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

Abstract
We investigate numerically the limits of the resonant magnetic response with a negative effective permeability μeff 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 μeff<0 increases with the number of cuts in the SRR. A LC circuit model provides explanation of the numerical data.