AbstractNegative permeability of single-ring split ring resonator (s-SRR) is theoretically investigated in the visible light frequency region [1, 2]. To estimate magnetic responses of conductive elements precisely, we determined internal impedance by considering the delay of the current inside the metal structure. The increase of the surface resistivity, which is the real part of the internal impedance, results in the decrease of the resonator's Q-value. This means the degradation of the tunable range of the permeability. The increase of the internal reactance results in the reduction of the resonant frequency. In our calculation, the surface resistivity saturates at the inherent frequency of each metal as the frequency increases. On the silver case, the saturation value is 0.4 Ω and this value is remarkably smaller than that of gold and copper. On the other hand, the internal reactance is increasing as the frequency increases independently of metal. We concluded that the internal reactance is dominant factor to realize the negative magnetic permeability in the optical frequency region. We also show the frequency dependence of the magnetic permeability of s-SRRs. In the case of s-SRRs made of copper, the minimum value of the magnetic permeability becomes positive value at 550 THz even in the high filling factor condition (11%). In the case of s-SRRs made of gold, only on the filling factor was 11%, the minimum value of the magnetic permeability takes negative value in the entire visible range. On the other hand, the silver SRR exhibits negative magnetic permeability in the visible range even under the low filling factor condition of 3%. Moreover, we concluded that reducing the geometrical capacitance and using silver for SRR are necessary to realize the negative magnetic permeability in the visible light range.
Flat-top optical resonance in a single-ring resonator based on manipulation of fast- and slow-light effects