Efficient Scattering Synthesis for Beyond-Diagonal Non-Local RISs Coupled with Passive Load Networks

Abstract

Realizing advanced functionalities with high efficiencies via reconfigurable intelligent surfaces (RISs) and reflectarrays requires configurations with strong electromagnetic non-local responses. The traditional approach to achieving strong non-locality has relied on modeling and synthesizing RISs with diagonal load impedance matrices composed of highly dense subwavelength structuring of arrays. In such designs, non-locality is not directly tunable, thereby limiting design flexibility and operational efficiency. This work proposes a rigorous co-simulation-based design and optimization framework for beyond-diagonal RISs with directly controllable non-locality. The co-simulation approach is based on non-local load and coupling networks, integrating electromagnetic antenna characterization with circuit-level modeling of cascaded load networks. The method benefits from additional degrees of freedom by generalizing the conventional diagonal load impedance matrix to a non-diagonal form through a non-local coupling network model. Wide-angle anomalous reflectors based on finite linear and infinite periodic arrays are designed and numerically validated, demonstrating that the proposed non-local loads embedded in realistic cascaded load networks with associated circuitry achieve significantly higher reflection efficiencies than diagonal load matrices at the given element density. Alternatively, for a fixed efficiency target, the required element density can be significantly reduced for efficient synthesis of beyond-diagonal RIS without compromising the performance of wave manipulations.

Figures (9)

• Figure 1: (a) 3D schematic of the multilayer BD-RIS structure composed of loaded radiating elements, illustrating plane-wave incidence at angle $\theta^{\rm i}$ and anomalous deflection toward the desired angle $\theta^{\rm r}$. The lowermost plot presents the radiation characteristics, indicating improved sidelobe suppression and higher reflected-power efficiency relative to the diagonal RIS configuration. (b) A magnified, exploded view of a two-element multilayer unit cell stack-up highlighting the transmission-line-based interconnection and individually tunable loads embedded within the non-radiating tunable layer.
• Figure 2: Conceptual cascaded multiport network representation of the proposed methodology. The RIS element ports are terminated by a composite load network, decomposed into a static non-radiating structure and individually tunable lumped loads, which emulates more controllable EM degrees of freedom beyond the number of physical RIS elements.
• Figure 3: Illustration of a cascaded multiport network formed by interconnecting an array antenna structure with $M$ ports with a feed network terminated in $N$ isolated loads. The feed network is characterized by an $(M+N)\times(M+N)$$Z$-parameter matrix $\mathbf{Z}^{\rm F}$.
• Figure 4: Illustration of the composite load network (the feed network and isolated loads) as seen from the antenna structure. In this scenario the $M$-element antenna array are connected to a $M$-port network with equivalent full load-matrix $\mathbf{Z}^{\rm O}$. This configuration is similar to the one used to optimize diagonal RISs.
• Figure 5: Schematic representing the interaction of the $N$ isolated loads with the $M$ antenna elements through the feed network. From the loads perspective, the antennas and the feed network are seen as an equivalent $N$-element array with an equivalent impedance matrix $\mathbf{Z}^{\rm I}$. This approach is also useful to determine the vector effective heights $\bar{\mathbf{h}}^\text{I}$ for a BD-RIS.