Negative beam displacements from negative-index photonic metamaterials

It is well known that refraction of light at interfaces leads to a beam displacement for oblique incidence of light onto a slab of material. In ray optics and for homogeneous isotropic materials, the sign of this beam displacement is strictly identical to the sign of the refractive index. Our numerical calculations reveal negative beam displacements from state-of-the-art double-fishnet-type photonic metamaterials. This holds true for the "main" polarization corresponding to a negative phase velocity for normal incidence as well as for the "secondary" polarization with positive phase velocity. To understand and interpret these results, we also present exact analytical calculations for thin metal films showing that, in wave optics, the sign of the beam displacement (i.e., the sign of refraction) is generally not identical to the sign of the refractive index.