An Analytical Solution of the Electric Field Excited by a Vertical Electric Dipole Above a Lossy Half-Space: From Radio to Microwave Frequencies

摘要

In this article, an analytical solution of the electromagnetic radiation from a vertical electric dipole (VED) above a lossy half-space is proposed. The expression for the traditional solution is associated with the Sommerfeld-type integral, which is difficult to evaluate due to its highly oscillating and slowly decaying integrand. The solution for the intermediate Hertz potential is decomposed into two integrals and a rigorous closed-form solution in the near and far-field regions are presented for each term. Then, the scattered electric-field components are calculated from the intermediate Hertz potential. A numerical evaluation of the solution for different lossy half-spaces, such as seawater, wet earth, dry earth, and lake water, validates the accuracy of the proposed solution at various frequencies, from radio to microwave frequencies, as well as different distances from the antenna in the near and far-field regions.