Reply to “Comments on `A Physics-Based Green\´s Function for Analysis of Vertical Electric Dipole Radiation Over an Imperfect Ground Plane\´”

In the comments on the commentator claims that the expression of the magnetic vector potential given in [1. eq. (14)] is not complete and consequently incorrect. The commentator builds his argument on a simple application of Cauchy´s integral theorem, which was exactly done by Sommerfeld in 1909. This procedure to solve Sommerfeld´s integral for a half-space problem yields results that were proven experimentally [3] and theoretically [4] to be incomplete. The numerical results shown in the comments are plotted for the two different formulations in a region which is one-tenth of a wavelength away from the source which is located at a distance of one-hundredth of a wavelength away from the interface. This distance is in the immediate vicinity of the source. It was mentioned clearly in [1] that the new formulation given in [1, eq. (14)] is suitable only for relatively large horizontal separations between the source and field points. It is important to point out that one of the formulation breaks down when the sources are close to the ground and the other breaks down when the transmitter and the receiver are close to each other. Therefore, it is not clear to us what this commentator is trying to accomplish by providing computational results in regions where either of the formulations becomes unstable and then claiming that since the two methods do not provide identical answers, therefore one must be wrong! Thus completely ignoring the fact that the two formulations provide consistent answers when the parameters of the computations are chosen outside these regions as illustrated in.