**3. Simulation**

The spectral components of the OPC system described in Section 2 was simulated using an experimentally confirmed model [32–40] that takes into account residual Raman gain from the primary pump at 1366 nm to the signal in the C-band as well as pump depletion from both pumps to the lower order pumps and the signal components, double Rayleigh scattering (DRS) and amplified spontaneous emission (ASE) noise for each of the signals. Noise was calculated in a room temperature of 24 ◦C and 0.1 nm bandwidth. Wavelength dependent Raman gain coefficient and attenuation factor were independently chosen for each WDM component as well as primary pump and lasing at the frequency of the FBG using tables for the SMF. Rayleigh backscattering coefficients for Raman pump, lasing and signal were 1.0 × <sup>10</sup>−4, 6.5 × 10−<sup>5</sup> and 4.5 × 10−<sup>5</sup> km−1, respectively. In [28] we showed that higher reflectivity (99%) provides lower nonlinear phase shift compared with 70% and 50% as well as better power efficiency performance without sacrificing output OSNR. To find the best gain profile, the center wavelength of high reflectivity (99%) FBGs was varied from 1456 to 1464 nm for WDM section of transmitted channels and from 1442 to 1454 nm for the conjugated copy with a 2 nm step. The loss and bandwidth of the FBG in the simulations was set to 0.2 dB and 200 GHz, respectively.

Figure 3 illustrates the WDM grid of the mid-link OPC system. Total bandwidth of 6 THz consists of 30 transmitted WDM channels with 100 GHz spacing ranging from 192–194.9 THz and 30 WDM conjugated copies of the original signal in the range 195.1–198 THz (we also present results for 191–197 THz grid). We assumed 200 GHz as the guardband in the middle of the grid centered at 195 THz for the optical phase conjugator. The signal power profile of each WDM component of the original and conjugated signal was simulated independently.

**Figure 3.** WDM grid of the transmitted (**left**) and the conjugated (**right**) WDM channels in a mid-link OPC system. "\*" denotes conjugated channels.

Forward pump power of the Raman fibre laser at 1366 nm was simulated from 0.7 to 1.6 W with 100 mW step. Backward pump power was simulated to give 0 dB net gain for the channel under investigation, then the rest of the WDM channels were simulated with the same forward and backward pump powers: one set of results consists of 30 possible combinations (optimisation towards first channel CH1, second channel CH2 and so on). Conjugated signals were simulated with the same pocedure. To summarise, we simulated every possible combination varying forward pump power (0.7–1.6 W) for each installed FBG (1442–1454 nm for original and 1456–1464 nm for conjugated WDM grid) and finally compared asymmetry between both WDM channel sets to achieve the best overall asymmetry performance in an OPC system with second order Raman amplification.

The asymmetry was calculated using formula:

$$\frac{\int\_{0}^{L} |P\_1(z) - P\_2(L-z)|dz}{\int\_{0}^{L} [P\_1(z) + P\_2(z)]/2dz} \times 100\tag{1}$$

where *L* is the span length and *P*1 and *P*2 represent signal power evolution of the transmitted and conjugated channels, respectively.

#### **4. Results and Discussion**

#### *4.1. 191–197 THz WDM Grid*

For a given WDM grid bandwidth, the key factors that need to be optimized for the best performance overall in a mid-link OPC system are the wavelength of the FBG and the forward and backward pump powers. Both optimizations must be done separately for the original and conjugated WDM grid. Our initial investigation was done for a WDM grid 191–197 THz. Firstly, we had to select the right set of FBGs that will have a performance impact for residual channels located at the beginning and the end of the band.

In Figure 4 we show the impact of the FBG wavelength on asymmetry performance in WDM grid under investigation. Here, the central wavelength of the FBG for original channels was set to 1462 nm (the best configuration) and the one of the FBG for conjugated channels was varied from 1442–1450 nm. The asymmetry of residual side channels can be improved by 12% (CH1: 21% with 1450 nm and 33% with 1442 nm). However, this advantage is lost for CH6 and CH7 where the asymmetry performance is reversed, hence we need average overall performance. In this case the matching FBGs pair was 1462 nm for original and 1446 nm for conjugated WDM grid (we also simulated FBG for original WDM grid from 1456–1464 nm, however, for clarity we only show the best performing configuration with 1462 nm). Next, we optimized forward and backward pump powers for original and conjugated WDM grid.

**Figure 4.** Impact of a FBG choice on asymmetry performance in 191–197 THz grid. Wavelength of a FBG for original WDM grid was set to 1462 nm and FBG for the conjugated copy was varied from 1442–1450 nm.

In Figure 5 we show the impact of pump power on asymmetry performance for original and conjugated WDM grid. Forward pump power for both configurations was varied from 1–1.6 W. Backward pump power from 2.6–2.9 W for original (191–193.9 THz) and 1.6–1.9 W for conjugated (194.1–197 THz) WDM grid. The difference in backward pump power for each WDM grid results from wavelength dependent Raman gain and fiber attenuation.

By analyzing all possible combinations of FBG, forward and backward pump powers for original and conjugated WDM grid, we found the profile that gave the best average asymmetry of 6.4%; however, this figure is biased by first residual channels that are on the edge of Raman gain profile.

**Figure 5.** Impact of pump power choice (original WDM grid) on asymmetry performance. Forward pump power of the conjugated grid fixed to be 1.3 W. FBG for original and conjugated WDM grid was set to 1462 and 1446 nm, respectively.

In Figure 6 we show the best profile with the following settings: FBG 1462 nm with forward pump power 1 W for the original, and FBG 1446 nm with 1.3 W forward pump power for the conjugated WDM grid.

#### *4.2. 192–198 THz WDM Grid*

Based on the results shown in Section 4.1, we decided to repeat the simulations with a grid shifted by 1 THz to avoid the worst performing channels in the beginning of the spectrum. The new grid was set to 192–198 THz. Based on the knowledge from the previous configuration we only tested the FBG sets 1458–1460 nm and 1450–1454 nm for original and conjugated WDM grid, respectively.

In Figures 7 and 8, we show the impact of a FBG choice on asymmetry performance in 192–198 THz grid. The optimum configuration giving the lowest average asymmetry was with FBG set to 1460 nm and 1450 nm for the original (Figure 9) and conjugated (Figure 10) WDM grid, respectively. The right choice of a FBG helps to optimize the gain profile of the WDM band, which will particularly have an impact for an on–off gain of residual front and end channels. This will directly affect asymmetry performance.

**Figure 7.** Impact of a FBG choice on asymmetry performance in 192–198 THz grid. FBG for original WDM grid was set to 1458 nm and conjugated varied from 1450–1454 nm.

**Figure 8.** Impact of a FBG choice on asymmetry performance in 192–198 THz grid. FBG for original WDM grid was set to 1460 nm and conjugated varied from 1450–1454 nm.

**Figure 9.** Impact of pump power choice (original WDM grid) on asymmetry performance. Forward pump power of the conjugated grid was fixed to be 1.3 W. FBG for original and conjugated WDM grid was set to 1460 and 1450 nm, respectively.

**Figure 10.** Impact of pump power choice (conjugated WDM grid) on asymmetry performance. Forward pump power of the original grid was fixed to be 1.1 W. FBG for original and conjugated WDM grid was set to 1460 and 1450 nm, respectively.

After choosing the right FBG set for our WDM band we optimized forward and backward pump powers. This time we extended the range and simulated 0.7–1.4 W forward pump power. Backward pump power was stable for all possible configurations and oscillated within the 50 mW range around 2.3 W for the original and 1.8 W for the conjugated WDM grid.

By shifting our band by 1 THz we managed to improve average asymmetry by 0.5% achieving 5.9% with only three channels (CH1, CH2 and CH30) with figures above 10%. In this regime (asymmetry below 10%) we exceeded 35 nm bandwidth of the C band (1530–1565 nm) from ~4.3 THz to 5.4 THz (27 WDM channels with asymmetry below 10%, giving total 54 channels). As seen in Figure 11, the majority of channels (CH7–CH24) were below 5%, which is a very impressive result covering 3.4 THz.

**Figure 11.** WDM grid with the best average asymmetry of 5.9%. Forward pump power was set to be 1.1 W and 1.3 W and FBG to 1460 nm and 1450 nm for original and conjugated WDM grid, respectively.

In a single channel regime CH21 achieved asymmetry 2.1%, which is the lowest asymmetry in a 60 km span up to date (see Figure 12). This value most likely would be even lower if a single channel only would be simulated with the same configuration due to

the Raman pump depletion. Signal power variation in the original and conjugated channels is very low, below 2 dB, comparing to 12 dB when using EDFA.

**Figure 12.** Signal power profile of original (blue) and conjugated (red) channel with lowest asymmetry of 2.1% in a 60 km standard SMF span.

In Figure 13 we show OSNR and NPS results for an optimized 6 THz WDM grid (192–198 THz) for both original (CH1–CH30) and conjugated (CH31–CH60) channels in a 60 km span. We can notice small OSNR variation within 1 dB range between the best and the worst performing channels for both simulated grids, thanks to the combined gain from the first order pump at 1366 nm and lasing at the wavelength of the FBG. NPS variation was also very low across all but the first two channels; however, at these values of NPS it is insignificant.

**Figure 13.** OSNR (blue) and NPS (red) simulations for original (CH1–CH30) and conjugated (CH31–CH60) channels.
