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We present a theoretical analysis supported by comprehensive numericalsimulations of quasi phase-matched four-wave mixing (FWM) of ultrashort opticalpulses that propagate in weakly width-modulated silicon photonic nanowiregratings. Our study reveals that, by properly designing the optical waveguidesuch that the interacting pulses co-propagate with the same group-velocity, aconversion efficiency enhancement of more than 15 dB, as compared to a uniformwaveguide, can readily be achieved. We also analyze the dependence of theconversion efficiency and FWM gain on the pulse width, time delay, walk-offparameter, and grating modulation depth.

Wavelength conversion and parametric amplification of optical pulses via quasi-phase-matched FWM in long-period Bragg silicon waveguides