Raman amplification of optical pulses in silicon waveguides: effects of finite gain bandwidth, pulse width, and chirp

We present a theoretical model capable of describing the evolution of pulse parameters when stimulated Raman scattering under continuous-wave pumping is employed for amplifying them inside a silicon waveguide. In our approach, pulse evolution is described analytically by a set of coupled equations derived using a variational formalism. Optical losses resulting from linear absorption or scattering, two-photon absorption, and free-carrier absorption are included by introducing the Rayleigh dissipation function. The influence of gain dispersion originated from a relatively narrow Raman-gain bandwidth is also considered. The role of initial pulse width and chirp is studied extensively because of its practical applications. To ensure the validity of the variational technique, all analytical results are compared with the numerical data obtained with the split-step Fourier algorithm. © 2009 Optical Society of America OCIS codes: 190.3270, 190.5650.