Frequency dependence of the magnetic response of split-ring resonators

The design principle of split-ring resonators (SRRs) for realizing the negative magnetic metamaterial is proposed through the theoretical investigation of magnetic properties of the SRRs from THz to the visible light region. To describe the frequency dispersion of metal throughout the frequency range, we consider the exact expression of the internal impedance formula. This formula can describe not only the conduction characteristics but also the dielectric behavior of metal in the optical frequency region. Based on this investigation, we successfully determine the magnetic responses of the SRRs, which are characterized by the metal's dispersive properties, from THz to the visible light region. Our results indicate that the design principle should be changed considerably at the transition frequency of 100 THz. Below 100THz, since the resistance of the SRRs determines the magnetic responses, the low resistance structures are essential. On the other hand, above 100THz region, because the decrease of the geometrical inductance dominantly reduces the magnetic responses, we should design the SRRs' structures maintaining large geometrical inductance. The theoretical limitation of the SRR's operating frequency with a negative permeability is also discussed from the viewpoint of the saturation of the magnetic response.