## 3 Performance Improvement of Three-Segment Raman Amplified Link  
The detail system parameters and their values used in the model analysis are listed in Table 1. The specific fiber parameters and their values for the three-segment hybrid fiber effective core area structure and conventional single fiber core structure are listed in Tables 2 and 3. In order to get a lower peak power of signal power density and a sufficient reduction in the Kerr nonlinear distortion measured as a nonlinear phase shift, the length of the first segment (core #1) is set to 90 km. In parallel, to improve the Raman gain in the signal power prior to reaching the minimum point of signal power and to maintain the power level of the backward Raman pump after fiber penetration, the length of the third segment (core #3) is set to 100 km. Both segment lengths are preliminary values to prove the concept of the three-segment hybrid fiber core systems, and we believe there is still room to fine-tune these values to obtain the optimum individual length in the future study. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **Notation** & **Value** & **Unit** \\ \hline Fiber span length & \(L\) & 390 & km \\ Signal wavelength & \(\lambda_{s}\) & 1550 & nm \\ Fiber attenuation at signal wavelength & \(\alpha_{s}\) & 0.166 & dB/km \\ Pump wavelength & \(\lambda_{p}\) & 1450 & nm \\ Fiber attenuation at pump wavelength & \(a_{p}\) & 0.21 & dB/km \\ Raman gain coefficient & \(gR\) & \(4\times 10^{-14}\) & m/W \\ Fiber effective core area & \(A_{eff}\) & 76, 82, 150 & \(\mu\)m\({}^{2}\) \\ Raman net gain & \(G_{opt}\) & 5 & dB \\ Filter optical bandwidth & \(B_{opt}\) & 0.1 & nm \\ Nonlinear Kerr parameter & \(n_{2}\) & \(2.7\times 10^{-20}\) & m\({}^{2}\)/W \\ Spontaneous scattering & \(n_{sp}\) & 1.13 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of parameters. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Core \#1** & **Core \#2** & **Core \#3** \\ \hline Fiber effective core area (\(\mu\)m\({}^{2}\)) & 150 & 82 & 76 \\ Segment length (km) & 90 & 200 & 100 \\ Segment attenuation (dB/km) & 0.166 & 0.166 & 0.166 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Conventional single fiber core structure. Figure 3 shows the distribution profile of bidirectional Raman pump power for both the conventional single-segment single fiber core structure and the three-segment hybrid fiber effective core area structure when the pump powers are adjusted to provide the equal 5 dB Raman net gain (\(G_{net}\)), which is the residual gain after the total Raman gain is reduced by total fiber attenuation loss. In both cases, the forward and backward pumps provide significant gain contributions in the initial 50 km and additional, but lower, contributions from 50 to 100 km. Due to continuous fiber attenuation at a rate of 0.21 dB/km for a pump wavelength of 1450 nm, the Raman pump power decreased significantly beyond 100 km. Therefore, the gain contribution at this stage can be considered negligible and the fiber span experiences a passive fiber loss. In the forward pump, the three-segment hybrid fiber core structure requires higher pump power to achieve equal Raman net gain compared to the conventional single fiber core structure due to the gain characteristic of Raman scattering, which has a lower gain on larger sized cores. In the backward pump, the pump power difference is small because the fiber core size difference is small. Figure 4 illustrates a comparison of signal power density \(I_{s}(z)\) between the three-segment hybrid fiber effective core area structure and the conventional single-segment single fiber core structure along the 390-km fiber transmission span. In the span with the three-segment hybrid fiber core structure, the first segment (0-90 km), with a larger effective core area, provides a lower signal power density that helps to reduce the nonlinear Kerr effect; the third segment (290-390 km), with a smaller effective core area, provides a higher signal power density that helps to improve the OSNR.