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针对单模光纤中四波混频-受激拉曼散射(FWM-SRS)强非线性耦合效应难以解析的问题, 本文提出了一种融合物理机理与神经网络的多尺度物理约束网络(MSPC-Net). 该模型通过将非线性薛定谔方程(NLSE)的频域残差作为物理约束项嵌入网络优化过程, 并设计多尺度空洞卷积模块融合局部细节、中程展宽及长程衰减特征, 实现了光谱成分分离与物理参数的联合高精度反演. 在250 m与500 m单模石英光纤实验中, MSPC-Net重建斯托克斯光谱的均方根误差(RMSE)分别低至0.014与0.0173, 较传统卷积神经网络降低超68%; 其频率偏移预测的平均绝对误差分别为0.03 nm和0.04 nm, 精度较现有方法提升约90%. 在信噪比(SNR)为6 dB的噪声环境下, MSPC-Net对FWM次峰信息的检测正确率高达95.3%, 伪峰率低于4.7%. 模型得益于物理约束的引导及轻量化结构设计, 在SNR = 15 dB噪声下RMSE增幅仅9.8%, 并具备良好的实时处理能力, 可部署于嵌入式设备, 为高功率光通信系统优化与分布式光纤传感提供高效解决方案. 本研究通过将严格物理规律与多尺度特征提取相结合, 有效解决了长距离光纤复杂非线性效应的解析难题, 显著提升了预测结果的理论符合度与噪声鲁棒性.
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
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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
Fig. 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) a fter start of the device.
表 1 250 m光纤模型性能对比
Table 1. Performance comparison of 250 m optical fiber model.
index CNN BiLSTM 250 m
MSPC-NetSRS reconstructs RMSE 0.014 0.0189 0.0098 Sub-peak positioning
error/nm0.18 0.15 0.05 Frequency shift prediction
deviation/nm0.38 0.24 0.03 Recognition rate
under noise/%67.5 63.8 95.3 Training time/s 95 128 87 
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表 2 500 m光纤模型性能对比
Table 2. Performance comparison of 500 m optical fiber model.
index CNN BiLSTM 500 m
MSPC-NetSRS reconstructs RMSE 0.0173 0.024 0.012 Sub-peak positioning
error/nm0.20 0.17 0.06 Frequency shift prediction
deviation/nm0.61 0.60 0.04 Recognition rate
under noise/%61.8 78.2 94.1 Training time/s 96 128 87
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表 3 物理参数反演精度对比
Table 3. Comparison of physical parameter inversion accuracy.
index MSPC-Net(500 m) CNN(500 m) BiLSTM(500 m) $ {\beta }_{2} $ <4.2% >22% >18% $ \gamma $ <5% >30% >25%
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