Reconfigurable Intelligent Surface: an angular spectrum representation approach

The design of Reconfigurable Intelligent Surfaces (RISs) is largely based on treating the RIS as an infinitely large, continuous surface that steers an incident plane wave towards the desired direction. In practical implementations, however, the RIS has finite size and the incident wave is a beam of finite extent, rather than a delocalized plane wave. To understand the implications of the finite extent of both the RIS and the incident beam, here we treat the RIS in the spectral domain, where the RIS acts as a spatial filter to transform the k-content of the incident wave. We extract analytical expressions that provide the necessary insight into the dependencies and trade-offs between crucial parameters such as the beam shape, the RIS response, and the link topology. We demonstrate how our approach provides an intuitive perspective to understand the underlying mechanisms that characterize and determine the performance of RIS-aided links and to design several complex functionalities that are crucial for future wireless communications.