Negative index of refraction in metallic metamaterial comprising split-ring resonators

We numerically investigate the negative index of refraction in a metamaterial composed of metallic split-ring resonators, which exhibits simultaneously negative permittivity and permeability without resorting to additional metallic wires. It is confirmed that, in the left-handed band, negative permittivity is generated in analogy to the cut-wire metamaterial and negative permeability comes from the antisymmetric resonant mode, which occurs at a frequency band about 3 times higher than the fundamental magnetic resonance proposed by Pendryet al. [IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)].