The radiation of a Hertzian dipole over a coated conductor

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Abstract
The idealized problems of an infinitesimal Hertzian dipole in and over a perfect dielectric coating a perfect conductor and an Abraham dipole lying on the conductor are treated. Unintegrated forms of the Hertz potentials are obtained both for electric and magnetic dipoles.Integrated far-zone forms of the potentials and fields are obtained for electric dipoles by means of asymptotic integrations. Far-zone radiation patterns are given in order to indicate the distortions of the fields and the magnitudes of the residue waves caused by the dielectric coatings. These show that such layers cause a very large increase in the relative field strength in the direction along the surface.It is proved that the power radiated by the dipole may be divided into two independent quantities—the power fed to radiation-type and that fed to surface or guided-type fields. For certain cases numerical results are given for the total power radiated and the relative powers fed to the two types of fields.Formulae are derived and illustrated with numerical examples of the radiation resistances of the dipoles and the attenuation coefficients of the surface modes due to finite conductivity of the ground plane.

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