Fast and Rigorous Modeling of Antenna--Medium Interactions Above Planar Stratified Media via the Generalized Scattering Matrix

TL;DR

The paper addresses efficient, rigorous prediction of antenna reflection coefficients above planar layered media. It develops a generalized scattering-matrix framework expressed in the spherical vector-wave basis and coupled to the planar medium via SVWF-to-PVWF transformations that embed the exact Fresnel response. The approach supports multiple reflections with a compact algebraic form and a fast single-integral evaluation of the transformation matrix, producing millisecond forward evaluations after a one-time GSM preprocessing. The results demonstrate near full-wave accuracy with several orders of magnitude speedups compared with FEKO, enabling real-time electromagnetic characterization and iterative/inverse modeling in planar layered environments.

Abstract

A rigorous and computationally efficient method is presented for evaluating the reflection coefficients of antennas operating above planar layered media. The approach reformulates the problem within the framework of the antenna's generalized scattering matrix (GSM), expressed in terms of spherical vector wave functions (SVWFs). The mutual interaction between the antenna and the layered structure is modeled through spherical-to-planar vector wave transformations that incorporate the exact Fresnel reflection response of the medium, without introducing any simplifying approximations. This formulation dramatically reduces algebraic complexity and enables fast, stable numerical implementation. Excluding the one-time preprocessing required to obtain the antenna's free-space GSM, each evaluation for a given layered configuration can be completed within milliseconds -- achieving several orders of magnitude speed improvement over full-wave solvers such as FEKO, while maintaining virtually identical accuracy. The proposed framework thus provides a powerful foundation for real-time electromagnetic characterization and inverse modeling involving planar layered environments.

Figures (11)

• Figure 1: Complex contours. (a) Contour of angle $\alpha$. (b) Contour of $u=\cos\alpha$.
• Figure 2: An antenna radiating above a planar interface. The origin of the reference coordinate system is set at the center of the antenna. Vectors $\mathbf{v}$ and $\mathbf{w}$ denote the expansion coefficients of the inward and outward waveguide eigenmodes of the antenna, respectively. $\mathbf{f}$ represents the coefficients of the outgoing SVWFs, and $\mathbf{a}$ those of the regular SVWFs. In this work, $\mathbf{f}$ is associated with the antenna-generated field ${\boldsymbol E}^s$, while $\mathbf{a}$ corresponds to the reflected field ${\boldsymbol E}^{sR}$.
• Figure 3: Signal-flow diagram illustrating the interactions between the antenna and the planar layered ground.
• Figure 4: S-parameters of the horn antenna above a PEC half-space environment. The interface is at $z_\mathrm{I}=-200$ mm. (a) Magnitude in dB scale. (b) $S_{11}$ computed considering different orders of reflections.
• Figure 5: Maximum absolute error of $\mathbf\Gamma^c$ for $z_\mathrm{I}=-200$ mm. The color scale (cool to warm) denotes the error magnitude (linear scale). Contours indicate equal-error regions, and yellow crosses mark $(L_{\max},\tilde{\kappa}_m)$ values determined by \ref{['eqn25']} and \ref{['eqn27']} at various frequencies.