Anomalous refraction, diffraction, and imaging in metamaterials

In the past several years, optical metamaterials (MMs) have attracted a considerable deal of interest because it may be anticipated that their properties can be shaped to an unprecedented extent relieving optics from some of its natural limitations. An inevitable first step toward this goal is the evaluation of the optical properties of specifically designed MMs. To date, apart from identifying chiral properties of very specific configurations, this is primarily done in retrieving an effective refractive index-mostly-only for normal incidence. On this basis suggestions for a perfect lens, exploiting this negative refractive index have been put forward by taking advantage of geometrical optics arguments. We show that this approach is pointless for realistic MMs. Instead we prove that the dispersion relation of normal modes in these MMs provides all the required information. Most of the relevant optical parameters, such as refraction and diffraction coefficients, can be derived from this relation. Imaging properties follow straightforwardly from that data. This general approach holds for any optical material, in particular, for all MMs in question. As an example, we apply it to the fishnet structure: one of the most prominent and best studied design approaches to date. We show that both refraction and diffraction properties are strongly spatially and temporally dispersive and they can even change sign. In detail, we study the effect of these peculiarities on imaging and refraction of finite beams. In particular, we discuss both the effect of the specific dispersion relation and the losses on the imaging properties. All our physical predictions are backed by rigorous numerical calculations and the agreement is almost perfect. Ultimately the main conclusion to be drawn is that a negative index of refraction is by no means a sufficient criterion to achieve negative refraction and/or perfect imaging.