The effect of phase mismatch on second harmonic generation in negative   index materials
  Second harmonic generation in negative index metamaterials is considered. Theoretical analysis of the corresponding model demonstrated significant difference of this phenomenon in conventional and negative index materials. In contrast to conceptional materials there is nonzero critical phase mismatch. The behavior of interacting weaves is dramatically different when phase mismatch is smaller or greater than critical value. 
Zhaxylyk Kudyshev, Ildar Gabitov, Andrei Maimistov
physics.optics cond-mat.mtrl-sci nlin.PS