Detection of high-resolution high-bandwidth fractional vortex beams under atmospheric turbulence

doi:10.3969/j.issn.1000-5641.2025.03.007

Abstract

Abstract:

In this study, a high-resolution fractional hybrid vortex beam is proposed. The hybrid scaling parameter $n $ used to generate the fractional hybrid vortex beam provides new degrees of freedom, extending the bandwidth of orbital angular momentum. The convolutional neural network from deep learning was adopted to accurately recognize the fractional hybrid vortex beam with an orbital angular momentum resolution $\Delta l $ of 0.1 and hybrid scaling parameter resolution $\Delta n $ of 0.01 under atmospheric turbulence conditions. The study investigated the effects of turbulence intensity and transmission distance on recognition accuracy. The results indicate that at a transmission distance of 150 m, the recognition accuracy reaches 82.09%, even under strong turbulence ($C_n^2 $ = 5×10^–14 m^–2/3). The recognition accuracy exceeded 99% under the conditions of medium and weak turbulence ($C_n^2 $ = 1×10^–14 m^–2/3 and 5×10^–15 m^–2/3, respectively). This scheme provides a reference for the accurate identification of fractional orbital angular momentum in turbulent environments.

Key words: vortex beam, fractional orbital angular momentum, atmospheric turbulence, deep learning

CLC Number:

O436

Luping CAO, Yong XIA. Detection of high-resolution high-bandwidth fractional vortex beams under atmospheric turbulence[J]. J* E* C* N* U* N* S*, 2025, 2025(3): 51-60.

Figures/Tables 8

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

References 33

1	ALLEN L, BEIJERSBERGEN M W, SPREEUW R J C, et al.. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Physical Review A, 1992, 45 (11): 8185- 8189.
2	ZHOU Z Y, DING D S, JIANG Y K, et al.. Orbital angular momentum light frequency conversion and interference with quasi-phase matching crystals. Optics Express, 2014, 22 (17): 20298- 20310.
3	PADGETT M, BOWMAN R.. Tweezers with twist. Nature Photonics, 2011, 5 (6): 343- 348.
4	MAIR A, VAZIRI A, WEIHS G, et al.. Entanglement of the orbital angular momentum states of photons. Nature, 2001, 412 (6844): 313- 316.
5	PATERSON C.. Atmospheric turbulence and orbital angular momentum of single photons for optical communication. Physics Review Letters, 2005, 94 (15): 153901.
6	BOZINOVIC N, YUE Y, REN Y X, et al.. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science, 2013, 340 (6140): 1545- 1548.
7	HUANG H, MILIONE G, LAVERY M P J, et al.. Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre. Scientific Reports, 2015, 5 (1): 14931.
8	HUANG H, XIE G D, YAN Y, et al.. 100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength. Optics Letters, 2014, 39 (2): 197- 200.
9	LEACH J, PADGETT M J, BARNETT S M, et al.. Measuring the orbital angular momentum of a single photon. Physics Review Letters, 2002, 88 (25): 257901.
10	LI P Y, WANG B, SONG X B, et al.. Non-destructive identification of twisted light. Optics Letters, 2016, 41 (7): 1574- 1577.
11	ZHOU H L, SHI L, ZHANG X L, et al.. Dynamic interferometry measurement of orbital angular momentum of light. Optics Letters, 2014, 39 (20): 6058- 6061.
12	HICKMANN J M, FONSECA E J S, SOARES W C, et al.. Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum. Physics Review Letters, 2010, 105 (5): 053904.
13	GHAI D P, SENTHILKUMARAN P, SIROHI R S.. Single-slit diffraction of an optical beam with phase singularity. Optics and Lasers in Engineering, 2009, 47 (1): 123- 126.
14	RASOULI S, FATHOLLAZADE S, AMIRI P.. Simple, efficient and reliable characterization of Laguerre-Gaussian beams with non-zero radial indices in diffraction from an amplitude parabolic-line linear grating. Optics Express, 2021, 29 (19): 29661- 29675.
15	DOSTER T, WATNIK A T.. Machine learning approach to OAM beam demultiplexing via convolutional neural networks. Applied Optics, 2017, 56 (12): 3386- 3396.
16	LOHANI S, GLASSER R T.. Turbulence correction with artificial neural networks. Optics Letters, 2018, 43 (11): 2611- 2614.
17	LIU Z W, YAN S, LIU H G, et al.. Superhigh-resolution recognition of optical vortex modes assisted by a deep-learning method. Physics Review Letters, 2019, 123 (18): 183902.
18	MAO Z X, YU H Y, XIA M, et al.. Broad bandwidth and highly efficient recognition of optical vortex modes achieved by the neural network approach. Physics Review Applied, 2020, 13 (3): 034063.
19	ZHANG N, DAVIS J A, MORENO I, et al.. Analysis of fractional vortex beams using a vortex grating spectrum analyzer. Applied Optics, 2010, 49 (13): 2456- 2462.
20	HUANG H C, LIN Y T, SHIH M F.. Measuring the fractional orbital angular momentum of a vortex light beam by cascaded Mach–Zehnder interferometers. Optics Communications, 2012, 285 (4): 383- 388.
21	ZHU J, ZHANG P, FU D Z, et al.. Probing the fractional topological charge of a vortex light beam by using dynamic angular double slits. Photonics Research, 2016, 4 (5): 187- 190.
22	DENG D, LIN M C, Li Y, et al.. Precision measurement of fractional orbital angular momentum. Physical Review Applied, 2019, 12 (1): 014048.
23	NA Y, KO D K.. Deep-learning-based high-resolution recognition of fractional-spatial-mode-encoded data for free-space optical communications. Scientific Reports, 2021, 11 (1): 2678.
24	JING G Q, CHEN L Z, WANG P P, et al.. Recognizing fractional orbital angular momentum using feed forward neural network. Results in Physics, 2021, 28, 104619.
25	NA Y, KO D K.. Adaptive demodulation by deep learning based identification of fractional orbital angular momentum modes with structural distortion due to atmospheric turbulence. Scientific Reports, 2021, 11 (1): 23505.
26	ZHOU J W, YIN Y L, TANG J H, et al.. Recognition of high-resolution optical vortex modes with deep residual learning. Physical Review A, 2022, 106 (1): 013519.
27	TIAN Q H, LI Z, HU K, et al.. Turbo-coded 16-ary OAM shift keying FSO communication system combining the CNN-based adaptive demodulator. Optics Express, 2018, 26 (21): 27849- 27864.
28	CAO M, YIN Y L, ZHOU J W, et al.. Machine learning based accurate recognition of fractional optical vortex modes in atmospheric environment. Applied Physics Letters, 2021, 119 (14): 141103.
29	GOPAUL C, ANDREW R.. The effect of atmospheric turbulence on entangled orbital angular momentum states. New Journal of Physics, 2007, 9 (4): 94.
30	ZHAO S M, LEACH J, GONG L Y, et al.. Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states. Optics Express, 2012, 20 (1): 452- 461.
31	ANDREWS L C.. An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere. Journal of Modern Optics, 1992, 39 (9): 1849- 1853.
32	高春清, 付时尧. 涡旋光束[M]. 北京: 清华大学出版社, 2019: 205.
33	XIE S N, GIRSHICK R, DOLLAR P, et al. Aggregated Residual Transformations for deep neural networks [C]// Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 2017: 1492-1500.

[1]	Caidie HUANG, Xinping WANG, Liangyu CHEN, Yong LIU. Research on a knowledge tracking model based on the stacked gated recurrent unit residual network [J]. Journal of East China Normal University(Natural Science), 2022, 2022(6): 68-78.
[2]	Yilin MA, Huiling TAO, Qiwen DONG, Ye WANG. Prediction of remaining useful life of aeroengines based on the Transformer with multi-feature fusion [J]. Journal of East China Normal University(Natural Science), 2022, 2022(5): 219-232.
[3]	Zejie WANG, Chaomin SHEN, Chun ZHAO, Xinmei LIU, Jie CHEN. Recognition of classroom learning behaviors based on the fusion of human pose estimation and object detection [J]. Journal of East China Normal University(Natural Science), 2022, 2022(2): 55-66.
[4]	Bo LIU, Xiaodong BAI, Gengxin ZHANG, Jun SHEN, Jidong XIE, Laiding ZHAO, Tao HONG. Review of deep learning in cognitive radio [J]. Journal of East China Normal University(Natural Science), 2021, 2021(1): 36-52.
[5]	ZHANG Xu, HUANG Dingjiang. Defect detection on aluminum surfaces based on deep learning [J]. Journal of East China Normal University(Natural Science), 2020, 2020(6): 105-114.
[6]	HAN Chengcheng, LI Lei, LIU Tingting, GAO Ming. Approaches for semantic textual similarity [J]. Journal of East China Normal University(Natural Science), 2020, 2020(5): 95-112.
[7]	YANG Kang, HANG Ding-jiang, GAO Ming. A review of machine reading comprehension for automatic QA [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(5): 36-52.
[8]	CHEN Yuan-zhe, KUANG Jun, LIU Ting-ting, GAO Ming, ZHOU Ao-ying. A survey on coreference resolution [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(5): 16-35.
[9]	LIU Heng-yu, ZHANG Tian-cheng, WU Pei-wen, YU Ge. A review of knowledge tracking [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(5): 1-15.
[10]	YE Jian, ZHAO Hui. A public opinion analysis model based on Danmu data monitoring and sentiment classification [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(3): 86-100.
[11]	YUAN Pei-sen, ZHANG Yong, LI Mei-ling, GU Xing-jian. Research on trademark image retrieval based on deep Hashing [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(5): 172-182.
[12]	YU Ruo-nan, HUANG Ding-jiang, DONG Qi-wen. Survey on scene text detection based on deep learning [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(5): 1-16.