Electromagnetic interaction in stacked split ring resonator arrays

We theoretically demonstrate the coupling between the unit cells and the interaction between constituents within each cell in metamaterials consisting of stacked split ring resonator arrays which are embedded in a homogeneous dielectric. It is found that the resonant frequency due to plasmon hybridization depends on the symmetry of resonance modes. Both for the first and third order plasmon resonances, we show that the resonances at lower frequency are not sensitive to the variation of lattice density, while the resonances at higher frequency rely on the coupling between cells due to the symmetric distribution of current. The underlying physics is qualitatively interpreted according to the quasistatic electric and magnetic dipole coupling model combined by the calculated field distributions.