Normal Incidence Scattering of Waveguide-Like Periodic Structures in Scalar 2D-FEM Mode-Matching Extracting the Frequency Dependence

The problem of scattering by periodic structures composed of waveguide-like unit cells can be tackled from a Mode-Matching perspective. Existing approaches for hybridisation through this technique using Floquet modes and the 2D Finite Element Method are based on full-wave representations of the field and do not consider any efficiency improvements in a wide-band frequency sweep, a typical case of application. In this work we present an alternative, holistic fast formulation directly derived from scalar potentials, which is also frequency independent up until the last step of the process of computing the generalised scattering matrix. It is formulated for incident angles normal to the periodicity plane, which are typically those first considered in the design workflow.