Compensating losses in negative-index metamaterials by optical parametric amplification.

Optical parametric amplification controlled by the auxiliary electromagnetic field enables transparency, amplification, and oscillation with no cavity in strongly absorbing negative-index metamaterials. The opposite directions of the wave vector and the Poynting vector in such materials result in extraordinary optical properties, including "backward" phase matching and the generation of entangled pairs of left- and right-handed counterpropagating photons.