Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides

We present a detailed analysis of the influence of the group velocity (GV) on the dynamics of optical pulses upon their propagation in one-dimensional photonic crystal waveguides (PhCW). The theoretical model used in our analysis incorporates the linear optical properties of the PhCW (GV dispersion and optical losses), free-carrier (FC) effects (FC dispersion and FC-induced optical losses) and nonlinear optical effects (Kerr nonlinearity and two-photon absorption). Our analysis shows that, unlike the case of uniform waveguides, the GV of the pulse, dispersion coefficients, and the waveguide nonlinear coefficient are periodic functions with respect to the propagation distance. We also demonstrate that linear and nonlinear effects depend on the group velocity, vg, as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$v_{g}^{-1}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$v_{g}^{-2}$\end{document}, respectively.