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

A recently developed high-frequency asymptotic solution for the famous “Sommerfeld radiation problem” is revisited. The solution is based on an analysis performed 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. We first demonstrate an efficient technique for the accurate numerical calculation of the well-known Sommerfeld integrals. The results are compared against alternative calculation approaches and validated with the corresponding Norton figures for the surface wave. In the second part, we introduce the asymptotic solution and investigate its performance; we compare the solution with the accurate numerical evaluation for the received EM field and with a more basic asymptotic solution to the given problem, obtained via the application of the Stationary Phase Method. 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 analytical field expressions close as well as far from the interface are examined.

On the Calculation of 2D Green's Functions Via Sommerfeld Integrals and the Spatial Singularity Method

<p>We provide a low-level review of the computation of Sommerfeld integration theory using the singularity expansion method (SEM) to analytically estimate the short-wavelength components of the 2-dimensional Green's function. The SEM is employed to replace the infinite tail of the spectral integral by a closed-form evaluation. The various steps in the SEM substitution and the calculations are elaborately presented and discussed with emphasis on giving the missing details often not included in the published literature.<b></b></p>

On the Calculation of 2D Green's Functions Via Sommerfeld Integrals and the Spatial Singularity Method

<p>We provide a low-level review of the computation of Sommerfeld integration theory using the singularity expansion method (SEM) to analytically estimate the short-wavelength components of the 2-dimensional Green's function. The SEM is employed to replace the infinite tail of the spectral integral by a closed-form evaluation. The various steps in the SEM substitution and the calculations are elaborately presented and discussed with emphasis on giving the missing details often not included in the published literature.<b></b></p>