Fast modal analysis for Hermite–Gaussian beams via deep learning

The eigenmodes of Hermite–Gaussian (HG) beams emitting from solid-state lasers make up a complete and orthonormal basis, and they have gained increasing interest in recent years. Here, we demonstrate a deep learning-based mode decomposition (MD) scheme of HG beams for the first time, to the best of our knowledge. We utilize large amounts of simulated samples to train a convolutional neural network (CNN) and then use this trained CNN to perform MD. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error of 0.013 when six eigenmodes are involved. The scheme takes only about 23 ms to perform MD for one beam pattern, indicating promising real-time MD ability. When larger numbers of eigenmodes are involved, the method can also succeed with slightly larger prediction error. The robustness of the scheme is also investigated by adding noise to the input beam patterns, and the prediction error is smaller than 0.037 for heavily noisy patterns. This method offers a fast, economic, and robust way to acquire both the mode amplitude and phase information through a single-shot intensity image of HG beams, which will be beneficial to the beam shaping, beam quality evaluation, studies of resonator perturbations, and adaptive optics for resonators of solid-state lasers.