Metaprism Design for Wireless Communications: Angle-Frequency Analysis, Physical Realizability Constraints, and Performance Optimization

Recent advancements in smart radio environment technologies aim to enhance wireless network performance through the use of low-cost electromagnetic (EM) devices. Among these, reconfigurable intelligent surfaces (RIS) have garnered attention for their ability to modify incident waves via programmable scattering elements. An RIS is a nearly passive device, in which the tradeoff between performance, power consumption, and optimization overhead depend on how often the RIS needs to be reconfigured. This paper focuses on the metaprism (MTP), a static frequency-selective metasurface which relaxes the reconfiguration requirements of RISs and allows for the creation of different beams at various frequencies. In particular, we address the design of an ideal MTP based on its frequency-dependent reflection coefficients, defining the general properties necessary to achieve the desired beam steering function in the angle-frequency domain. We also discuss the limitations of previous studies that employed oversimplified models, which may compromise performance. Key contributions include a detailed exploration of the equivalence of the MTP to an ideal S-parameter multiport model and an analysis of its implementation using Foster's circuits. Additionally, we introduce a realistic multiport network model that incorporates aspects overlooked by ideal scattering models, along with an ad hoc optimization strategy for this model. The performance of the proposed optimization approach and circuits implementation are validated through simulations using a commercial full-wave EM simulator, confirming the effectiveness of the proposed method.