Maximization of Gain in Slow-Light Silicon Raman Amplifiers

We theoretically study the problem of Raman gain maximization in uniform silicon photonic-crystal waveguides supporting slowoptical modes. For the first time, an exact solution to this problem is obtained within the framework of the undepleted-pumpapproximation. Specifically, we derive analytical expressions for the maximum signal gain, optimal input pump power, andoptimal length of a silicon Raman amplifier and demonstrate that the ultimate gain is achieved when the pump beam propagatesat its maximum speed. If the signal’s group velocity can be reduced by a factor of 10 compared to its value in a bulk silicon,it may result in ultrahigh gains exceeding 100 dB. We also optimize the device parameters of a silicon Raman amplifier in theregime of strong pump depletion and come up with general design guidelines that can be used in practice