Continuous-wave Raman amplification in silicon waveguides: beyond the undepleted pump approximation.

We present approximate analytical expressions describing nonlinear interaction of two optical waves copropagating inside a silicon waveguide in the presence of linear losses, stimulated Raman scattering, and free-carrier absorption. Our approach avoids the undepleted-pump approximation, which we show to be inadequate to describe accurately the Raman-gain process. Based on our calculations, we propose a new generalized definition for the effective length and show that it provides better insight into the impact of nonlinear absorption on Raman amplification in silicon waveguides.