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

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.