Theoretical Analysis of Pulse Dynamics in Silicon Photonic Crystal Wire Waveguides

In this paper, we present a comprehensive theoretical description of the propagation of optical pulses in 1-D waveguides consisting of a line defect in a photonic crystal (PhC) slab waveguide made of silicon. We incorporate in our analysis linear optical effects, such as group-velocity dispersion and optical losses, as well as nonlinear effects induced by the Kerr nonlinearity of the PhC. We also include in our model the free-carrier (FC) dispersion and FC-induced optical losses, and thus study the influence of FCs generated through two-photon absorption on the pulse dynamics. Our analysis reveals that important quantities, such as the pulse group velocity, dispersion coefficients, or the waveguide nonlinear coefficient are strongly affected by the periodic nature of the guiding structure. Finally, we demonstrate that both linear and nonlinear effects are stronger in the case of slow-light modes, with the nonlinear effects being enhanced more as compared to the linear ones.