Analytical approach to low-frequency scattering and homogenisation of split ring elements

The elementary split ring resonator is a key structure in so-called ldquometamaterialrdquo mediums. In this presentation, low-frequency electromagnetic scattering by a split ring, modelled as a perfectly conducting wire ring furnished with a narrow gap, is presented and analytical results are given for the electric and magnetic dipole moments for different kinds of incidence and polarisation in the quasi-static approximation. Through the process of homogenisation, the expressions discovered for the dipole moments and the related polarisation dyadics are linked with the macroscopic constitutive equations for the medium.