Design of the pump power spectrum for the distributed fiber Raman amplifiers using incoherent pumping

The method to design the incoherent pump power spectrum described with a set of piece-wise continuous functions (PWCFs) for the distributed fiber Raman amplifier (DFRA) is presented. The pump power spectrum is divided into a number of sub-bands, in which each sub-band is described with a polynomial. The power spectral density function (PSDF) is the absolute value of the set of PWCFs, in which the polynomial coefficients are optimized with the least-square minimization method for reducing the signal gain ripple. Two 100-km TW-Reach DFRAs using backward pumping and bidirectional pumping respectively are taken as examples. The numerical results show that the gain ripple of less than 0.02 dB over 70-nm bandwidth can be achieved. The spectral characteristics of the optimized PSDF for the ultra-low gain ripple are investigated. The optimized PSDF can be synthesized with multiple incoherent pumps. The synthesis examples using the multiple Gaussian incoherent pumps are shown, in which the gain ripples are increased to 0.3 dB due to the discrepancy between the optimized PSDF and the synthesized PSDF. The gain ripples can be reduced to 0.05 dB by further optimizing the parameters of the multiple Gaussian incoherent pumps.