipole located over a fiat surface with a specifi ed surface impedance Z is d erived from t he form al integra l solution by a modified saddlepoint m ethod . Using t he value of Z appropriate for a homogeneous conducting g round, the general expressions reduce to those given bgr Norton. In this case the phase of Z li es between 0 a nd 45. When t he phase exceed s 45 , as it m ay for a stratified ground, t h e r adiated wave of the dipole becomes partially t rapp ed to t he interface. This effect is most pronounced for an inductive surface where t he phase of Z is 90 0 , in which case t he energy of the wave is confin ed within a sm all distance from t h e surface. Such inductivc surfaces are a metallic pla ne with a t hin dielectric film or a co rrugated s urface.
James R. Wait (1957) studied this question.