Effective parameters of split-ring arrays, numerically determined by frequency-dependent homogenization

In this paper, we develop a method to homogenize split-ring arrays in the frequency domain. The expected resonance and negative permeability are obtained via numerical simulations with the finite elements method. A subtle modelization of the split-ring with a closed ring pemits us to avoid meshing the small split, while maintaining the resonant behaviour of this metamaterial. Therefore, our homogenization technique simulates these metamaterials with a minimal computational cost. Simulations were made for several ring orientations, dimensions and shapes.