Perfectly Reflecting Metasurface Reflectarrays: Mutual Coupling Modeling Between Unique Elements Through Homogenization

This article presents a new technique for the accurate design of metasurface reflectarrays. The design technique accounts for mutual coupling between distinct reflectarray elements. Contrary to the conventional approach, no local periodicity assumptions are made in the design of the reflectarray elements. The reflectarray considered consists of a subwavelength-patterned metallic cladding (metasurface) over a ground plane. The cladding is homogenized and modeled as an inhomogeneous impedance sheet. The inhomogeneous impedance sheet is designed through the solution of an integral equation. The integral equation is solved using the method of moments. In the design, both the scattered field amplitude and phase are specified. The scattered field amplitude is chosen to conserve local power density at the reflectarray surface. This condition results in complex sheet impedances. An optimization technique is subsequently used to obtain a purely reactive sheet which gives the same performance as the complex sheet. The process used to extract the reactance of printed geometries is detailed. An example of a $20 \lambda $ wide array is presented. All the results are validated through COMSOL Multiphysics simulations. The presented design approach is compared to the conventional approach and is shown to more accurately predict the far-field patterns of a reflectarray.