Homogenization methods: From thick to thin metamaterials

We present a homogenization method for thin metamaterials based on a matched asymptotic expansion technique. We show that a metamaterial with thickness e and periodicity h can be replaced by an equivalent interface associated to effective jump conditions. The method is validated by comparison with direct numerics and results are compared to the results given by the classical homogenization of layered media. The interface homogenization is shown to be accurate for ke; kh <; 1 while the classical homogenization applies for kh <; 1, e > h.