High-precision analysis of nonlinear effects in single-mode fiber based on physically constrained neural network (MSPC-Net)

ZHU Mu; TONG Shoufeng; DING Yunfeng; ZHANG Peng

doi:10.7498/aps.74.20250804

Abstract

In view of the difficulty in analyzing the strong nonlinear coupling effect between four-wave mixing and stimulated Raman scattering in single-mode optical fibers, this paper introduces a novel multi-scale physically constrained network (MSPC-Net), which effectively integrates fundamental physical mechanisms with advanced neural network techniques. The proposed model incorporates the frequency domain residual derived from the nonlinear Schrödinger equation directly into the network optimization procedure as a differentiable physical constraint term. This strategic inclusiveness ensures that the learning process is consistent with the fundamental physical principles governing light propagation in optical fibers. Furthermore, the model architecture adopts a multi-scale dilated convolution module specifically designed to capture and fuse features across different granularities, including fine local spectral details, intermediate-range broadening effects, and long-range attenuation trends. This multi-scale approach can realize the simultaneous and high-precision inversion of both separated spectral components and critical physical parameters.Experimental evaluations are conducted using single-mode quartz fibers with lengths of 250 meters and 500 meters, respectively. The results demonstrate that the Stokes spectra reconstructed by MSPC-Net achieve remarkably low root mean square errors, only 0.014 and 0.0173 for the two fiber lengths respectively. This performance represents a reduction of more than 68% compared with that of traditional convolutional neural networks. Additionally, the average absolute errors of frequency offset prediction are as low as 0.03 nmr and 0.04 nm, with an accuracy improvement of approximately 90% compared with those of existing state-of-the-art methods. Under noisy conditions with a signal-to-noise ratio of 6 dB, the model maintains an exceptional detection accuracy of up to 95.3% for identifying four wave mixing (FWM) sub-peak information, while keeping the pseudo-peak rate below 4.7%.Owing to the embedded physical constraints and lightweight structural design, the proposed model shows just a 9.8% increase in root mean square error even under challenging noise conditions with a signal-to-noise ratio of 15 dB. Moreover, MSPC-Net demonstrates satisfactory real-time processing capabilities, making it suitable for deployment on embedded devices. This practical efficiency makes the model a promising solution for optimizing high-power optical communication systems and advancing distributed optical fiber sensing applications. By successfully combining strict physical laws with multi-scale feature extraction, this research presents an effective approach to resolving the analytical difficulties associated with complex nonlinear effects in long-distance optical fibers, while significantly improving both the theoretical consistency and noise robustness of the prediction outcomes.

Keywords:

nonlinear optics /
physically constrained neural networks /
multi-scale feature extraction /
spectral separation

Authors and contacts

1.
National Local Joint Engineering Research Center for Space Optoelectronic Technology, Changchun University of Science and Technology, Changchun 130022, China
2.
School of Mechanical and Electrical Engineering, Changchun University of Science and Technology, Changchun 130022, China

Corresponding author: ZHANG Peng, zp@cust.edu.cn

Funds: Project supported by the Joint Funds of the National Natural Science Foundation of China (Grant No. U22A2008), the Research Foundation for Basic Research of Jilin Province, China (Grant No.YDZJ202301ZYTS394), and the Key Laboratory of Underwater Acoustic Countermeasure Technology Development Fund, China (Grant No.CX-2022-032).

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References

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图 1 高峰值功率Nd³⁺: YAG脉冲激光器泵浦单模光纤产生非线性效应实验装置　(a) 实验装置原理图, 其中1为激光对准器, 2为1064 nm高反射镜, 3为1/4载玻片, 4为磷酸二氢钾晶体(KDP), 5为布儒斯特板, 6为脉冲氙灯, 7为Nd³⁺: YAG晶体棒腔, 8为输出镜, 9为磷酸氧钛钾晶体(KTP), 10为偏振片, 11为全反射镜, 12为聚焦透镜, 13为光纤法兰盘, 14为单模硅光纤, 15为接收仓, 16为光谱仪, 17为计算机; (b) 装置启动前; (c) 装置启动后

Figure 1. Experimental setup for nonlinear effects generated by pumping single-mode fiber with high peak power Nd³⁺: YAG pulse laser: (a) Experimental device schematic, where 1 represents laser aligner, 2 represents 1064 nm high reflecting mirror, 3 represents 1/4 glass slide, 4 represents Potassium dihydrogen phosphate crystal (KDP), 5 represents brewster plate, 6 represents pulse Xenon lamp, 7 represents Nd³⁺: YAG crystal rod cavity, 8 represents output mirror, 9 represents potassium titanyl phosphate crystal (KTP), 10 represents polaroid plate, 11 represents total reflective mirror, 12 represents focusing len, 13 represents optical fiber flange plate, 14 represents single mode silicon fiber, 15 represents receiving magazine, 16 represents spectrometer, 17 represents computer; (b) before start of the device; (c) after start of the device.

DownLoad: Full-Size Img PowerPoint

图 2 MSRA-Net和MSPC-Net模型架构图

Figure 2. MSRA-Net and MSPC-Net model architecture diagram.

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图 3 250 m 光纤非线性光谱

Figure 3. 250 m fiber nonlinear spectrum.

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图 4 500 m 光纤非线性光谱

Figure 4. 500 m fiber nonlinear spectrum.

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图 5 250 m 光纤训练表现

Figure 5. Training performance of 250 m optical fiber.

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图 6 500 m 光纤训练表现

Figure 6. Training performance of 500 m optical fiber.

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图 7 误差增幅对比

Figure 7. Comparison of error increase.

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图 8 光纤长度对最终RMSE的影响

Figure 8. Effect of fiber length on the final RMSE.

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图 9 训练效率与收敛特性图

Figure 9. Training efficiency and convergence characteristic diagram.

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图 10 噪声鲁棒性图

Figure 10. Noise robustness diagram.

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图 11 分步傅里叶法

Figure 11. Split-step Fourier method.

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图 12 频移预测误差对比

Figure 12. Frequency shift prediction error.

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图 13 频移预测相关性分析

Figure 13. Prediction correlation analysis.

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表 1 250 m光纤模型性能对比

Table 1. Performance comparison of 250 m optical fiber model.

参数	CNN	BiLSTM	250 m MSPC-Net
SRS重构RMSE	0.014	0.0189	0.0098
次峰定位误差/nm	0.18	0.15	0.05
频移预测偏差/nm	0.38	0.24	0.03
噪声下识别率/%	67.5	63.8	95.3
训练时间e/s	95	128	87

DownLoad: CSV

表 2 500 m光纤模型性能对比

Table 2. Performance comparison of 500 m optical fiber model.

参数	CNN	BiLSTM	500 m MSPC-Net
SRS重构RMSE	0.0173	0.024	0.012
次峰定位误差/nm	0.20	0.17	0.06
频移预测偏差/nm	0.61	0.60	0.04
噪声下识别率/%	61.8	78.2	94.1
训练时间/s	96	128	87

DownLoad: CSV

表 3 物理参数反演精度对比

Table 3. Comparison of physical parameter inversion accuracy.

参数	MSPC-Net(500 m)	CNN(500 m)	BiLSTM(500 m)
$ {\beta }_{2} $	<4.2%	>22%	>18%
$ \gamma $	<5%	>30%	>25%

DownLoad: CSV

[1]	姚天甫, 范晨晨, 郝修路, 李阳, 黄善旻, 张汉伟, 许将明, 叶俊, 冷进勇, 周朴 2024 中国激光 51 1901010 Google Scholar Yao T P, Fan C C, Hao X L, Li Y, Huang S W, Zhang H W, Xu J M, Ye J, Leng J Y, Zhou P 2024 Chin. J. Lasers. 51 1901010 Google Scholar
[2]	张帆, 李健, 李璐磊, 曹康怡, 薛晓辉, 张明江 2025 红外与激光工程 54 289 Zhang F, Li J, Li L L, Cao K Y, Xue X H, Zhang M J 2025 Infrared Laser Eng. 54 289
[3]	张鹏, 田春林, 乔勇, 吕栋栋 2018 激光与光电子学进展 55 061901 Google Scholar Zhang P, Tian C L, Qiao Y, Lyu D D 2018 Laser Optoelectron. Prog. 55 061901 Google Scholar
[4]	张鹏, 田春林 2016 光学学报 36 0819001 Google Scholar Zhang P, Tian C L 2016 Acta Opt. Sin. 36 0819001 Google Scholar
[5]	毛昕蓉, 寇召飞, 张建华 2017 激光与光电子学进展 54 080601 Google Scholar Mao X R, Kou Z F, Zhang J H 2017 Laser Optoelectron. Prog. 54 080601 Google Scholar
[6]	郑也, 倪庆乐, 张琳, 刘小溪, 王军龙, 王学锋 2021 中国激光 48 0701005 Google Scholar Zheng Y, Ni Q L, Zhang L, Liu X X, Wang J L, Wang X F 2021 Chin. J. Lasers 48 0701005 Google Scholar
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[17]	侯悦, 项水英, 邹涛, 黄志权, 石尚轩, 郭星星, 张雅慧, 郑凌, 郝跃 2025 物理学报 74 148701 Google Scholar Hou Y, Xiang S Y, Zou T, Huang Z Q, Shi S X, Guo X X, Zhang Y H, Zheng L, Hao Y 2025 Acta Phys. Sin. 74 148701 Google Scholar
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[19]	刘圆凯, 侯云龙, 杨宜霖, 侯刘敏, 李渊华, 林佳, 陈险峰 2025 物理学报 74 140303 Google Scholar Liu Y K, Hou Y L, Yang Y L, Hou L M, Li Y H, Lin J, Chen X F 2025 Acta Phys. Sin. 74 140303 Google Scholar
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