Sign of the refractive index in lossy metamaterials

One of the criteria for determining the existence of negative index of refraction in artificial electromagnetic structures (metamaterials) is the occurrence of opposite directions of the group and phase velocities. In this work, we study specific examples of metamaterials where we show that the above criterion does not hold when losses are taken into account and dominate the interaction of light with the metamaterial. The structure are three-dimensional superlattices of consisting of plasmonic and polaritonic particles and are studied by a rigorous multiple-scattering theory and effective-medium approximation.