3D system of randomly detuned ring resonators

A homogenization procedure aimed at analyzing a metamaterial designed as a system composed of point magnetic dipoles is presented in this paper. These dipoles represent broad side coupled split ring resonators and/or conducting loops terminated by capacitors. A non-precise fabrication process causes dispersion of the geometrical and material parameters of the resonators, and thus dispersion of their resonance frequencies. The homogenization procedure takes into account random distribution of resonator resonance frequencies with the normal probability distribution. The resonant band of the effective permeability of the metamaterial is significantly widened, the values of both real and imaginary parts of the permeability are reduced. The band of negative permeability real part disappears at high dispersion. The paper also comments on the design of a lens aimed at improving the imaging properties of the MRI system. This lens is composed of cells with cubic symmetry. The proposed homogenization method is verified by measuring the scattering parameters of the metamaterial in a rectangular waveguide, and by proving the isotropic response of the metamaterial of the lens.