Exactly calculable field components of electric dipoles in planar boundary

The Sommerfeld integrals for the electromagnetic fields in the planar bound ary between air and a homogeneous, isotropic medium, due to a horizontal an d a vertical electric dipole each lying along the interface, are examined i n detail. In the case of the horizontal dipole, the tangential electric fie ld is given in terms of series that involve confluent hypergeometric functi ons, namely, the Fresnel and exponential integrals. A similar exposition is presented for the magnetic and vertical electric fields of the vertical di pole. When the index of refraction of the adjacent space is of a sufficient ly large magnitude, the derived series converge rapidly and uniformly with the distance from the source. Specifically, their rates of convergence are shown to be independent of distance. It is pointed out that the correspondi ng formulas of King are valid down to any distance close to the source, whe re they smoothly connect to known "quasi-static" approximations. (C) 2001 A merican Institute of Physics.