Theory of slow light enhanced four-wave mixing in photonic crystal waveguides

The equations for Four-Wave-Mixing in a photonic crystal waveguide are derived accurately in the hypotesis of negligible nonlinear absorption. The dispersive nature of slow-light enhancement, the impact of Bloch mode reshaping in the nonlinear overlap integrals and the tensor nature of the third order polarization are therefore taken into account. Numerical calculations reveal substantial differences from simpler models, which increase with decreasing group velocity. We predict that the gain for a 1.3 mm long, un-optimized GaInP waveguide will exceed 10 dB if the pump power exceeds 1 W.