A complex image method for the vertical component of the magnetic potential of a horizontal dipole in layered media

Abstract

In applying mixed-potential integral equation methods to the electromagnetic analysis of vertical and horizontal conducting structures in a multilayered environment, various Green's functions for the magnetic vector potentials and electric scalar potentials are required. With the Cartesian coordinates defined the present paper, an infinitesimal vertical electric dipole (VED) will produce magnetic vector potential G/sub a//sup zz/ where the first and second superscript designate, respectively, the component of the vector potential and the direction of the source. The pulsating point charge associated with a VED will produce an electric scalar potential G/sub q//sup v/. From these potentials, one can compute both the horizontal and vertical fields generated by a VED. However, G/sub a//sup xx/ and G/sub q//sup h/, counterparts generated by a horizontal electric dipole (HED) in the x direction allow one to compute the horizontal fields only. Sommerfeld [1949] showed that assuming that the magnetic vector potential from an HED has only an x-component is insufficient to satisfy all boundary conditions for the fields, except in the homogeneous case, He then invented a z-component of the vector potential G/sub a//sup zx/ to correct this problem. The present authors continue by discussing a complex image method. >