Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies

We investigate numerically the limits of the resonant magnetic response with a negative effective permeability μ_eff for single-ring multicut split-ring resonator (SRR) designs up to optical frequencies. We find the breakdown of linear scaling due to the free electron kinetic energy for frequencies above ∼100THz. Above the linear scaling regime, the resonance frequency saturates, while the amplitude of the resonant permeability decreases, ultimately ceasing to reach negative value. The highest resonance frequency at which μ_eff<0 increases with the number of cuts in the SRR. A LC circuit model provides explanation of the numerical data.