Frequency dependence of the magnetic response of split-ring resonators

The design principle of split-ring resonators (SRRs) for realizing negative magnetic metamaterial is proposed through theoretical investigation of magnetic properties of SRRs from terahertz (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. Our results indicate that the design principle should be changed completely at the transition frequency of 100 THz. Below 100 THz, since the resistance of the SRRs determines the magnetic responses, low-resistance structures are essential. On the other hand, we should design the SRRs'structures maintaining large geometrical inductance above the 100 THz region, because the decrease of the geometrical inductance dominantly reduces the magnetic responses.