Orbital angular momentum-mediated machine learning for high-accuracy mode-feature encoding.

Machine learning with optical neural networks has featured unique advantages of the information processing including high speed, ultrawide bandwidths and low energy consumption because the optical dimensions (time, space, wavelength, and polarization) could be utilized to increase the degree of freedom. However, due to the lack of the capability to extract the information features in the orbital angular momentum (OAM) domain, the theoretically unlimited OAM states have never been exploited to represent the signal of the input/output nodes in the neural network model. Here, we demonstrate OAM-mediated machine learning with an all-optical convolutional neural network (CNN) based on Laguerre-Gaussian (LG) beam modes with diverse diffraction losses. The proposed CNN architecture is composed of a trainable OAM mode-dispersion impulse as a convolutional kernel for feature extraction, and deep-learning diffractive layers as a classifier. The resultant OAM mode-dispersion selectivity can be applied in information mode-feature encoding, leading to an accuracy as high as 97.2% for MNIST database through detecting the energy weighting coefficients of the encoded OAM modes, as well as a resistance to eavesdropping in point-to-point free-space transmission. Moreover, through extending the target encoded modes into multiplexed OAM states, we realize all-optical dimension reduction for anomaly detection with an accuracy of 85%. Our work provides a deep insight to the mechanism of machine learning with spatial modes basis, which can be further utilized to improve the performances of various machine-vision tasks by constructing the unsupervised learning-based auto-encoder.