An analytical approach for gain optimization in multimode fiber Raman amplifiers.

In this paper, an analytical approach is proposed to minimize the mode dependent gain as well as the wavelength dependent gain for the multimode fiber Raman amplifiers (MFRAs). It is shown that the optimal power integrals at the corresponding modes and wavelengths can be obtained by the non-negative least square method (NNLSM). The corresponding input pump powers can be calculated afterwards using the shooting method. It is demonstrated that if the power overlap integrals are not wavelength dependent, the optimization can be further simplified by decomposing the optimization problem into two sub optimization problems, i.e. the optimization of the gain ripple with respect to the modes, and with respect to the wavelengths. The optimization results closely match the ones in recent publications.