2D Waveguide-Fed Metasurfaces: Physically Consistent Modeling, Validation, and Optimization

Antenna array architectures based on programmable metasurfaces are emerging as a promising solution for scalable implementations of the eXtremely Large Multiple-Input Multiple-Output (XL-MIMO) systems paradigm, envisioned for 6-th Generation (6G), and beyond, wireless networks. However, their accurate modeling, quantifying the role of key structural features, such as strong mutual coupling and guided-wave excitation, remains challenging, amplifying the need for physically consistent representations of the constituent metamaterial elements. In this paper, capitalizing on the coupled dipole formulation, we develop a comprehensive electromagnetics-compliant framework for 2-Dimensional (2D) waveguide-fed metasurface antennas. The proposed model extends relevant existing modeling approaches by incorporating both electric and magnetic dipoles' responses, accounting for multiple excitation feeds, and enabling accurate characterization in both the near- and far-field regimes. Radiation-reaction corrections based on passivity constraints are derived and shown to ensure the passivity of the overall dipole system. In addition, we present a novel input impedance model for the considered architecture enabling explicit computation of the accepted power, and facilitating efficient beamforming design under realistic power constraints. All modeling components developed in this paper are validated against full-wave electromagnetic simulations. Furthermore, the analytical structure of the proposed model enables the formulation of a differentiable beamforming design optimization problem over both the considered metasurface geometry and its feed excitations. The presented numerical results demonstrate the effectiveness of the proposed modeling framework in achieving both directive beamforming and sector-wide coverage.