Computational studies are used to show that the crystalline structure of Si causes the waveguide Kerr effective nonlinearity, γ, to vary by 10% for in-plane variation of the orientation of a silicon nanowire waveguide (SiNWG) fabricated on a standard silicon-on-insulator wafer. Our analysis shows that this angular dependence of γ can be employed to form a nonlinear Kerr grating in dimensionally uniform SiNWGs based on either ring resonators or cascaded waveguide bends. The magnitude of the nonlinear index variation in these gratings is found to be sufficient for phase matching in four-wave mixing and other optical parametric processes.
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