## 2 Optimized Distributed Raman Amplification Design over Single Fiber Span
### Distributed Raman Amplification with Backward Pumping Only  
Figure 1a shows the schematic diagram of the conventional first-order backward-pumped DRA, including the 50.4 km SSMF pumped by a fully depolarized fiber laser at 1455 nm. Because the fiber length is only \(\sim\)50.4 km mainly for short reach or multiple spans in long-haul transmission systems, the span loss was fully compensated which means that the pump power was commonly set to achieve zero dB net gain [43; 44; 45; 46; 47; 48]. Figure 1b shows both experimentally measured and numerically simulated signal power profiles along the fiber using the modified optical time domain reflectometer (OTDR) technique [44]. The symmetry/asymmetry level of the signal power profile is based on the calculation method in [12; 13], which gave 89% symmetry (11% asymmetry) for this Raman scheme. Figure 2a shows a dual-order backward-pumping DRA scheme including both a 1365 nm Raman fiber laser and a 1455 nm pump seed [49; 50]. Figure 2b shows the simulated and experimentally measured signal power profiles along the fiber. The use of the dual-order BW-pumping scheme can improve the symmetry of signal power profile, but it requires the optimization of the first- and second-order pump power [23]. As shown in Figure 2b, to achieve 97% symmetry, the first- and second-order pump power was set to \(\sim\)100 and \(\sim\)330 mW respectively. When the second-order pump power is increased beyond this optimum, the signal power symmetry degrades to 92% with \(\sim\)33 and \(\sim\)600 mW first- and second-order pump powers, respectively. This asymmetry accumulation was mainly because the signal power was increased near the signal output, as the signal gain was pushed into the middle of the fiber span using higher second-order pump power [23], whilst for lower second-order pump powers, the asymmetry approaches that of the first-order pumped configuration. As the alternative to the dual-order Raman scheme, the pump seed at 1455 nm can be replaced by a highly reflective fiber Bragg grating (FBG) as shown in Figure 3a [35]. In this case, a random distributed feedback (DFB) fiber laser at 1455 nm was generated due to the distributed Rayleigh backscattering (originating from the SSMF) and the fixed reflection of the FBG [35; 36; 37]. This scheme is more cost-effective in comparison with the dual-order scheme, as no active pump at 1455 nm is required. However, in terms of flexibility when optimizing the signal power symmetry, a random DFB fiber laser is not flexible compared to independent separate pumps as a minimum second-order pump power is determined by the grating reflectivity and the stimulated Brillouin scattering (SBS) coefficient. The same parameters also determine the ratio of first to second-order pump power. For a typical  
Figure 1: (**a**) First-order backward pumping; (**b**) signal power profiles along the fiber. grating reflectivity of 99%, the power symmetry was simulated to be only 75% for the 50.4 km SSMF span. We have theoretically predicted the power of the nonlinear Kerr product generated by two co-polarized CW lasers (3 dBm each) along a 50.4 km backward-pumped DRA system with and without mid-link OPC. Figure 4 shows the configuration used to predict the power of the Kerr nonlinear product as a function of frequency separation of the two lasers [23]. Figure 5 demonstrates the nonlinear product power versus laser frequency separation using the three different Raman schemes described above without and with mid-link OPC. For the conventional first-order DRA, the nonlinear product power without OPC was up to \(-11.5\) dBm at low frequency ranges. With OPC, the peak Kerr product power was suppressed by 27 dB. Using an optimized dual-order Raman scheme would improve the symmetry of signal power distributions and therefore further decrease the nonlinear Kerr product using the mid-link OPC.