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

Aiming at the challenging problem of 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, designated as 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 inclusion ensures that the learning process remains consistent with the underlying physical principles governing light propagation in optical fibers. Furthermore, the model architecture employs a multiscale dilated convolution module specifically designed to capture and fuse features across different granularities, including fine local spectral details, intermediaterange broadening effects, and long-range attenuation trends. This multi-scale approach enables the simultaneous and high-precision inversion of both separated spectral components and critical physical parameters.Experimental evaluations were conducted using single-mode quartz fibers with lengths of 250 meters and 500 meters. The results demonstrate that the Stokes spectra reconstructed by MSPC-Net achieve remarkably low root mean square errors, measuring only 0.014 and 0.0173 for the two fiber lengths respectively. This performance represents a reduction of more than sixty-eight percent compared to conventional convolutional neural networks. Additionally, the average absolute errors for frequency offset prediction are as low as 0.03 nanometer and 0.04 nanometer, corresponding to an accuracy improvement of approximately ninety percent relative to existing state-of-the-art methods. Under noisy conditions with a signal-to-noise ratio of 6 decibels, the model maintains an exceptional detection accuracy of up to 95.3 percent for identifying FWM sub-peak information, while keeping the pseudo-peak rate below 4.7 percent.Benefiting from the strong guidance provided by embedded physical constraints and its lightweight structural design, the proposed model exhibits only a 9.8 percent increase in root mean square error even under challenging noise conditions with a signal-to-noise ratio of 15 decibels. Moreover, MSPC-Net demonstrates satisfactory real-time processing capabilities, making it suitable for deployment on embedded devices. This practical efficiency positions the model as a promising solution for optimizing high-power optical communication systems and advancing distributed optical fiber sensing applications. By successfully combining rigorous physical laws with multi-scale feature extraction, this research provides an effective approach to resolving the analytical difficulties associated with complex nonlinear effects in long-distance optical fibers, while significantly enhancing both the theoretical consistency and noise robustness of the prediction outcomes.