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The equations for Four-Wave-Mixing in a Photonic Crystal waveguide arederived accurately. The dispersive nature of slow-light enhancement, the impactof Bloch mode reshaping in the nonlinear overlap integrals and the tensornature of the third order polarization are therefore taken into account.Numerical calculations reveal substantial differences with simpler models,which increase with decreasing group velocity. We predict that the gain for a1.3 mm long, unoptimized GaInP waveguide will exceed 10 dB if the pump powerexceeds 1 W.

Theory of Slow Light Enhanced Four-Wave Mixing in Photonic Crystal Waveguides