## 2 Optimized Distributed Raman Amplification Design over Single Fiber Span
### Distributed Raman Amplification with Bidirectional Pumping
Full results using random DFB laser amplification (Figure 7c) are shown in Figure 8. Data provide a broader picture of the asymmetry evolution in transmission over a broad range of forward pump powers up to 2.5 W and lengths with the optimal backward pumping (0 dB net gain). The lowest asymmetry point is found to be at 62 km, with signal power asymmetry just below 3% (97% symmetry). Further optimization is possible based on simultaneous ASE noise minimization and nonlinearity compensation [29]. In order to confirm the simulation results, in Figure 9 we compare the simulated prediction and experimentally measured asymmetry vs. forward pump power split for a signal at 1545 nm in a 60 km span (the particular length was chosen due to availability of a SSMF fiber reels). The discrepancies between measurement and simulation are attributable mainly to the noisy experimental power profiles, as well as the mismatch of Raman gain and attenuation coefficients, since for consistency with previous simulations we used standard values for SSMF instead of measured coefficients. Figure 7: Schematic design of (**a**) first-order Raman, (**b**) second-order ultra-long fiber laser and (**c**) second-order random DFB Raman laser amplifiers. Finally we numerically compare three amplification schemes shown in Figure 7 using the same method as described in Figure 8: In each case we simulate all possible FPPs adjusting backward pump to give 0 dB net gain and choose the point with the best asymmetry level (with the favor of a lower forward pump power in case if the same asymmetry is achieved for two different FPP). The results are summarized in Figure 10 below. The random DFB Raman laser amplification setup (red) achieved the lowest asymmetry levels for span lengths above 58 km. The URFL amplification option displayed better symmetry for lengths between 40 and 58 km, with optimal forward/backward pumping power ratios close to 1 in spans of up to 50 km but requiring higher contribution from the backward pump as span length grows. The random DFB configuration requires a higher contribu  
Figure 8: Signal power asymmetry (%) as a function of different span lengths and pump powers (backward pump power was adjusted to give 0 dB net gain). Figure 9: Asymmetry dependence on the forward pump power split measured at the central wavelength at 1545 nm in a 60 km span. tion of the backward pump for lengths of up to 30 km, but forward/backward pump power ratio achieves close to 1 for longer spans. Optimal symmetry in first-order Raman amplification is found for backward pumping only. The bottom of Figure 10 shows the potential accumulated residual phase shift after optimal OPC, defined as the product of the optimal asymmetry at a given distance and the corresponding nonlinear phase shift. The combined results for high symmetry and residual phase shift results, together with resiliency to forward- pumping RIN in coherent transmission applications [29], suggest that a bidirectionally pumped random DFB laser with a single grating seems to be the best option, performance-wise, for amplification in long spans with OPC. Thus, we chose this as the option for further study. Figure 11 shows the Kerr product reduction versus frequency separation using almost symmetrical signal power profile (bidirectional pumping with random distributed feedback fiber laser). In Figure 11, without OPC, the nonlinear product power was up to \(-6.8\) dBm near the low frequency range, but with OPC, the nonlinear product power was decreased to \(-44.4\) dBm at 18 GHz. There was 37.6 dB nonlinear product degradation with the 97% symmetrical signal power profiles over 62 km SSMF, which was comparable with the optimized dual-order backward pumping Raman amplification over 50 km SSMF. Figure 10: Lowest signal power asymmetry for a given length with pump powers adjusted to give zero net gain (**top**) and the accumulated residual phase shift (**bottom**) for a given amplification scheme.