Wavelength conversion and parametric amplification of optical pulses via   quasi-phase-matched FWM in long-period Bragg silicon waveguides
  We present a theoretical analysis supported by comprehensive numerical simulations of quasi phase-matched four-wave 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 co-propagate 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. 
Spyros Lavdas, Shuang Zhao, Jeffrey B. Driscoll, Richard R. Grote,   Richard M. Osgood, Nicolae C. Panoiu
physics.optics