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

TL;DR

This work addresses the challenge of achieving angle-dependent beam shaping over frequency with a passive, low-reconfiguration metasurface, by introducing Metaprism (MTP) as a static frequency-selective metasurface. It develops an ideal MTP with a monotonic angle–frequency mapping $\mathcal{M}(f)$, analyzes its bandwidth, and derives a frequency-aware end-to-end channel model within a comprehensive S-parameter multiport framework. The authors then propose a realistic Foster-circuit-based circuit implementation and extend the model to a realistic multiport network, formulating an AO-based optimization to synthesize reflection coefficients under a linear-phase constraint to ensure practical realizability. They validate the approach with full-wave EM simulations, show performance gains over oversimplified models, and quantify the impact of model mismatch on capacity, highlighting the practical viability and advantages of MTPs in low-reconfiguration wireless systems. Overall, the paper provides a rigorous design, optimization, and validation path for passive, frequency-selective beams that can significantly reduce control overhead while delivering reliable angle–frequency beam steering.

Abstract

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.

Figures (14)

• Figure 1: 3D coordinate system for an MTP placed in the $(\nu, \zeta)$ with normal along $\eta$.
• Figure 2: MTP in the elevational direction placed along the (y-z) axis, illuminating the angular range between $\theta_m$ and $\theta_M$
• Figure 3: Channel gain for the ideal MTP implementation as in \ref{['eq:Meta_Davide']}, for $\Delta_y = \lambda_0/2$.
• Figure 4: Channel gain for $f \in \mathcal{F}$ for the ideal MTP implementation as in \ref{['eq:Meta_Davide']}, for $\Delta_y = \lambda_0/2$.
• Figure 5: Channel gain for the ideal $\Delta_y = \lambda_0/2$MTP implementation as in \ref{['eq:Meta_Davide']}, for $f \in \mathcal{F}$ and $\theta \in \mathcal{T}$.

Theorems & Definitions (3)

• Definition 1
• Lemma 1
• proof