Negative permeability of split ring resonator in the optical frequency region

Negative magnetic permeability of split ring resonator (SRR) is theoretically investigated in the optical frequency region. In our calculations, we considered the delay of the current inside the metal SRR in order to estimate the permeability of the SRR precisely; we used the complete formula of the internal impedance, which is valid to the visible range, to estimate the dispersion of both surface resistivity and internal reactance accurately. Our results indicates that in the optical frequency region, the effect of the internal reactance on the magnetic responses of the SRR is more dominant than that of the surface resistivity, because the surface resistivity is already saturated at the frequency lower than 100 THz. At the same time, the internal reactance does not saturate and moves away from zero drastically as frequency increases. From the results, we concluded that the silver SRR array with small capacitance exhibits negative permeability form THz to the visible light region. We also demonstrated that the array of the silver SRRs employing a single ring with divisions exhibits the negative μ at 428 THz (700 nm wavelength).