A Mode-Matching Approach to the Design of RIS-Aided Communications

Reconfigurable intelligent surface (RIS) is an emerging technology for application to wireless communications. In this paper, we consider the problem of anomalous reflection and model the RIS as a periodic surface impedance boundary. We utilize the mode matching method and Floquets expansion representation to compute the field reflected from a spatially periodic RIS, and evaluate the performance versus implementation complexity tradeoffs of RIS aided communications based on the global design criterion. This allows us to maximize the power reflected towards the intended direction of propagation, while minimizing the power reradiated towards undesired directions of propagation. In addition, we discuss the advantages of the proposed electromagnetically consistent approach to the design of RIS aided wireless systems.

💡 Research Summary

This paper addresses the design of reconfigurable intelligent surfaces (RIS) for anomalous reflection by modeling the RIS as a periodic surface‑impedance boundary and applying a mode‑matching technique combined with Floquet‑harmonic expansion. The authors first formulate the RIS as an electrically thin sheet located in the xy‑plane with a spatially varying surface impedance (Z_s(y)). Assuming a transverse‑electric (TE) polarized incident plane wave, they express the reflected field as an infinite sum of Floquet modes, each characterized by a tangential wavenumber (k_{y,n}=k_y+2\pi n/D) and a longitudinal component (k_{z,n}) that may be propagating or evanescent.

The boundary condition (E_t = -Z_s H_t) relates the total tangential electric and magnetic fields at the surface, leading to an implicit relationship between the unknown Floquet reflection coefficients (B_n) and the prescribed impedance profile. To solve for (B_n), the authors employ the mode‑matching method: they expand the periodic impedance into a Fourier series, construct a Toeplitz matrix (Z_s) from its coefficients, and combine it with a diagonal matrix of TE modal admittances (Y_a). The reflection matrix is then obtained as
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