Accurate approximation of Green´s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves

A robust and computationally-expedient methodology is presented for accurate, closed-form approximation of the Green´s functions used in the mixed-potential integral equation statement of the electromagnetic boundary value problem in planar stratified media. The proposed methodology is based on the fitting of the spectrum of the Green´s function, after the extraction of the quasistatic part, making use of rational functions. The effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit. The resulting closed-form approximation is in terms of both spherical and cylindrical waves. Thus, high accuracy is obtained in the approximation of the Green´s function irrespective of the distance of the observation point from the source. The methodology is validated through its application to the approximation of the Green´s function for a multi-layered, planar dielectric stack