## 4 Analysis and Simulation
### Noise Suppression  
Table 1 lists the parameters used in the simulation of the second-order noise-suppression structure, and Figure 9 shows the simulation diagram. The input optical signal with a center frequency of 193.1 THz is first multiplexed with the continuous light Pump 1, whose center frequency is 193.3 THz, and then input into HNLF1, where the FWM effect occurs. After passing through BPF1 with a center frequency of 192.9 THz and a bandwidth of 100 GHz, the output of HNLF1 gives the first-stage noise-suppressed signal. This signal is multiplexed with continuous light Pump 2, whose center frequency is 193.3 THz, and then input into HNLF2, where the FWM effect reoccurs. After passing through a BPF2 with a center frequency of 193.7 THz and a bandwidth of 100 GHz, the output signal of the second-order noise-suppression structure is obtained. The power transfer curve is plotted as the power relationship between the input optical signal and the output signal. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Module** & **Parameters** & **Values** \\ \hline
**Input signal** & Center frequency & 193.1 THz \\ \hline
**Pump1** & Center frequency & 193.3 THz \\  & Power & 300 mW \\ \hline
**Pump2** & Center frequency & 193.3 THz \\  & Power & 310 mW \\ \hline  & Length & 1200 m \\  & Attenuation & \(0.2\times 10^{-3}\) dB/m \\
**HNLF1** & Nonlinear Index & \(2.6\times 10^{-20}\) m\({}^{2}\)/W \\  & Core Area & \(4.0\times 10^{-13}\) m\({}^{2}\) \\  & Dispersion & \(-4.0\times 10^{-6}\) s/m\({}^{2}\) \\  & Dispersion slope & \(-1.5508\times 10^{2}\) s/m\({}^{3}\) \\ \hline  & Length & 1000 m \\  & Attenuation & \(0.2\times 10^{-3}\) dB/m \\
**HNLF2** & Nonlinear Index & \(2.6\times 10^{-20}\) m\({}^{2}\)/W \\  & Core Area & \(6.0\times 10^{-13}\) m\({}^{2}\) \\  & Dispersion & \(-4.0\times 10^{-6}\) s/m\({}^{2}\) \\  & Dispersion slope & \(0.50\times 10^{2}\) s/m\({}^{3}\) \\ \hline
**BPF1** & Center frequency & 192.9 THz \\  & Bandwidth & 100 GHz \\ \hline
**BPF2** & Center frequency & 193.7 THz \\  & Bandwidth & 100 GHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters for the second-order noise-suppression structure. For HNLFs, the nonlinearity coefficient \(\gamma\) is inversely proportional to the core area \(A_{\text{eff}}\) when all other parameters are consistent, which is expressed as \(\gamma\propto 1/A_{\text{eff}}\). The design employs a smaller-core HNLF1 to maximize FWM efficiency through enhanced nonlinearity, while the larger-core HNLF2 strategically reduces the power density to suppress nonlinear noise and improve phase-matching tolerance. This configuration optimizes the trade-off between noise conversion efficiency and system stability. The first stage generates strong nonlinear interactions for noise suppression, while the second stage mitigates residual noise accumulation and maintains signal integrity by lowering nonlinear impairments. Figure 10 shows the power transfer curve of the designed second-order noise-suppression structure, which was obtained through the VPItransmissionMaker simulation. When the input signal power ranges from 20 to 30 mW, the output signal power stabilizes at approximately 54 mW. However, when the input signal power falls below 15 mW, the output signal power decreases to nearly 0 mW. This noise-suppression structure effectively mitigates both input and mismatch noise, thereby enhancing the accuracy and stability of symbol matching. These results demonstrate that the step of the power transfer curve can be improved by cascading two single-order FWM effect noise-suppression structures. In addition, the flat area of the curve is extended, indicating that the suppression range of the symbol \"1\" amplitude is improved. The input signal power is appropriately amplified and maintained within the range of the flat area of the power transfer curve, thereby resulting in a more ideal noise-suppression effect. Figure 11 shows a diagram of the QPSK-oriented all-optical matching system optimized using the proposed second-order noise-suppression structure.