Time-domain study of arbitrary dipole in planar geometry with discontinuity in permittivity and permeability

Transient fields arising from a general impulsive dipole above ground characterized by permittivity and permeability are studied. A detailed analysis for arbitrary electric dipole excitation is given, and the fields arising from the analog magnetic sources can be obtained by applying the duality transform. The mathematical description of this problem is done using the Hertz vector, whose solution in the time domain is derived in a novel way using the exact image theory. From this solution, which involves a definite integral, the actual fields are obtained through simple differentiations. The efficiency of the method is demonstrated by solving 14 previously unknown closed-form results for various field components in certain specific cases. Seven of these are obtained for electric dipole excitation and listed, whereas the corresponding results in the case of magnetic excitation can be easily written by applying the duality transform