A Novel Comprehensive Multiport Network Model for Stacked Intelligent Metasurfaces (SIM) Characterization and Optimization

Reconfigurable Intelligent Surfaces (RIS) represent transformative technologies for next-generation wireless communications, offering advanced control over electromagnetic wave propagation. While RIS have been extensively studied, Stacked Intelligent Metasurfaces (SIM), which extend the RIS concept to multi-layered systems, present significant modeling and optimization challenges. This work addresses these challenges by introducing an optimization framework for SIM that, unlike previous approaches, is based on a comprehensive model without relying on specific assumptions, allowing for broader applicability of the results. We first present a model based on multi-port network theory for characterizing a general electromagnetic collaborative object (ECO) and derive a framework for ECO optimization. We then introduce the SIM as an ECO with a specific architecture, offering insights into SIM optimization for various configurations and discussing the complexities associated with each case. Finally, we demonstrate that the comprehensive model considered in this work simplifies to the model traditionally used in the literature when the assumption of unilateral propagation between the levels of the SIM is made, and mutual coupling between the SIM elements is neglected. To assess the applicability of these assumptions, a case study focused on the realization of a 2D DFT was undertaken. In this context, we highlight that these assumptions introduce a significant mismatch between the SIM model and its behavior as described by the complete model, making these approximations inadequate for optimizing the SIM. Conversely, we show that employing the complete model proposed in this paper can yield excellent performance.