Single unit cell approach to effective index retrieval of bulk metamaterials

A method is introduced which retrieves the effective index for bulk metamaterials. It is shown that the index can be obtained by probing the phase change of scattered fields in the median cell(s) of a bulk metamaterial. By using this approach, the index converges faster than the conventional inverse scattering method to the exact bulk values for a large number of unit cells, and the complexity associated with the determination of the correct cosine branch reduces. The convergence of the index versus number of unit cells is compared for the two methods. A modal approach is employed to examine the accuracy and convergence of the results with respect to the asymptotic index.