Nonlinear ultrashort laser pulse propagation in optical fibers, which is the physical principle of fiber-based optical devices, optical signal transmission, and processing, comprises a series of complex nonlinear dynamics. It finds extensive application in the fields of fiber lasers, fiber amplifiers, and fiber communications. Generally, nonlinear ultrashort pulse propagation is governed by the nonlinear Schr?dinger equation (NLSE) and can be solved using model-driven methods such as the split-step Fourier (SSF) and finite-difference methods. However, NLSE-based systems are sensitive to both the initial pulse and fiber parameters, making it difficult for traditional numerical methods to control the complex nonlinear pulse evolution in a time-efficient manner.
As a powerful tool for system parameter optimization and the construction of models of complex dynamics from observed data, deep learning (DL) algorithms have recently been applied to ultrafast photonics, optical communications, optical networks, optical imaging, and the modeling and control of nonlinear pulse propagation to reap the benefits of purely data-driven methods without any underlying governing equations. In this paper, the current key technologies and applications of the DL method for predicting nonlinear pulse dynamics in fiber optics, reconstructing ultrashort pulses, and evaluating critical pulse characteristics are summarized, and the development trends are predicted.
First, a brief introduction to the DL method and practical DNN is presented. Second, the applications of DL for predicting nonlinear ultrashort pulse propagation are listed. Several types of neural networks, i.e., LSTM, CNN, and FNN, have been applied to predict nonlinear pulse evolution, i.e., predicting the effects of GVD and SPM on ultrashort pulse propagation, higher-order soliton compression, and supercontinuum generation, in both the temporal and spectral domains with high prediction precision. Moreover, DL methods are used for modeling optical fiber channels, resulting in a significant reduction in computation demand. Further, the PINN is verified in multiple nonlinear pulse propagations governed by the NLSE, which considers the physical and boundary constraints of the physics model. Subsequently, the optimized PINN, i.e., subnet structure and adapted loss function, is applied to solve the NLSE and predict the nonlinear soliton dynamics with higher prediction accuracy and generalizability.
Third, the DL applications for solving the inverse problems of nonlinear propagation of ultrashort pulses are discussed. Therefore, FNNs and CNNs are utilized to reconstruct the ultrashort pulse and counteract the effects of nonlinearity without prior knowledge. The ultrashort pulse profiles are precisely recovered using SPM and four-wave mixing effects. Furthermore, CNNs have been applied as alternatives to the DBP algorithm to compensate for the nonlinear distortions in the ?ber-optic transmission systems. In addition, DNNs are used extensively in parameter estimation and optimization of optical fiber systems, including the optimal design of the pump power and pump wavelength in the FOPA (fiber optical parametric amplifier) system, predicting the collision between a single soliton and soliton molecule, realizing the extraction of important soliton characteristics, evaluating soliton properties in a quantum noise environment, and estimating the M2 factor in few-mode fibers.
The DL methods have become a development frontier and research hotspot in the field of predicting, modeling, controlling, and designing nonlinear pulse propagation in optical fibers. Compared to the conventional SSF method, lightweight neural networks can significantly improve computing efficiency and reduce computing demand, making it simple and convenient to study nonlinear pulse dynamics and optimize fiber-based optical systems. In addition, DL methods have the following potential advantages: (1) They can conduct pure data-driven modeling for complex propagation scenarios that lack accurate mathematical theories or physical models. (2) They can achieve flexible end-to-end modeling for typical nonlinear dynamics or transmission systems, avoiding a nested function structure and repeated iterations, which effectively reduces the complexity of the simulation system.
However, the generalization of neural networks is a critical issue that restricts the prediction of precision and accuracy. Several methods have been developed to improve the generalization of neural networks, such as adding physical constraints to the loss function, coupling a physical model to a neural network, and embedding physical parameters into the neural network input. Further, scientific training methods such as transfer learning and reinforcement learning are conducive to enhancing the scalability of the network in an actual system and reducing the time and data cost of network training. As alternatives to the traditional numerical method, the application of DL methods could aid in the understanding of nonlinear ultrashort pulse propagations as well as the design and optimization of ultrashort pulse-based optical systems.
