%X We present a theoretical analysis supported by comprehensive numerical simulations of quasi-phase-matched fourwave mixing (FWM) of ultrashort optical pulses that propagate in weakly width-modulated silicon photonic nanowire gratings. Our study reveals that, by properly designing the optical waveguide such that the interacting pulses copropagate with the same group velocity, a conversion efficiency enhancement of more than 15 dB, as compared to a uniform waveguide, can readily be achieved. We also analyze the dependence of the conversion efficiency and FWM gain on the pulse width, time delay, walk-off parameter, and grating modulation depth. © 2014 Optical Society of America. %O This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. %K Wavelength conversion devices; Nonlinear optical devices; Waveguides, channeled; Nonlinear optics, four-wave mixing; (190.4975) Parametric processes; Nonlinear optics, integrated optics. %J Optics Letters %L discovery1443006 %P 4017 - 4020 %D 2014 %T Wavelength conversion and parametric amplification of optical pulses via quasi-phase-matched four-wave mixing in long-period Bragg silicon waveguides %A S Lavdas %A S Zhao %A NC Panoiu %A JB Driscoll %A RR Grote %A RM Osgood %V 39 %N 13