Sommerfeld half-space and path loss improvement in near-ground wave propagation

Abstract

This paper is a communication about the near-ground propagation and the condition under which the proximity of a lossy interface improves the path loss [1]. The well-known Sommerfeld half-space problem is treated by Sommerfeld formulation which is widely accepted in the community and can be validated by rigorous mathematical treatment [2]. The asymptotic approximation (steepest descent) of the electric field radiated by an elementary vertical electric dipole (VED) over a half-space is of interest. It is important to note that the formulation includes not only the direct and reflected waves, but also a third field component generated thanks to diffraction at the interface between the two media. This third component is naturally ignored by ray based techniques and in some cases can become predominant and improves the near-ground path loss. The appropriately simplified field expression brings out the important intervening parameters, such as the working frequency, the heights of the elementary dipoles and the interface’s electrical properties (permittivity and conductivity). In this paper, the condition for the optimal near-ground path loss is presented explicitly as a function of these three parameters. More information about the optimised path loss zone can be extracted using two distances. The first distance (ρ min ) is calculated to estimate the shortest possible distance to achieve the optimised path loss. The second distance (ρ break ) is calculated to predict the end of the advantageous zone. These three easy-to-use expressions (Figure 1.a) help to take full advantage of the near-ground link and will be presented and discussed in the final submission.