Effective, Frequency-Dependent, Permeability of "Split-Ring" Metamaterials via Homogenization

Homogenization, which reduces the cost of numerical simulations in materials with repetitive structure, is a promising approach to the design of metamaterials. We justify the procedure by a convergence result and apply it to the case of an array of split rings, where a negative effective permeability can be expected, on physical grounds, near some resonant frequency. A simplified model confirms this.