Eigenmodes of metallic ring systems: A rigorous approach

To study the eigenmodes of a metallic system in ring geometry, we develop an approach which rigorously considers all inductive/capacitive effects within the quasistatic approximation. Application to a single-ring split ring resonator (SRR) reveals that the odd-numbered modes exhibit both magnetic and electric responses while the even ones only exhibit electric responses, and the SRR shows a bianisotropy for the odd-numbered resonances. Symmetry restriction allows a plane wave to excite only certain resonance modes of a SRR. Simulations on realistic structures verify all theoretical predictions. Calculations for a double-ring case suggest optic (acoustic) modes of asymmetric bianisotropy that are much more electric (magnetic) in character.