  Efficient Green's function evaluation in layered media is a holy-grail of
wave theory in general and for electromagnetics in particular. While there is a
very large amount of knowledge in this context with vast literature, there are
yet challenging cases such as the Green's function in thick lossy media and the
Green's function at 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-Pad\'{e}
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.
