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.