Characterization of Edge-Coupled Broadside- Coupled and Complementary Split-Ring Resonator Periodic Media Based on Numerical Solutions of Eigenvalue Problems

We study the behavior of 3-D periodic composite media consisting of several types of split-ring resonators. By initially introducing the H-D periodic eigenmode finite element method (FEM) formulation, the dual counterpart of our formerly proposed E-B formulation, we are able to extract accurate dispersion diagrams and field distributions of electromagnetically complex structures and compare the returned characteristics of the supported modes. Using Babinet’s principle, we design the corresponding complementary resonators and evaluate their dual characteristics. Particular attention is given to the explanation of the behavior of these composite media under wave incidence perpendicular to the scatterers’ plane. Additionally, we perform a cross-check with excitation problem results, to interpret the response predicted by analytical models existing in literature and confirmed by the eigen-analysis of the structures. Useful conclusions are drawn concerning the potential utilization of the studied resonators in more complex structures in the field of microwave applications.