I. Introduction
The use of stimulated Raman scattering (SRS) for optical amplification in lightwave systems initially required kilometers of optical fiber as gain medium [1], but with the introduction of silicon-on-insulator (SOI) technology became possible on a millimeter scale [2], [3]. The increase of optical intensity due to small mode profile was exploited in SOI waveguides to achieve three to four orders of magnitude increase in Raman gain as compared to gain provided by silica fibers [4]–[6]. The recent studies of SRS [7] in low-dimensional silicon have put forward silicon-nanocrystal composites as a unique material base for the next-generation, ultra-compact optical amplifiers. The enhanced third-order nonlinearities of silicon nanocrystals promise gain in such composites to be much higher than in SOI waveguides [8]–[10], with a strong dependency on composite geometry and silicon concentration [11], [12]. A further three to four orders of remarkable enhancement of Raman gain (as compared to bulk silicon) was recently demonstrated in silicon-nanocrystal slabs with an inhomogeneous distribution of the nanocrystals [13]. In addition to linear losses, which are the only intrinsic losses in optical fibers, intense pump and Stokes fields propagating through silicon-nanocrystal waveguides suffer from detrimental nonlinear effects of two-photon absorption (TPA) and free-farrier absorption (FCA). The aim of this study is to explore theoretically whether or not silicon-nanocrystal waveguides can offer high Raman gain at moderate powers while enjoying submillimeter dimensions.