Retrieving the effective parameters of metamaterials from the single interface scattering problem

In order to better understand when man-made structures may be considered as metamaterials with effective properties at optical frequencies, we study the scattering (reflection, transmission) of light at a single interface between a uniform half-space and a bulk metamaterial, i.e., a semi-infinite three-dimensional periodic structure. We accurately compute the scattering coefficients between plane waves and Bloch modes and test the validity of the single-Bloch-mode approximation within the metamaterial. The knowledge of the single-interface scattering coefficients allows us to propose an innovative method for deriving effective optical parameters.