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

Abstract

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.

Fig. 1. Conceptual illustration of the OAM-mediated machine learning and the application of all-optical information mode-feature encoding.

a OAM mode combs with normalized weight coefficients of the data-specific images. The pseudo-colors represent different OAM orders (l). b The architecture of the all-optical CNN for OAM-mediated machine learning, which can be applied to encode a data-specific image into OAM states. The photonic neural network comprises a trainable convolutional layer which can provide an OAM mode-dispersion impulse to densify the input OAM mode comb and extract the feature, and successive phase-engineered diffractive layers with finite size as a classifier to reduce the dense OAM mode spectrum to a couple of target terms due to the OAM mode-dispersion selectivity. c The proposed CNN with an appropriate OAM modes decoder can be applied in image classification, end-to-end switchable image display, and all-optical abnormal detection, respectively. Due to the weighting coefficients of the target OAM states are set as amplitude only (without phase differences), only the energy weighting coefficients of the output OAM spectrum terms are needed to be detected in the last two machine leaning tasks

Fig. 2. Physical principles of the CNN for mode-feature encoding.

a Illustration of a convolution operation of an OAM mode comb with an OAM mode-dispersion impulse based on superposed electrical fields in the spatial domain. b Diffraction losses of LG modes and the evolution of the OAM mode combs due to a single diffractive layer with finite size. c Encoding MNIST database into ten OAM modes based on the CNN. For ten blinding testing images, the intensity distributions and the OAM information are shown, respectively. d The confusion matrix with a testing encoding accuracy of 96.0%

Fig. 3. All-optical information mode-feature encoding in the application of anti-eavesdropping wireless image transmission.

a The optical setup of the all-optical communication systems including encoding, transmission, and decoding. b The intensity distributions of the encoding OAM mode states for six testing images from the Fashion MNIST database. c The OAM information of the received beams. d The confusion matrix using 30 testing images and the overall testing encoding accuracy is 93.3%. e The influence of the deviation distance on the energy of target encoding OAM mode states

Fig. 4. Information all-optical dimension reduction based on mode-feature encoded into six multiplexed OAM states.

a The flowchart of all-optical dimension reduction-based abnormal detection, wherein CNN is utilized for OAM modes feature encoding and a fork-grating phase plate is introduced to achieve OAM modes decoding. b The decoded OAM information of the selected 4 normal images and 4 abnormal images. c The PCA and the spectral clustering results. d The confusion matrix illustrating the true-positive rate of classifying the abnormal image is 90.0% and the false-positive rate is 5.26%, respectively