Abstract
This paper presents a coupled-mode theoretical framework for deriving the propagation equations of the modal envelope functions in a silicon photonic crystal waveguide (PCW), taking into account the influence of linear coupling, Raman scattering, Kerr effect, two-photon absorption, free-carrier index change, and free-carrier absorption. Compared to previous work in the literature, we include the three-dimensional nature of the carrier density in our calculations, analyze the influence of carrier dynamics in the coupling of the modes, and show how higher-order nonlinear terms can be derived. The framework presented here is useful for analyzing a number of signal-processing schemes based on nonlinear PCWs.
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