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

Fang et al. Light: Science & Applications (2024)13:49 https://doi.org/10.1038/s41377-024-01386-5 ARTICLE Official journal of the CIOMP 2047-7538 www.nature.com/lsa Open Access Orbital angular momentum-mediated machine learning for high-accuracy mode-feature encoding 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Xinyuan Fang 1✉ , Xiaonan Hu1,2, Baoli Li1, Hang Su1,2, Ke Cheng1,2, Haitao Luan1 and Min Gu 1✉ 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-topoint 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. Introduction Artificial neural networks (ANNs) provide a mathematical model that emulates the brain function for machine learning1, which can be performed in various physical domains2, such as electronics, optics and mechanics. To dramatically improve computing speed and energy efficiency3, various photonic computing approaches have been proposed to construct optical neural networks (ONNs), wherein different properties of light (e.g. time4, space5, wavelength6, polarization7) could be utilized for photonic multiplexing to achieve high parallelism, largedata throughput and large-scale interconnectivity. As Correspondence: Xinyuan Fang () or Min Gu () 1 Institute of Photonic Chips, University of Shanghai for Science and Technology, Shanghai 200093, China 2 Centre for Artificial-Intelligence Nanophotonics, School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China These authors contributed equally: Xinyuan Fang, Xiaonan Hu, Baoli Li another unique degree of freedom of light, the orbital angular momentum (OAM) division8–10 with unlimited orthogonal states could be utilized to convey information, creating the concepts of digital spiral imaging11, highcapacity optical communications12, optically addressable video holography13–15 and display16, six-dimensional data storage17, spatiotemporal light fields18, and highdimensional quantum entanglement19. However, OAM has never been adopted to represent the signal of the input/output nodes in the neural network model. Photonic matrix-vector operations on various physical dimensions are necessary to provide the fundamental building block for ONNs. As such, to physically interpret OAM information as matrix-vector of ONNs, the input raw data in the space domain should be transformed into indistinguishable and large OAM mode combs with most non-zero amplitude coefficients terms concentrating on the low-order OAM mode components (Fig. 1a)11,20, which indicates sparse OAM information feature with © The Author(s) 2024 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Fang et al. Light: Science & Applications (2024)13:49 a 1 1 Weighting coefficients (Normalized amplitude) Page 2 of 12 c 1 0 1 … … 0 1 … … 0 1 … … 0 1 … … 0 1 … … 0 1 … … 0 … 0 … 0 … … … 1 … End-to-end switchable image display l= –5 –4 –3 –2 –1 0 1 2 3 4 5 b ut Inp a-s dat p age ic im ecif OAM-mediated machine learning des M OA c om mo b 1 0 M OA -dis per n sio 2π 2π1 0 OAM multiplexing hologram e Target OAM state(s) Error backp rop ag at 0 0 0 Helical phase 2π 2π Amplitude Classification n io Phase Amplitude 1 de mo uls imp Abnormal detection Phase Classifier Fork grating Convolutional layer Encoding OAM states OAM decoders Abnormal class 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 underlying commonaliti (...truncated)