A Design Framework for Reconfigurable Intelligent Metasurfaces Enabling Full-Space Beamforming Using Auxiliary Surface Waves

Electromagnetic metasurfaces (MTSs) and Reconfigurable Intelligent Surfaces (RISs) have revolutionized wave manipulation by enabling precise control over the reflected and transmitted waves. While traditional MTSs rely on static designs, RISs incorporate tunable elements, allowing dynamic adaptation to external illuminations for real-time wavefront optimization. This paper provides a complete design framework for RISs based on the Method of Moments (MoM) to establish a multiport network and an efficient optimization scheme. By incorporating auxiliary surface waves and accounting for mutual coupling, precise control over amplitude and phase can be achieved. As a result, our designs enable wide-angle beamsteering of up to 70° in a single plane, as well as out-of-plane anomalous reflection. To further demonstrate the capabilities of the design framework for complex wave manipulation, a Chebyshev pattern with a -20 dB sidelobe level, as well as sector patterns in a single plane and across a hemisphere, are achieved using the designed RIS. The effectiveness of the proposed method is validated through full-wave simulations, supplemented by an additional measurement of a static MTS exhibiting out-of-plane anomalous reflection.