Fabry-P\'erot Huygens' Metasurfaces: On Homogenization of Electrically Thick Composites

Realization of the anomalous refraction effects predicted by Huygens' metasurfaces (HMS) have required tedious and time-consuming trial-and-error numerical full-wave computations. It is shown herein that these requirements can be alleviated for transverse magnetic (TM) propagation by a periodic dielectric-based HMS consisting of an electrically thick array of cascaded Fabry-P\'erot etalons. This "Fabry-P\'erot HMS" (FP-HMS) is easily designed to mimic the local scattering coefficients of a standard zero-thickness HMS (ZT-HMS) which, according to homogenization theory, should result in the desired anomalous refraction. To probe the characteristics of this practical FP-HMS, a method based on Floquet-Bloch (FB) analysis is derived for predicting the fields scattered from it for arbitrary angles of incidence. This method produces simple closed-form solutions for the FB wave amplitudes and the resulting fields are shown to agree well with full-wave simulations. These predictions and full-wave simulations verify the applicability of homogenization and scattering properties of zero-thickness HMS's to thick structures. They also verify the proposed semi-analytical microscopic design procedure for such structures, offering an effective alternative path to implementation of theoretically envisioned intricate field manipulating devices.