Floquet-Bloch analysis of refracting Huygens metasurfaces

We investigate the response of passive lossless Huygens metasurfaces (HMS), designed to implement a prescribed refraction, to arbitrary plane-wave excitations. Applying a rigorous Floquet-Bloch (FB) analysis of the cotangent electric and magnetic surface reactance modulations, we discover that the scattered FB modes follow an extraordinary ray-optical model. According to this model, the HMS can be replaced by a virtual region of constant wave impedance; incident power is incoupled into this virtual Fabry-P\'erot etalon, gradually leaking to successively higher-order FB modes. Analytical closed-form expressions are derived for the FB coefficients, indicating that the first FB mode in transmission is always dominant; this clarifies previous experimental findings which implied that the HMS retained its functionality over a broad angular range. Furthermore, we point out the implementation problems inherent in the cotangent function and offer a simple, realizable form of the reactive modulation which does not significantly deteriorate the HMS performance. These results provide fundamental physical insight into the working mechanism of passive lossless Huygens metasurfaces in general, revealing a new degree of freedom which enables control of the transmitted field amplitude: the virtual region wave impedance. Importantly, the implied broad acceptance angle of the HMS may be harnessed for synthesis of low-profile multifunctional devices, designed to respond to several excitations with reduced reflections.