Electric and magnetic resonances in broadside coupled split ring resonators: An extended mode-expansion theory

We extend the previously established mode-expansion theory to study the eigenmodes of metallic ring systems made by thin wires possessing film-like rectangular cross sections. Applications of the theory to a single split ring resonator (SRR) yield essentially the same results with finite-difference-time-domain (FDTD) simulations on realistic structures, which justify some basic assumptions adopted in the theory. We then apply the theory to study the resonance properties of a double-stack SRR, and show that such a planar resonator exhibits magnetic responses along all three dimensions under different conditions. FDTD simulations on realistic structures are performed to successfully verify the predictions based on the extended mode-expansion theory, and reveal that mutual-SRR interactions in a periodic SRR array may lead to a significant change of the eigenmode properties, including a reversal of the frequency sequence for two resonance modes.