Spatial dispersion in negative-index composite metamaterials

The metamaterials exhibiting negative permittivity and permeability that have been under numerical and experimental study recently generally operate at frequencies between the homogeneous (λ≫period) and heterogeneous (λ≈period) regimes, a region characterized by the phenomenon of spatial dispersion. However, since many interesting applications such as the superlens rely on nondispersive homogeneous behavior, one needs a means to diagnose spatial dispersion efficiently as well as to explore in more detail the physics of dispersive media. In this work, we put forward and illustrate the notion of an inhomogeneous effective medium model. We use it to explore the spatial dispersion in negative-index composites, and we show that it is an ideal tool for studying the behavior of composite metamaterials in the intermediate-frequency region where homogeneous effective medium models become spatially dispersive or nonlocal.