Optimization of Raman Amplification in Silicon Waveguides With Finite Facet Reflectivities

Increasing the amplifying efficiency in silicon-on-insulator waveguides plays a crucial role in future adaptation of this technology for integrated optics applications. Such improvements not only lead to a reduced overall footprint size but also the overall reduction in the operating energy consumption of the device. In this paper, we address the design optimization of silicon optical amplifiers working in the continuous wave domain. We seek to optimize the efficiency of a silicon optical amplifier by varying the cross-section area along the waveguide length that coerces judicious minimization of the pernicious influence of free-carrier absorption and two-photon absorption on Raman amplification. Using a recently proposed semi-analytical technique, we recasted the above problem as a boundary-value problem that contains eight coupled nonlinear differential equations for four waves´ powers and four auxiliary functions. The numerical solution of these equations allows one to find the axial profile of the effective mode area (EMA), providing the largest output signal power for given waveguide length, input pump power and a preset, input-facet EMA. We have illustrated utility of our method by applying it to several practically realizable amplification scenarios. In particular, optimizing the EMA profiles with different input-facet EMAs, we calculated the optimum signal gain of a silicon optical amplifier with a given (i.e., preset) amplifier length.