## 3 Second-Order Noise-Suppression Structure
When the parameters of the pump light, signal light, and HNLF are known, the numerical solution of Equations (7)-(10) [32] can be obtained using the Runge-Kutta method, and the power transfer curve can be drawn using the numerical solution. In the QPSK-oriented all-optical matching system, the information is primarily represented by the power levels of each symbol in the signal. However, noise within the system  
Figure 4: Schematic of the FWM effect. can affect the power of the optical pulses in the output signal. Consequently, the powers of the low-power optical pulse representing \"0\" and the high-power optical pulse representing \"1\" may become similar, causing errors during the logic calculations of the optical signal. This can lead to incorrect final matching results. Using a noise-suppression structure, power amplification and shaping can be applied to the optical signal. In principle, the noise-suppression structure adjusts the input-output relationship of the signal power. Figure 5 shows a graphical representation of the noise-suppression process. When the power of the input signal lies in the AB section, the output power signal can be suppressed to 0 mW. When the power of the input signal reaches the BC section, the power of the output signal is a certain value D, which can be set manually. Finally, the noise-affected input signal is regenerated into the red signal and output, as shown in Figure 5. The longer the length of section BC, the better the noise-suppression effect. Figure 6 shows the second-order noise-suppression structure. The input signal and pump light 1 (P1) enter HNLF1 for the first FWM and then filter the signal at the desired frequency through the first filter (BPF1). The signal outputs from BPF1 and pump light 2 (P2) enter HNLF2 through the multiplexer for the second FWM, and the filter (BPF2) outputs the suppression result. The power transfer curve of the second-order noise-suppression structure is similar to the step curve. Figure 7 shows the noise-suppression process of this structure. Figure 7a shows the power transfer curve for the first-stage noise-suppression structure. The output power ranges from A to B when the power of the input optical signal varies between C and D. The output from the first-stage noise-suppression structure is then input into the second-stage structure, and the corresponding power transfer curve is shown in Figure 7b. When the output of the first-stage noise-suppression structure is between A and B, the output of the second-stage structure maintains a relatively stable value. Figure 7c shows the power transfer curve of the input signal and output of the second-order noise-suppression structure. When the power of the input signal is between C and D, the system outputs a stable value P. Through this second-order suppression structure, the power of the high-power optical pulses in the output signal can be controlled to a relatively stable value, and the low-power optical pulses are compressed to near zero, ensuring a quality output optical signal from the system. Because \(L_{2}\gg L_{1}\), the length of the flat region is significantly increased  
\[\frac{\mathrm{d}A_{1}}{dz}=-\frac{1}{2}\alpha A_{1}+i\gamma\Big{(}2|A_{2}|^{2} +|A_{1}|^{2}+2|A_{3}|^{2}\Big{)}A_{1}+2i\gamma A_{2}A_{3}A_{1}^{*}e^{i\Delta Kz} \tag{4}\]0 Ideal power transfer curve of the second-order noise-suppression structure. \[\frac{\mathrm{d}A_{1}}{dz}=-\frac{1}{2}\alpha A_{1}+i\gamma\Big{(}2|A_{2}|^{2} +|A_{1}|^{2}+2|A_{3}|^{2}\Big{)}A_{1}+2i\gamma A_{2}A_{3}A_{1}^{*}e^{i\Delta Kz} \tag{4}\]1 Second-order noise-suppression structure. compared to that of the single-order structure, and it is easy to limit the output power to a certain range. Therefore, the second-order noise-suppression structure can effectively suppress noise, thereby reducing the impact of noise on the all-optical matching system. The output performance of the structure can be evaluated using parameters such as the ER, CR, Q factor, and BER.