Recently, high-power fiber lasers (HPFLs) have become a popular topic in laser science and technology. Rare earth-doped active fibers are key components of HPFL. In contrast to common active fibers, one or more auxiliary refractive index layers are added between the core and cladding of multi-layer active fibers. These types of fibers exhibit special mode properties; therefore, they are expected to further enhance the output power of HPFLs. Evaluating the mode properties of multilayer active fibers under different fiber structural parameters is important because the corresponding results reveal the relationship between the structural parameters and fiber properties, indicate which structural parameter has the best performance, and provide guidance for fiber design. Traditional methods, such as finite difference, finite element, and transfer matrix methods, have been adopted to evaluate the mode properties of such fibers. However, these traditional approaches typically require a long time to repeatedly solve Maxwell's equations under different structural parameters. Doubtlessly, a faster approach to evaluating multilayer active fibers would be vital. In this study, we used machine learning to predict the mode properties of multilayer active fibers for the first time. This new approach can achieve fast and accurate predictions without solving Maxwell's equations.

We introduce a shallow neural network (NN) to learn the mapping from input structural parameters to output mode properties. The structural parameters include the refractive index difference between the core and cladding, thickness of the auxiliary layers, and working wavelength. The mode properties included the effective index, mode field area, and power-filling factor of the fundamental mode (FM) and higher-order mode (HOM). The NN approach can be divided into three steps: data generation, network training, and rapid evaluation (Fig. 2). In the data generation step, 0.1% of the training samples in the defined data space (Table 1) were generated using the transfer matrix method. An NN with one hidden layer is trained using the mean square error (MSE) loss function between the label and output in the network training step. After training, the NN can quickly and accurately predict the mode properties of the multilayer active fibers.

We trained the shallow NN for 200 epochs, and the MSE was finally close to 2.5×10^-5. The total training time was approximately 18 s. To test the accuracy of the trained NN, 256 testing samples were randomly generated. Three typical samples with different mode field distributions (Fig. 5) were used to test the accuracy of the trained NN, and the predicted mode properties agreed well with the ground truths (Fig. 6). The predicted mode properties for all testing samples were then collected and compared to the corresponding ground truths (Fig. 7). The predicted values remained very close to the ground truths. In addition to the randomly generated testing samples, we successfully utilized an NN to predict the mode properties under different wavelengths (Fig. 8), aiming at a special multilayer active fiber with a fixed refractive index difference and auxiliary layer thickness. The accuracy and cost of the NN approach were analyzed statistically. The averaged prediction error of the mode properties was less than 0.6% (Table 2), indicating the high accuracy of this shallow NN. Besides, the total time required to evaluate 256 samples was approximately 177 s for the traditional method and 23 ms for the NN approach. That is, NN takes only 0.09 ms to complete the evaluation for one sample, which is 7000 times faster than traditional methods.

In this study, we used machine learning for the first time to achieve a fast and accurate prediction of the mode properties of multilayer active fibers. This method requires only 0.1% of the samples in the data space to learn the complex mapping between the fiber's structural parameters and mode properties. Thus, fast and accurate prediction can be achieved without solving Maxwell's equations. The average prediction error of this method is less than 0.6%, and the prediction speed is 7000 times higher than that of the traditional method, providing a new way to evaluate the mode properties of multilayer active fibers.