Wood's anomaly beyond the Meixner-Schäfke theorem: Analytical and experimental investigation of sinusoidally modulated metasurfaces with normal susceptibilities

Abstract

We present a rigorous analysis of plane-wave-illuminated sinusoidally modulated metasurfaces (MSs) with normal susceptibility components, without limiting the modulation-index values. In contrast to tangentially polarizable scenarios, which are treated within the conventional continued-fraction framework of Meixner and Sch\"afke, the unconventional structure of the generalized sheet transition conditions with regard to normal components manifests exotic stability conditions, which were not addressed by this framework. By introducing small losses into the constituents of such MSs (inevitable in practice), we resolve these stability issues and establish a valid solution for the scattered fields. Such solutions reveal that for a certain range of modulations these surfaces feature a resonant absorptive notch at an angle related to the period, associated with strong coupling to the weakly evanescent first-order Floquet-Bloch harmonic. Based on our observations, we identify this phenomenon as Wood's anomaly for MSs with normal susceptibilities. We verify these observations numerically and experimentally using suitable, systematically designed, printed-circuit-board prototypes. This work highlights the fundamental intricacies involving theoretical analyses of inhomogeneous normally polarizable MSs and constitutes a firm ground for further exploration and utilization of nonuniform configurations with these mostly ignored degrees of freedom.