Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations

The parameter retrieval is a procedure in which effective material properties are assigned to a given metamaterial. A widely used technique bases on the inversion of reflection and transmission from a metamaterial slab. Thus far, local constitutive relations have been frequently considered in this retrieval procedure to describe the metamaterial at the effective level. This, however, is insufficient. The retrieved local material properties frequently fail to predict reliably the optical response from the slab in situations that deviate from those that have been considered in the retrieval, e.g., when illuminating the slab at a different incidence angle. To significantly improve the situation, we describe here a parameter retrieval, also based on the inversion of reflection and transmission from a slab, that describes the metamaterial at the effective level with nonlocal constitutive relations. We retrieve the effective material parameters at the example of a basic metamaterial, namely, dielectric spheres on a cubic lattice but also on a more advanced, anisotropic metamaterial of current interest, i.e., the fishnet metamaterial. We demonstrate that the nonlocal constitutive relation can describe the optical response much better than local constitutive relation would do. Our approach is widely applicable to a large class of metamaterials.