, Volume 109, Issue 4, pp 1043-1051

Dynamic homogenization of split-ring metamaterials by Floquet–Bloch decomposition

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Abstract

We apply a novel dynamic homogenization technique to determine the frequency-dependent effective permeability of split-rings arrays. The Floquet–Bloch decomposition of Maxwell equations in this metamaterial is applied when the wavelength is much bigger than the material’s period. We replace the inclusion with a closed ring, and numerically simulate the model by nodal finite elements and a reasonable number of tetrahedral mesh elements. Our results show a good agreement with an analytical permeability law for 2D structures. This work also proposes an accurate method to model the magnetic field in the unit cell.