On the Use of the Padé-Fourier Approximation in Fast Evaluation of the Green's Function of Layered Media

Efficient Green's function (GF) evaluation in layered media is a holy grail of wave theory in general and electromagnetics in particular. While there is a very large amount of knowledge in this context with a vast literature, there are yet challenging cases such as the GF in thick lossy media and the GF in thick media with negative parameters. Here, we propose a technique that can nicely tackle these issues. Our approach is based on a rational function approximation of the spectra using the Fourier-Padé approximation that is carried out in a conformal mapped spectral plane. We show that this approach can be used in challenging scenarios, such as very thick and lossy layers, materials with negative parameters such as in plasmonics, and even to approximate a dominant branch-cut contribution far from the source.