Mei, FengQu, GeyangSha, XinboHan, JingYu, MoxinLi, HaoChen, QinmiaoJi, ZihengNi, JinchengQiu, ChengweiSong, QinghaiKivshar, YuriXiao, Shumin2025-02-032025-02-032041-1723https://hdl.handle.net/1885/733734637We introduce a new paradigm for generating high-purity vortex beams with metasurfaces. By applying optical neural networks to a system of cascaded phase-only metasurfaces, we demonstrate the efficient generation of high-quality Laguerre-Gaussian (LG) vortex modes. Our approach is based on two metasurfaces where one metasurface redistributes the intensity profile of light in accord with Rayleigh-Sommerfeld diffraction rules, and then the second metasurface matches the required phases for the vortex beams. Consequently, we generate high-purity LGp,l optical modes with record-high Laguerre polynomial orders p = 10 and l = 200, and with the purity in p, l and relative conversion efficiency as 96.71%, 85.47%, and 70.48%, respectively. Our engineered cascaded metasurfaces suppress greatly the backward reflection with a ratio exceeding −17 dB. Such higher-order optical vortices with multiple orthogonal states can revolutionize next-generation optical information processing.This research was supported by National Key Research and Development Program of China (Grant Nos. No. 2022YFA1404700, 2021YFA1400802), National Natural Science Foundation of China (Grant Nos. 12334016, 6233000076, 12025402, 62125501, 12261131500, 92250302, 11934012), New Cornerstone Science Foundation through XPLORER PRIZE, Shenzhen Fundamental Research Project (Grant Nos.JCYJ20210324120402006, JCYJ20220818102218040, JCYJ20200109112805990, GXWD20220817145518001), and Fundamental Research Funds for the Central Universities (Grant Nos. 2022FRRK030004). C.-W.Q. acknowledges the support of the AME Individual Research Grant (IRG) funded by A*STAR, Singapore (Grant No. M22K2c0088, with NUS WBS No. A-8001322-00-00). C.-W.Q. acknowledges financial support from the NRF, Prime Minister’sOffice, Singapore, under the Competitive Research Program Award (NRFCRP22-2019-0006).application/pdfen-AU© 2023 The authorshttp://creativecommons.org/licenses/by/4.0/202310.1038/s41467-023-42137-12024-01-07Creative Commons Attribution licence