[1] A E Willner, H Huang, Y Yan, et al. Optical communications using orbital angular momentum beams. Advances in Optics and Photonics, 7, 66-106(2015).
[2] F Zhu, S Huang, W Shao, et al. Free-space optical communication link using perfect vortex beams carrying orbital angular momentum. Optics Communications, 396, 50-57(2017).
[3] A M Yao, M J Padgett. Orbital angular momentum: Origins, behavior and applications. Advances in Optics and Photonics, 3, 161-204(2011).
[4] M J Padgett, R Bowman. Tweezers with a twist. Nature Photonics, 5, 343-348(2011).
[5] S Franke-Arnold, L Allen, M J Padgett. Advances in optical angular momentum. Laser and Photonics Reviews, 2, 299-313(2008).
[6] Xuanhui Lu, He Chen, Chengliang Zhao. Research on vortex beams and optical vortices. Infrared and Laser Engineering, S1, 174(2007).
[7] L Allen, M W Beijersbergen, R J C Spreeuw, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Physical Review A, 45, 8185(1992).
[8] J Wang, J Y Yang, I M Fazal, et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nature Photonics, 6, 488-496(2012).
[9] B Nenad, Y Yue, Y X Ren, et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science, 340, 1545-1548(2013).
[10] C Paterson. Atmospheric turbulence and orbital angular momentum of single photons for optical communication. Physical Review Letters, 94, 153901(1-4)(2005).
[11] Y Ren, H Huang, G Xie, et al. Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing. Optics Letters, 38, 4062-4065(2013).
[12] X L Zhu, L Guo, Q Zhu, et al. The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence. IEEE Photonics Journal, 10, 112-114, 135(2018).
[13] Ce Yu, Tianshu Wang, Ying Zhang, et al. Research on transmission performance on OAM beam and Gaussian beam in atmospheric turbulence channel. Infrared and Laser Engineering, 50, 20200400(2021).
[14] Y Zhang, P Wang, T Liu, et al. Performance analysis of a LDPC coded OAM-based UCA FSO system exploring linear equalization with channel estimation over atmospheric turbulence. Optics Express, 26, 22182-22196(2018).
[15] S H Li, S Chen, C Q Gao, et al. Atmospheric turbulence compensation in orbital angular momentum communications: advances and perspectives. Optics Communications, 408, 68-81(2018).
[16] S M Zhao, L Wang, L Zou, et al. Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing. Optics Communications, 376, 92-98(2016).
[17] Li Zou, Le Wang, Shibing Zhang, et al. Compensation of orbital-angular-momentum multiplexed communication system with wavefront correction. Journal on Communications, 36, 76-84(2015).
[18] L Zou, L Wang, S M Zhao. Turbulence mitigation scheme based on spatial diversity in orbital-angular-momentum multiplexed system. Optics Communications, 400, 123-127(2017).
[19] Chunqing Gao, Shikun Zhang, Shiyao Fu, et al. Adaptive optics wavefront correction techniques of vortex beams. Infrared and Laser Engineering, 46, 0201001(2017).
[20] M Aftab, H J Choi, R G Liang, et al. Adaptive Shack-Hartmann wavefront sensor accommodating large wavefront variations. Optics Express, 26, 34428-34441(2018).
[21] S M Zhao, J Leach, L Y Gong, et al. Aberration corrections for free-space optical communications in atmosphere turbulence using Orbital Angular Momentum states. Optics Express, 20, 452-461(2012).
[22] L J Hu, S W Hu, W Gong, et al. Learning-based Shack-Hartmann wavefront sensor for high-order aberration detection. Optics Express, 27, 33504-33517(2019).
[23] M Li, Y Li, J Han, et al. Gerchberg–Saxton algorithm based phase correction in optical wireless communication. Physical Communication, 25, 323-327(2017).
[24] S Fu, S Zhang, T Wang, et al. Pre-turbulence compensation of orbital angular momentum beams based on a probe and the Gerchberg-Saxton algorithm. Optics Letters, 41, 3185-3188(2016).
[25] G Xie, Y Ren, H Huang, et al. Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm. Optics Letters, 40, 1197-1200(2015).
[26] Z L Xie, H T Ma, X J He, et al. Adaptive piston correction of sparse aperture systems with stochastic parallel gradient descent algorithm. Optics Express, 26, 9541-9551(2018).
[27] Ping Yang, Bing Xu, Wenhan Jiang, et al. Study of a genetic algorithm used in an adaptive optical system. Acta Optica Sinica, 27, 1628-1632(2007).
[28] Zhan Yu, Haotong Ma, Shaojun Du. Adaptive near-field beam shaping based on simulated annealing algorithm. Acta Optica Sinica, 31, 163-167(2011).
[29] J Li, M Zhang, D S Wang, et al. Joint atmospheric turbulence detection and adaptive demodulation technique using the CNN for the OAM-FSO communication. Optics Express, 26, 10494-10508(2018).
[30] Q H Tian, Z Li, K Hu, et al. Turbo-coded 16-ary OAM shift keying FSO communication system combining the CNN-based adaptive demodulator. Optics Express, 26, 27849-27864(2018).
[31] R G Lane, M Tallon. Wave-front reconstruction using a Shack-Hartmann. Applied Optics, 31, 6902-6906(1992).
[32] Zhao S M, Leach J, Zheng B Y. Crection effect of SharkHartmann algithm on turbulence aberrations f free space optical communications using bital angular momentum[C]International Conference on Communication Technology Proceedings, ICCT, 2010: 580583.
[33] Y Ren, G Xie, H Huang, et al. Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence. Optics Letters, 39, 2845-2848(2014).
[34] M A Vorontsov, V P Sivokon. Stochastic-parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction. Journal of the Optical Society of America A, 15, 2745-2758(1998).
[35] Wang Xiayao. Research on adaptive optics crection technology of vtex beam[D]. Xi''an: Xi''an University of Technology, 2018. (in Chinese)
[36] Yin X L, Lin J L, Chang H, et al. A new version of Stochasticparallelgradientdescent algithm (SPGD) f phase crection of a distted bital angular momentum (OAM) beam[C]Proceedings of the SPIE, 2018: 106973B.
[37] Y LeCun, Y Bengio, G Hinton. Deep learning. Nature, 521, 436-444(2015).
[38] T Doster, A T Watnik. Machine learning approach to OAM beam demultiplexing via convolutional neural networks. Applied Optics, 56, 3386-3396(2017).
[39] Q H Tian, C D Lu, B Liu, et al. DNN-based aberration correction in a wavefront sensorless adaptive optics system. Optics Express, 27, 10765-10776(2019).
[40] H M Ma, H Q Liu, Y Qiao, et al. Numerical study of adaptive optics compensation based on Convolutional Neural Networks. Optics Communications, 433, 283-289(2019).
[41] J M Liu, P P Wang, X K Zhang, et al. Deep learning based atmospheric turbulence compensation for orbital angular momentum beam distortion and communication. Optics Express, 27, 16671-16688(2019).
[42] Y W Zhai, S Y Fu, J Q Zhang, et al. Turbulence aberration correction for vector vortex beams using deep neural networks on experimental data. Optics Express, 28, 7515-7527(2020).
[43] Y Zhao, A Wang, L Zhu, et al. Performance evaluation of underwater optical communications using spatial modes subjected to bubbles and obstructions. Optics Letters, 42, 4699-4702(2017).
[44] B Cochenour, K Morgan, K Miller, et al. Propagation of modulated optical beams carrying orbital angular momentum in turbid water. Applied Optics, 55, C34-C38(2016).
[45] J Baghdady, K Miller, K Morgan, et al. Multi-gigabit/s underwater optical communication link using orbital angular momentum multiplexing. Optics Express, 24, 9794-9805(2016).
[46] Tianxing Yang, Shengmei Zhao. Random phase screen model of ocean turbulence. Acta Optica Sinica, 37, 1201001(2017).
[47] S X Pan, L Wang, W N Wang, et al. An effective way for simulating oceanic turbulence channel on the beam carrying orbital angular momentum. Scientific Reports, 9, 14009(2019).
[48] H C Zhan, L Wang, W N Wang, et al. Experimental analysis of adaptive optics correction methods on the beam carrying orbital angular momentum mode through oceanic turbulence. Optik, 240, 166990(2021).