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.

翻译：本文提出了一种严格且计算高效的方法，用于评估在平面分层介质上方工作的天线的反射系数。该方法在天线的广义散射矩阵（GSM）框架内重新表述了该问题，该矩阵以球面矢量波函数（SVWF）表示。天线与分层结构之间的相互作用通过球面到平面矢量波变换进行建模，该变换包含了介质的精确菲涅尔反射响应，而未引入任何简化近似。此公式极大地降低了代数复杂度，并实现了快速、稳定的数值计算。除了获取天线自由空间GSM所需的一次性预处理外，针对给定分层结构的每次评估均可在毫秒级时间内完成——相较于FEKO等全波求解器，实现了数个数量级的速度提升，同时保持了几乎完全相同的精度。因此，所提出的框架为涉及平面分层环境的实时电磁表征和逆向建模提供了强大的基础。