Active metamaterials: sign of refraction index and gain-assisted dispersion management

We derive an approach to define the causal direction of the wavevector of modes in optical metamaterials, which in turn, determines signs of refractive index and impedance as a function of {\it 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 dispersion-less index and impedance matching in active nanowire-based negative index materials. Our work opens new practical applications of negative index composites for broadband lensing, imaging, and pulse-routing.