Surface electric fields and spatial derivatives of Green's function of layered media based on half-space extraction

We consider the case when both source and field points are located on the s ame interface separating two different dielectric media. The electric field s and spatial derivatives of an electric-field Green's function in the spat ial domain are calculated numerically without using potentials. For the ele ctric field and its spatial derivatives, the integrand of th Sommerfeld int egral grows with k(p) for large k(p). For the fourth derivative, the integr and grows as the k(p)(11/2) power. To evaluate the integrals, we use a half -space extraction technique. After the half-space extraction, the integrand of the Sommerfeld integral of layered media decays exponentially, and the integral is calculated along the Sommerfeld integration path. The half-spac e extraction part is calculated by numerical integration along the vertical branch cuts. Numerical results of the surface electric fields and spatial derivatives up to the fourth order for multilayered media are illustrated f or distances from 0.02 to 20 free-space wavelengths. Results are illustrate d for various layer thicknesses. (C) 2000 John Wiley & Sons, Inc.