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We apply the moment method to nonlinear pulse propagation in siliconwaveguides in the presence of two-photon absorption, free-carrier dispersionand free-carrier absorption. The evolution equations for pulse energy, temporalposition, duration, frequency shift and chirp are obtained. We derive analyticexpressions for the free-carrier induced blueshift and acceleration and showthat they depend only on the pulse peak power. Importantly, these effects areindependent of the temporal duration. The moment equations are then numericallysolved to provide fast estimates of pulse evolution trends in silicon photonicswaveguides. We find that group-velocity and free-carrier dispersion dominatethe pulse dynamics in photonic crystal waveguides. In contrast, two-photon andfree-carrier absorption dominate the temporal dynamics in silicon nanowires. Toour knowledge, this is the first time the moment method is used to provide aconcise picture of multiphoton and free-carrier effects in silicon photonics.The treatment and conclusions apply to any semiconductor waveguide dominated bytwo-photon absorption.

Nonlinear silicon photonics analyzed with the moment method