Theory of Light Amplification in Active Fishnet Metamaterials

We establish a theory that traces light amplification in an active double-fishnet metamaterial back to its microscopic origins. Based on ab initio calculations of the light and plasmon fields we extract energy rates and conversion efficiencies associated with gain and loss channels directly from Poynting's theorem. We find that for the negative refractive index mode both radiative loss and gain outweigh resistive loss by more than a factor of 2, opening a broad window of steady-state amplification (free of instabilities) accessible even when a gain reduction close to the metal is taken into account.