Raman amplification of optical pulses in silicon nanowaveguides: Impact of spectral broadening of pump pulses

We consider the Raman amplification problem for silicon waveguides in the regime in which both the pump and signal pulses are relatively short but wide enough that their duration exceeds the phonon lifetime (about 3 ps in silicon). We use the coupled pump-signal equations for numerical simulations that include all competing nonlinear effects such as selfand cross-phase modulations, two-photon and free-carrier absorptions, and changes in the refractive index induced by the free carriers. However, numerical simulations do not provide much physical insight. For this reason, we also develop an approximate analytic approach for solving the Raman amplification problem. We introduce the concept of an effective Raman gain and show analytically how it depends on the pump bandwidth. As the pump spectrum broadens inside the silicon waveguide, the effective Raman gain is reduced considerably. We obtain an analytical form of the nonlinear phase accumulated during propagation inside a silicon waveguide and use it to calculate the total spectral broadening experienced by a pump pulse. Using this result, we can predict changes in the effective Raman gain as a function of pump pulse energy. A comparison of our predictions with the recent experimental data shows that our model is reasonable and captures the essential physics. [DOI: 10.2971/jeos.2011.11030]