The strength of Raman interaction between optical fields propagating through a silicon-nanocrystal waveguide is known to significantly differ from that in bulk silicon and silicon-on-insulator waveguides. Here we present the first theoretical study of continuous-wave Raman amplification in silicon-nanocrystal waveguides with improved mode confinement. By calculating numerically the mode-overlap factors and effective refractive indices of the pump and Stokes fields, we analyze how the maximal Stokes intensity and the optimal waveguide length depend on the cross-section parameters of the composite, density of silicon nanocrystals, and input conditions. In particular, we demonstrate that the maximal Stokes intensity peaks at certain waveguide height and volume fraction of silicon nanocrystals for fixed input intensities, and at certain waveguide width for fixed input powers. These features enable simple performance optimization of Raman amplifiers and lasers based on silicon nanocrystals.
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