The Evaluation of a Novel Asymptotic Solution to the Sommerfeld Radiation Problem using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

TL;DR

This paper revisits a spectral domain asymptotic solution to the Sommerfeld Radiation Problem, introducing an efficient numerical method for Sommerfeld integrals and validating the solution against numerical and analytical benchmarks across various scenarios.

Contribution

It presents a novel asymptotic solution in the spectral domain and an efficient technique for calculating Sommerfeld integrals, improving accuracy and computational efficiency.

Findings

The spectral domain asymptotic solution closely matches numerical evaluations.

The new integral calculation method outperforms traditional approaches.

Analytic expressions are derived for special cases near and far from the interface.

Abstract

In this work, a recently developed novel solution of the famous "Sommerfeld Radiation Problem" is revisited. The solution is based on an analysis performed entirely in the spectral domain, through which a compact asymptotic formula describes the behavior of the EM field, which emanates from a vertical Hertzian radiating dipole, located above flat, lossy ground. The paper is divided into two parts. First, we demonstrate an efficient technique for the accurate numeric calculation of the well - known Sommerfeld integrals, required for the evaluation of the field. The results are compared against alternative calculation approaches and validated with the corresponding Norton figures for the Surface Wave. Then, in the second part, we briefly introduce the asymptotic solution of interest and investigate its performance; we contrast the solution versus the accurate numerical evaluation for the total received EM field and also with a more basic asymptotic solution to the given problem, obtained via the application of the Stationary Phase Method (SPM). Simulations for various frequencies, distances, altitudes and ground characteristics are illustrated and inferences for the applicability of the solution are made. Finally, special cases, leading to analytic field expressions, close as well as far from the interface, are examined.