Strong diamagnetic response of metamaterials

We demonstrate that there is a strong diamagnetic response of metamaterials, consisting of open or closed split ring resonators (SRRs). Detailed numerical work shows that for densely packed SRRs the magnetic permeability, $\mu (\omega )$, does not approach unity, as expected for frequencies lower and higher than the resonance frequency, ${\omega }_0$. Below ${\omega }_0$, $\mu (\omega )$ gives values ranging from 0.9 to 0.6 depending of the width of the metallic ring, while above ${\omega }_0$, $\mu (\omega )$ is close to 0.5. Closed rings have $\mu \approx 0.5$ over a wide frequency range independently of the width of the ring. A simple model that uses the inner and outer current loop of the SRRs can easily explain theoretically this strong diamagnetic response, which can be used in magnetic levitation.