  Second harmonic generation and optical parametric amplification in
negative-index metamaterials (NIMs) are studied. The opposite directions of the
wave vector and the Poynting vector in NIMs results in a "backward"
phase-matching condition, causing significant changes in the Manley-Rowe
relations and spatial distributions of the coupled field intensities. It is
shown that absorption in NIMs can be compensated by backward optical parametric
amplification. The possibility of distributed-feedback parametric oscillation
with no cavity has been demonstrated. The feasibility of the generation of
entangled pairs of left- and right-handed counter-propagating photons is
discussed.
