Metasurfaces with engineered reflection and transmission: Optimal designs through coupled-mode analysis

Gradient metasurfaces have recently received significant attention for the unique opportunities they offer for advanced wave manipulation. Such metasurfaces are usually discrete implementations of surface impedance profiles, which are analytically derived to yield the desired operation. Several recent numerical and experimental studies have shown that gradient metasurfaces can work very well over large bandwidths, extending to frequencies where the definition of surface impedance is not straightforward. Here, we develop an alternative description of such metasurfaces based on coupled-mode theory and provide an explanation for this intriguing effect. Quite surprisingly, our theory shows that broadband anomalous reflection and transmission, does not necessarily require the use of spatial gradients, but they can be achieved through suitably designed periodic arrays of resonant particles. In addition to their theoretical importance, our results can be important for the design of efficient metasurfaces with specified frequency response.