A closed form analytical solution to the radiation problem from a short dipole antenna above flat ground using spectral domain approach

TL;DR

This paper presents a novel closed-form analytical solution for the electromagnetic fields radiated by a short dipole antenna above a lossy flat ground, using spectral domain methods and inverse Fourier transforms.

Contribution

It introduces the first known closed-form solutions for the Sommerfeld radiation problem in this configuration, enhancing analytical understanding.

Findings

Derived explicit formulas for electric and magnetic fields in the far field.

Validated the solutions through physical interpretation and analysis.

Provides a foundation for further studies on antenna radiation above ground.

Abstract

In this paper we consider the problem of radiation from a vertical short dipole above flat ground with losses, which represents the well known in the literature Sommerfeld radiation problem. We end up with a closed form analytical solution to the above problem for the received electric and magnetic field vectors above the ground in the far field area. The method of solution is formulated in the spectral domain, and by inverse three dimensional Fourier transformation and subsequent application of the Stationary Phase Method the final solutions in the physical space are derived. To our knowledge, the above closed form solutions are novel in the literature for the Sommerfeld radiation problem. Finally, the physical interpretation for the received fields formulae derived this paper are provided.