## 3 Optimized Distributed Raman Amplification Design over Multiple Fiber Spans  
We have studied the optimization of Raman amplification schemes with backward pumping only over multiple fiber spans in [2], and this has been the only study so far regarding multiple fiber span links. In order to investigate the impact of multi-span DRA schemes on the nonlinearity compensation, we demonstrated the signal profiles of three dual-order DRA schemes over 2 \(\times\) 50.4 km SSMF spans and illustrated four-wave mixing (FWM) conversion efficiencies and inline/long-haul transmission performances. Scheme 1 was the dual-order DRA with backward pumping which was the same as Figure 2 in each individual span that included both the first-order pump seed at 1455 nm and the second-order pump at 1366 nm [49; 50]. The gain of the dual-order DRA compensated only the loss from the SSMF, and the losses of the passive components (e.g., signal pump combiners, isolators) was not compensated. In scheme 2, the experimental setup was the same as scheme 1, and the pump power for the second span also remained the same, but the 1.5 dB loss due to fiber attenuation and passive components between the two spans was compensated by more Raman power from the first span. This means that the signal output power from the first SSMF was overpowered by \(\sim\)1.5 dB. In scheme 3, to compensate the loss from passive components without sacrificing the symmetry of the two-span link, a 25 cm EDF (Fibrecore M-12(980/125)) was used between the SSMF and the WDM coupler at the end of the first span as illustrated in Figure 12b, which enabled 1.5 dB amplification within this 25 cm erbium-doped fiber. Figure 13 shows the experimentally measured and numerically simulated signal power profiles along the fiber for all three DRA schemes using the modified OTDR setup [44]. In scheme 1, the pump power was 330 mW at 1366 nm and 100 mW at 1455 nm. In the two-span link, \(\sim\)1.5 dB signal power difference between two spans existed which reduced the overall signal power profile symmetry across the two spans to 65.8%, a drop dominated by the launch power difference. Figure 11: Theoretical predication of nonlinear Kerr product power as a function of frequency separation between the two CW lasers using rDFB bidirectional-pumping Raman amplification over 62 km SSMF span. Figure 12: (a) Schemes 1 and 2: Dual-order BW-propagated pumping DRA over 2 \(\times\) 50.4 km SSMF (including two pump power settings). (b) Scheme 3: EDF-assisted dual-order BW-propagated pumping DRA over 2 \(\times\) 50.4 km SSMF. Figure 13: Experimentally measured and simulated signal power profiles along the fiber with three Raman amplification schemes; (a) DRA compensating only the fiber loss. (b) DRA compensating the fiber and the passive components loss between the two spans. (c) EDF-assisted DRA compensating fiber and the passive components loss between the two spans. In scheme 2, the pump power in the first span was 330 mW at 1366 nm and 115 mW at 1455 nm, higher than in scheme 1 to compensate the 1.5 dB loss between the spans. Matching launch powers thus improved the symmetry to 80.9%. In scheme 3, the pump power before passing through the EDF in the first span was 330 mW at 1366 nm and 108 mW at 1455 nm. The 1.5 dB EDF amplification was powered by both Raman pumps (primarily by 1455 nm; however, the power from 1366 nm pump would be transferred to 1455 nm and contribute to the gain at low C band simultaneously) and therefore compensated the loss of passive components between spans [35]. This is different from the conventional hybrid Raman/EDFA: Instead of using 980/1480 nm laser pumps to invert the EDF fiber [51] we relied on the Raman pumps at 1366 and 1455 nm. By matching both launch power and signal evolution in the two-span Scheme enables the signal power symmetry level of 93.4% over 2 \(\times\) 50.4 km spans. The symmetry level of 93.4% over two spans is also comparable to the best symmetry level of 97% over a single 50 km span using an optimized dual-order Raman amplification shown in [2].