Robust, efficient evaluation of EM Green´s tensors in generally anisotropic, planar-stratified media via complex-plane Gauss-Laguerre Quadrature

We propose a direct numerical integration-based eigenfunction expansion method to address long-standing computational efficiency, robustness, accuracy, and compute speed-related challenges concerning the full-wave evaluation of time-harmonic electromagnetic (EM) fields radiated by Hertzian (point) dipole antennas embedded in planar-stratified media of general anisotropy and loss. Robust and accurate, yet also rapid and computationally efficient, EM field evaluation in layered, anisotropic media is required both for validating faster, but more approximative methods (e.g., Closed Form Green´s Function methods), as well as for conducting simulations in support of myriad applications either requiring a numerical forward modeler (e.g., microwave circuit and antenna radiation analysis) or to catalyze the inversion of environmental parameters (common in remote sensing applications, for example). However, numerous practical evaluation challenges impede the more routine, widespread exploitation of the eigenfunction expansion method´s potent attributes (robustness, etc.) in said applications. Primarily, we refer to oscillatory behavior (limiting accuracy and computational efficiency), slow convergence, integral truncation error, and the need for rigorous error-controllability. Solution of these problems, on the other hand, would facilitate far greater forward and inverse-modeling flexibility with regard to the range of problems that can be simulated. We demonstrate that through employing a multi-level p refinement scheme paired with numerical evaluation, via Gauss-Laguerre quadrature, of the Fourier-like integrals upon a robust, judiciously-chosen integration path deformation, our proposed evaluation methodology summarily resolves said issues of convergence, truncation error, oscillatory behavior, and need for error-controllability in one coherent, streamlined formulation. Numerical results demonstrate the method´s efficacy as compared to previous eigenfunction evaluation- techniques.