Electrodynamic Green's functions in layered media: Accurate closed-form approximations for both electric and magnetic sources

A robust way to calculate the electrodynamic Green's functions in the presence of a planar stack of layered media is proposed. The methodology relies on the separation of the spatial spectrum of the Green's function into two parts. The quasi-static part contains the most slowly decaying components of the spatial spectrum. In the space domain, the quasi-static part translates to spherical wave terms. Each one of these terms is called a quasi-static image. A general procedure for the extraction of an arbitrary number of quasi-static images for each one of the components of the Green's function is proposed, which results in analytic, closed-form expressions for this component of the Green's functions both in the spectral and in the space domain. The second part of the spatial spectrum, which is called the dynamic part, is fitted in terms of rational functions with use of a modified version of the VECTFIT algorithm. The transition in the space domain is done in an analytic, closed-form manner, which results in cylindrical wave terms in the space domain.;The final result of this methodology is the approximation of the Green's function in terms of a finite sum of spherical and cylindrical waves. The spherical waves capture the correct behavior of the fields in the source neighborhood, including any possible singularities. The cylindrical waves enhance the accuracy in the calculation of the Green's function farther away from the source, as they include any possible propagating modes of the structure.;Since all other steps in the proposed methodology are carried out analytically, the accuracy of the generated closed-form expression for the Green's function is dictated by the accuracy of the rational function fitting of the dynamic part.;The proposed methodology has been implemented in a computer tool suitable for the calculation of the electrodynamic Green's function in the presence of planar media composed of layers of arbitrary material composition and thickness. Special emphasis was placed on making the computer tool robust to ensure the accuracy of the calculated Green's function over a very broad range of frequencies, thus making it suitable for applications ranging from radio wave propagation above Earth, to the design of planar microwave/millimeter-wave frequencies and of integrated optical waveguides. In addition, special attention was paid to making the tool as transparent as possible to the user. In this manner, the user does not need to have an in-depth knowledge of the underlying physics of the electromagnetic boundary value problem at hand and its impact on the numerical computation of the Green's function, making the computer tool quite general and very user-friendly.