Uniformly Accurate Electrostatic Layered Medium Green’s Function Approximation via Scattered Field Formulation

摘要

A novel approach to evaluation of electrostatic multilayered media Green’s functions is presented. Total field of the point charge in layered substrate is represented as a sum of known closed-form incident field in homogeneous space and scattered field which accounts for the effect of the layers. The former accurately approximates the field near the source while the latter is approximated with cylindrical waves and accurately represents the intermediate and far fields. The cylindrical waves approximation is performed via numerical solution of the differential equation formulated with respect to the scattered field as opposed to the total field as it was done in previous work. The spectral domain scattered field solution is cast into the pole-residue form. It allows for the subsequent analytical evaluation of the Sommerfeld integrals producing closed-form space domain approximation.