Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations.

We demonstrate continuous wave four-wave mixing in silicon photonic crystal waveguides of 396 μm length with a group index of ng=30. The highest observed conversion efficiency is -24 dB for 90 mW coupled input pump power. The key question we address is whether the predicted fourth power dependence of the conversion efficiency on the slowdown factor (η≈S4) can indeed be observed in this system, and how the conversion efficiency depends on device length in the presence of propagation losses. We find that the expected dependencies hold as long as both realistic losses and the variation of mode shape with slowdown factor are taken into account. Having achieved a good agreement between a simple analytical model and the experiment, we also predict structures that can achieve the same conversion efficiency as already observed in nanowires for the same input power, yet for a device length that is 50 times shorter.