Active metamaterials: Sign of refractive index and gain-assisted dispersion management

We derive an approach to determine the causal direction of wavevectors of modes in optical metamaterials, which, in turn, determines signs of refractive index and impedance as a function of real and imaginary parts of dielectric permittivity and magnetic permeability. We use the developed technique to demonstrate that the interplay between resonant response of constituents of metamaterials can be used to achieve efficient dispersion management. Finally, we demonstrate broadband dispersionless index and impedance matching in active nanowire-based negative index materials. Our work has a potential to open new practical applications of negative index composites for broadband lensing, imaging, and pulse routing.