Maximization of net optical gain in silicon-waveguide Raman amplifiers.

We present a novel method for maximizing signal gain in continuously pumped silicon-waveguide Raman amplifiers made with silicon-on-insulator technology. Our method allows for pump-power depletion during Raman amplification and makes use of a variational technique. Its use leads to a system of four coupled nonlinear differential equations, whose numerical solution provides the optimal axial profile of the effective mode area along the waveguide length that maximizes the output signal power for a given amplifier length and a preset input (or output) cross-section area. In practice, the optimum profile can be realized by varying the cross-section area of a silicon waveguide along its length by tapering its width appropriately.