Deep learning enabled superfast and accurate M²evaluation for fiber beams

We introduce deep learning technique to predict the beam propagation factor M^2 of the laser beams emitting from few-mode fiber for the first time, to the best of our knowledge. The deep convolutional neural network (CNN) is trained with paired data of simulated near-field beam patterns and their calculated M^2 value, aiming at learning a fast and accurate mapping from the former to the latter. The trained deep CNN can then be utilized to evaluate M^2 of the fiber beams from single beam patterns. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error smaller than 2% even when up to 10 eigenmodes are involved in the fiber. The error becomes slightly larger when heavy noises are added into the input beam patterns but still smaller than 2.5%, which further proves the accuracy and robustness of our method. Furthermore, the M^2 estimation takes only about 5 ms for a prepared beam pattern with one forward pass, which can be adopted for real-time M^2 determination with only one supporting Charge-Coupled Device (CCD). The experimental results further prove the feasibility of our scheme. Moreover, the method we proposed can be confidently extended to other kinds of beams provided that adequate training samples are accessible. Deep learning paves the way to superfast and accurate M^2 evaluation with very low experimental efforts.