Toward Analytical Electromagnetic Models for Reconfigurable Intelligent Surfaces

Physically accurate and mathematically tractable models are presented to characterize the scattering and reflection properties of reconfigurable intelligent surfaces (RISs). We describe a single metallic patch and patch array, as well as their interactions with multiple incident electromagnetic (EM) waves using continuous and discrete strategies. Our models take into account the effect of the incident and scattered angles, polarization features, and the topology and geometry of RISs. In particular, we propose a simple system of linear equations to characterize the multiple-input multiple-output (MIMO) behaviors of RISs under appropriate assumptions. This model can be used as a fundamental tool for analyzing and optimizing the performance of RIS-aided systems in the far-field regime. Using the proposed models, we identify the advantages and limitations of three typical configurations. An important discovery is that the popular phase compensation designs cannot provide complicated beam reshaping functionality. A possible solution is the simultaneous configurations of collecting area and phase shifting. Numerical simulations validate the effectiveness of the proposed configuration schemes.