Dynamics of short pulses and phase matched second harmonic generation in negative index materials

We study pulsed second harmonic generation in metamaterials under conditions of significant absorption. Tuning the pump in the negative index range, a second harmonic signal is generated in the positive index region, such that the respective indices of refraction have the same magnitudes but opposite signs. This insures that a forward-propagating pump is exactly phase matched to the backward-propagating second harmonic signal. Using peak intensities of ~500 MW/cm(2), assuming chi((2))~80pm/V, we predict conversion efficiencies of 12% and 0.2% for attenuation lengths of 50 and 5microm, respectively.