The radiation problem from a vertical short dipole antenna above flat   and lossy ground. Novel formulation in the spectral domain with closed form   analytical solution in the high frequency regime
  In this paper we consider the problem of radiation from a vertical short Hertzian dipole above flat lossy ground, which represents the well known in the literature Sommerfeld radiation problem. The problem is formulated in a novel spectral domain approach, and by inverse three dimensional Fourier transformation the expressions for the received electric and magnetic field in the physical space are derived as one dimensional integrals over the radial component of wavevector, in cylindrical coordinates. Subsequent use of the Stationary Phase Method in the high frequency regime yields closed form analytical solutions for the received EM field vectors, which coincide with the corresponding reflected EM field originating from the image point. In this way, we conclude that the so called in the literature space wave, i.e. line of sight plus reflected EM field, represents the total solution of the Sommerfeld problem in the high frequency regime, in which case the surface wave can be ignored. Finally, numerical results in the high frequency regime are presented in this paper, in comparison with corresponding numerical results based on Norton solution of the problem, i.e. space and surface waves. 
Ch. Christakis, K. Ioannidi, S.Sautbekov, P. Frangos and S.K. Atanov
physics.class-ph