Determination of effective parameters in negative-index optical metamaterials

We present an enhanced algorithm based on the Kramers-Kronig (K-K) relations, which extracts the effective parameters such as the electric permittivity ε and magnetic permeability μ of a composite electromagnetic structure from calculated or measured transmission and reflection data. For the general structure, the retrieved parameters are broadly similar whether obtained by the traditional retrieval algorithm or the improved one. For the multilayer negative-index optical metamaterials, the improved algorithm is competent instead of the traditional one due to the calculation involves a branching problem, and the K-K relations can be applied to remove the problem.