Free-carrier driven spatio-temporal dynamics in amplifying silicon waveguides

We theoretically investigate the free-carrier induced spatio-temporal dynamics of continuous waves in silicon waveguides embedded in an amplifying medium. Optical propagation is governed by a cubic Ginzburg-Landau equation coupled with an ordinary differential equation accounting for the free-carrier dynamics. We find that, owing to free-carrier dispersion, countinuous waves are modulationally unstable in both anomalous and normal dispersion regimes and chaotically generate unstable accelerating pulses.