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

In this paper we consider the problem of radiation from a vertical short (Hertzian) 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 (SPM) 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.