A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic field expressions and the emergence of the Surface Waves

TL;DR

This paper presents a new asymptotic analytical solution to the Sommerfeld radiation problem, providing explicit field expressions and insights into surface wave emergence for a vertical dipole above lossy ground.

Contribution

It introduces a novel asymptotic approach using the Saddle Point method to derive closed-form solutions for the electromagnetic field in the Sommerfeld problem.

Findings

Derived explicit integral expressions for EM fields.

Obtained analytical formulas including sliding observation angles.

Discussed conditions for surface wave emergence.

Abstract

The well-known "Sommerfeld radiation problem" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral expressions for the received Electromagnetic (EM) field. Then, using the Saddle Point method, novel analytical expressions for the scattered EM field are obtained, including sliding observation angles. As a result, a closed form solution for the subject matter is provided. Also, the necessary conditions for the emergence of the so-called Surface Wave are discussed as well. A complete mathematical formulation is presented, with detailed derivations where necessary.