Closed-Form Solution for the Scattering Coefficients in the Canonical Problem of Anomalous Reflection

Metasurfaces (MTSs) enable efficient manipulation of electromagnetic radiation. Control over reflection direction is one of the most popular applications, especially in the context od smart radio environment. In the past years, significant progress has been made in designing anomalous reflectors, leading to the development of various synthesis approaches, ranging from analytical models to optimization-based methods. In this paper, we derive a closed-form solution for the complex scattering coefficients of all the propagating and evanescent Floquet modes (FMs) in the canonical problem of anomalous reflection based on a homogenized impenetrable impedance MTS with a tangent-like profile. Our findings reveal that the phase of the scattered FMs is influenced by the spatial discretization of the MTS. This insight is crucial for the practical applications of anomalous reflectors, as real-world MTSs are implemented using physical elements discretizing the continoud homogenized impedance profile. We believe that our study is particularly interesting for researchers working on metasurfaces, communication technologies, and reconfigurable intelligent surfaces.