A Physics-Based Green's Function for Analysis of Vertical Electric Dipole Radiation Over an Imperfect Ground Plane

Comments on “A Physics Based Green's Function for Analysis of Vertical Electrical Dipole Radiation Over an Imperfect Ground Plane” $ $

“…A mirror image of these cuts also exists in the second quadrant, which is, however, immaterial to the present discussion. It is important to keep in mind that the other popular choice of branch cuts, viz., that of vertical cuts emanating from are not relevant to the present discussion because a straight-forward analysis will reveal that with such a choice the contribution obtained by wrapping around the branch cut would result in a final representation involving complex values of , whereas the paper under question, [1], is concerned with a final representation involving real . For the branch cuts shown in Fig.…”

“…In [1], the integral representations with respect to the vertical wavenumber given in (14) and (15) of that paper for the potentials of a vertical Hertzian dipole above an arbitrary ground plane are incomplete and, consequently, incorrect. The errors made in [1] are of fundamental nature and the representations provided therein cannot be obtained from first principles for a material half-space.…”

“…The errors made in [1] are of fundamental nature and the representations provided therein cannot be obtained from first principles for a material half-space. The purpose of the present comment is to derive correct representations adopting the same notation as in [1]. Here, we focus on the -component of the secondary field only in region-1 above the horizontal interface.…”

“…The orientation of branch cuts is dictated by the final representation one is seeking. If an alternate representation with respect to vertical wavenumber along the real axis is desired as in [1], then branch cuts must be chosen as in Fig. 1, where only the cuts in the fourth quadrant emanating from and are shown.…”

“…Other serious errors in [1] are the complete absence of additional terms that must exist with the choice of the branch cuts shown in Fig. 1.…”