Owing to recent progress in silicon-on-insulator (SOI) technology for signal processing of optical pulses, a detailed intuitive understanding of the different processes governing pulse propagation through SOI waveguides is desired. Even though it is possible to carry out numerical simulations to characterize device performance by varying material and pulse parameters, such an approach does not provide an intuitive understanding. For this reason, we develop an analytic approach in this paper and present approximate solutions that are valid under realistic conditions and characterize with reasonable accuracy the dynamical evolution of a short optical pulse through SOI waveguides. Our analytical expressions take into account linear losses, Kerr nonlinearity, two-photon absorption, and free-carrier effects (both absorptive and dispersive) and thus are likely to be useful for a variety of applications in the area of silicon photonics. Even though free-carrier absorption is included, we limit our analysis to the case where its influence on the temporal pulse shape is minimal. To provide a comprehensive understanding of our results and to validate their accuracy, we consider general properties of our analytical solutions, analyze their applicability in different parametric ranges relevant for applications, and compare them with published results. We envision utilizing these results in optimizing the design of SOI-based devices aimed at integrated optics applications.
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