Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence

Compared to metallic composite metamaterials of double split-ring resonators with wires, double-ring resonators without additional wires are simple to engineer. In this paper, we have numerically studied the transmittance of double split- and closed-ring resonators at normal-to-plane incidence and identified their fundamental resonance modes. It is found that the antisymmetric and symmetric resonance modes originate from the out-of-phase and in-phase oscillations of surface charges in the neighboring legs of the double-ring resonators, respectively. The coupling of the antiparallel induced currents in the neighboring legs gives rise to magnetic resonance and consequently negative permeability of the antisymmetric mode. The negative refraction transmission of the double-ring resonators at normal-to-plane incidence is verified by dispersion curve and wedge-shaped model simulations. Our study provides a route to negative refraction metamaterial design by using the antisymmetric resonance mode of the simple double-ring structure at normal-to-plane incidence which is of particular importance for the terahertz and infrared domain.