Generalized Scattering Matrix Framework for Modeling Implantable Antennas in Multilayered Spherical Media

Abstract: This paper presents a unified and efficient framework for analyzing antennas embedded in spherically stratified media -- a model broadly applicable to implantable antennas in biomedical systems and radome-enclosed antennas in engineering applications. The proposed method decouples the modeling of the antenna and its surrounding medium by combining the antenna's free-space generalized scattering matrix (GSM) with a set of extended spherical scattering operators (SSOs) that rigorously capture the electromagnetic interactions with multilayered spherical environments. This decoupling enables rapid reevaluation under arbitrary material variations without re-simulating the antenna, offering substantial computational advantages over traditional dyadic Green's function (DGF)-based MoM approaches. The framework supports a wide range of spherical media, including radially inhomogeneous and uniaxially anisotropic layers. Extensive case studies demonstrate excellent agreement with full-wave and DGF-based solutions, confirming the method's accuracy, generality, and scalability. Code implementations are provided to facilitate adoption and future development.