Surface electric fields and impedance matrix elements of stratified media

For the various geometrical configurations of waves in stratified media, we consider the important case when both source and field points are located on the same interface separating two different dielectric media. We shall denote this configuration as surface electric field case. In this paper, the electric fields are calculated numerically without using potentials. For the surface electric field case the integrand of the electric field grows with k_ρ^3/2 for large k_ρ making the Sommerfeld integral singular. To calculate the surface electric fields in the spatial domain, we recently applied a technique of higher order asymptotic extraction. In the higher order asymptotic extraction, the higher order asymptotic parts were calculated analytically. The remainder, which has an integrand decays as k_ρ^-3/2, was calculated numerically along the Sommerfeld contour path of integration. In this paper, we use a different extraction technique, the half-space extraction. After the half-space extraction, the integrand of the Sommerfeld integral of stratified media decays exponentially and the integral is calculated along the Sommerfeld integration path. The half-space extraction part is calculated by numerical integration along the vertical branch cuts. The surface electric fields for stratified media using half-space extraction and higher order asymptotic extraction are in good agreement. To validate the accuracy of the solution, we also compute the impedance matrix elements using surface electric fields, testing, and basis functions all in spatial domain. The results are then compared with the results of the spectral domain method. The comparisons of the complex impedance matrix elements are tabulated and show that the difference is less than 2%.