The optimization of pumping schemes of distributed Raman amplifiers employed in long-haul optical transmission systems is investigated in detail. Considering the received optical signal to noise ratio (OSNR) as well as nonlinear distortion and the optimal signal power distribution, i.e. uniform distribution, is achieved by using variational method. But the analytical optimal distribution does not exist when taking double Rayleigh backscattering (DRB) into account. Comparison between three Raman amplification schemes, i.e. bidirectional dual-order, first-order pumping and Raman-plus-Erbium doped fiber amplifier hybrid amplification, is carried out at identical nonlinear phase shifts. The results show that symmetric bidirectional dual-order pumping can achieve the best OSNR performance through appropriate choice of the second-order pump wavelength and second-to-first-order pump power ratio in most cases for both short- and long-span applications. However, hybrid amplification will be a better choice when the DRnoise is dominant. These results will be helpful for designing long-haul transmission systems.
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