Modeling of Quantized RIS Reradiation: A Fourier-Based Method

Reconfigurable Intelligent Surfaces (RIS) are emerging as a key enabling technology for next-generation wireless networks. However, most analytical and ray-based models rely on the assumption of continuous and differentiable phase functions across the RIS surface, while real RISs are inherently composed of discrete unit cells with quantized phase responses. This paper proposes a methodology to extend ray-based simulation models to account for discrete and quantized phase profiles, by exploiting a Fourier-optics interpretation of the re-radiated field. The approach enables the identification of the main propagation modes and their associated powers, allowing quantization effects to be represented within a ray-based framework. A reference example demonstrates the appearance of undesired spectral modes as the quantization resolution decreases. The proposed method is validated against a reference Huygens-based model, showing good agreement and reduced computational complexity.