1. State key laboratory of precision spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China 2. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China 3. NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai 200062, China
Orbital angular momentums (OAMs) greatly enhance the channel capacity in free-space optical communication. However, demodulation of superposed OAM to recognize them separately is always difficult, especially upon multiplexing more OAMs. In this work, we report a directly recognition of multiplexed fractional OAM modes, without separating them, at a resolution of 0.1 with high accuracy, using a multi-task deep learning (MTDL) model, which has not been reported before. Namely, two-mode, four-mode, and eight-mode superposed OAM beams, experimentally generated with a hologram carrying both phase and amplitude information, are well recognized by the suitable MTDL model. Two applications in information transmission are presented: the first is for 256-ary OAM shift keying via multiplexed fractional OAMs; the second is for OAM division multiplexed information transmission in an eightfold speed. The encouraging results will expand the capacity in future free-space optical communication.
E. Willner A. , Huang H. , Yan Y. , Ren Y. , Ahmed N. , Xie G. , Bao C. , Li L. , Cao Y. , Zhao Z. , Wang J. , P. J. Lavery M. , Tur M. , Ramachandran S. , F. Molisch A. , Ashrafi N. , Ashrafi S. . Optical communications using orbital angular momentum beams. Adv. Opt. Photonics, 2015, 7(1): 66 https://doi.org/10.1364/AOP.7.000066
2
Rubinsztein-Dunlop H. , Forbes A. , V. Berry M. , R. Dennis M. , L. Andrews D. , Mansuripur M. , Denz C. , Alpmann C. , Banzer P. , Bauer T. , Karimi E. , Marrucci L. , Padgett M. , Ritsch-Marte M. , M. Litchinitser N. , P. Bigelow N. , Rosales-Guzmán C. , Belmonte A. , P. Torres J. , W. Neely T. , Baker M. , Gordon R. , B. Stilgoe A. , Romero J. , G. White A. , Fickler R. , E. Willner A. , Xie G. , McMorran B. , M. Weiner A. . Roadmap on structured light. J. Opt., 2017, 19(1): 013001 https://doi.org/10.1088/2040-8978/19/1/013001
3
Allen L. , Beijersbergen M. , Spreeuw R. , Woerdman J. . Orbital angular momentum of light and transformation of Laguerre‒Gaussian laser modes. Phys. Rev. A, 1992, 45(11): 8185 https://doi.org/10.1103/PhysRevA.45.8185
J. Padgett M., Orbital angular momentum 25 years on, Opt. Express 25(10), 11265 (2017) (Invited)
6
J. Shen Y. , J. Wang X. , W. Xie Z. , J. Min C. , Fu X. , Liu Q. , L. Gong M. , C. Yuan X. . Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. Light Sci. Appl., 2019, 8(1): 90 https://doi.org/10.1038/s41377-019-0194-2
7
Forbes A. , Ramachandran S. , W. Zhan Q. . Photonic angular momentum: Progress and perspectives. Nanophotonics, 2022, 11(4): 625 https://doi.org/10.1515/nanoph-2022-0035
8
J. Li S. , Y. Li Z. , S. Huang G. , B. Liu X. , Q. Li R. , Y. Cao X. . Digital coding transmissive metasurface for multi-OAM-beam. Front. Phys., 2022, 17(6): 62501 https://doi.org/10.1007/s11467-022-1179-9
9
Jin L. , W. Huang Y. , W. Jin Z. , C. Devlin R. , G. Dong Z. , T. Mei S. , H. Jiang M. , T. Chen W. , Wei Z. , Liu H. , H. Teng J. , Danner A. , P. Li X. , M. Xiao S. , Zhang S. , Y. Yu C. , K. W. Yang J. , Capasso F. , W. Qiu C. . Dielectric multi-momentum meta-transformer in the visible. Nat. Commun., 2019, 10(1): 4789 https://doi.org/10.1038/s41467-019-12637-0
10
Y. Fang X. , J. Wang H. , C. Yang H. , L. Ye Z. , M. Wang Y. , Zhang Y. , P. Hu X. , N. Zhu S. , Xiao M. . Multichannel nonlinear holography in a two-dimensional nonlinear photonic crystal. Phys. Rev. A, 2020, 102(4): 043506 https://doi.org/10.1103/PhysRevA.102.043506
11
J. Guo J. , P. Zhang Y. , Ye H. , Y. Wang L. , C. Chen P. , J. Mao D. , Z. Xie C. , H. Chen Z. , W. Wu X. , Xiao M. , Zhang Y. . Spatially structured-mode multiplexing holography for high-capacity security encryption. ACS Photonics, 2023, 10(3): 757 https://doi.org/10.1021/acsphotonics.2c01943
12
E. Willner A. , Zhao Z. , Liu C. , Zhang R. , Song H. , Pang K. , Manukyan K. , Song H. , Su X. , Xie G. , Ren Y. , Yan Y. , Tur M. , F. Molisch A. , W. Boyd R. , Zhou H. , Hu N. , Minoofar A. , Huang H. . Perspectives on advances in high-capacity, free-space communications using multiplexing of orbital-angular-momentum beams. APL Photonics, 2021, 6(3): 030901 https://doi.org/10.1063/5.0031230
13
Lin J. , C. Yuan X. , H. Tao S. , E. Burge R. . Multiplexing free-space optical signals using superimposed collinear orbital angular momentum states. Appl. Opt., 2007, 46(21): 4680 https://doi.org/10.1364/AO.46.004680
14
Wang J. , Y. Yang J. , M. Fazal I. , Ahmed N. , Yan Y. , Huang H. , X. Ren Y. , Yue Y. , Dolinar S. , Tur M. , E. Willner A. . Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics, 2012, 6(7): 488 https://doi.org/10.1038/nphoton.2012.138
15
Bozinovic N. , Yue Y. , Ren Y. , Tur M. , Kristensen P. , Huang H. , E. Willner A. , Ramachandran S. . Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science, 2013, 340(6140): 1545 https://doi.org/10.1126/science.1237861
16
Vallone G. , D’Ambrosio V. , Sponselli A. , Slussarenko S. , Marrucci L. , Sciarrino F. , Villoresi P. . Free-space quantum key distribution by rotation-invariant twisted photons. Phys. Rev. Lett., 2014, 113(6): 060503 https://doi.org/10.1103/PhysRevLett.113.060503
17
Huang H.Xie G.Yan Y.Ahmed N.Ren Y.Yue Y.Rogawski D.J. Willner M.I. Erkmen B.M. Birnbaum K.J. Dolinar S.P. J. Lavery M.J. Padgett M.Tur M.E. Willner A., 100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wave-length, Opt. Lett. 39(2), 197 (2014)
18
Krenn M. , Fickler R. , Fink M. , Handsteiner J. , Malik M. , Scheidl T. , Ursin R. , Zeilinger A. . Communication with spatially modulated light through turbulent air across Vienna. New J. Phys., 2014, 16(11): 113028 https://doi.org/10.1088/1367-2630/16/11/113028
19
J. Willner A. , Ren Y. , Xie G. , Zhao Z. , Cao Y. , Li L. , Ahmed N. , Wang Z. , Yan Y. , Liao P. , Liu C. , Mirhosseini M. , W. Boyd R. , Tur M. , E. Willner A. . Experimental demonstration of 20 Gbit/s data encoding and 2 ns channel hopping using orbital angular momentum modes. Opt. Lett., 2015, 40(24): 5810 https://doi.org/10.1364/OL.40.005810
20
Krenn M. , Handsteiner J. , Fink M. , Fickler R. , Ursin R. , Malik M. , Zeilinger A. . Twisted light transmission over 143 km. Proc. Natl. Acad. Sci. USA, 2016, 113(48): 13648 https://doi.org/10.1073/pnas.1612023113
21
Zhang H. , Zeng J. , Y. Lu X. , Y. Wang Z. , L. Zhao C. , J. Cai Y. . Review on fractional vortex beam. Nanophotonics, 2022, 11(2): 241 https://doi.org/10.1515/nanoph-2021-0616
22
W. Liu Z. , Yan S. , G. Liu H. , F. Chen X. . Superhigh-resolution recognition of optical vortex modes assisted by a deep-learning method. Phys. Rev. Lett., 2019, 123(18): 183902 https://doi.org/10.1103/PhysRevLett.123.183902
23
Na Y. , K. Ko D. . Adaptive demodulation by deep-learning-based identification of fractional orbital angular momentum modes with structural distortion due to atmospheric turbulence. Sci. Rep., 2021, 11(1): 23505 https://doi.org/10.1038/s41598-021-03026-z
24
Leach J. , Padgett M. , Barnett S. , Franke-Arnold S. , Courtial J. . Measuring the orbital angular momentum of a single photon. Phys. Rev. Lett., 2002, 88(25): 257901 https://doi.org/10.1103/PhysRevLett.88.257901
25
Berkhout G. , Lavery M. , Courtial J. , Beijersbergen M. , Padgett M. . Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett., 2010, 105(15): 153601 https://doi.org/10.1103/PhysRevLett.105.153601
26
Mirhosseini M. , Malik M. , Shi Z. , Boyd R. . Efficient separation of the orbital angular momentum eigenstates of light. Nat. Commun., 2013, 4(1): 2781 https://doi.org/10.1038/ncomms3781
27
H. Wen Y. , Chremmos I. , J. Chen Y. , B. Zhu J. , F. Zhang Y. , Y. Yu S. . Spiral transformation for high-resolution and efficient sorting of optical vortex modes. Phys. Rev. Lett., 2018, 120(19): 193904 https://doi.org/10.1103/PhysRevLett.120.193904
28
Gibson G. , Courtial J. , J. Padgett M. , Vasnetsov M. , Pas’ko V. , M. Barnett S. , Franke-Arnold S. . Free-space information transfer using light beams carrying orbital angular momentum. Opt. Express, 2004, 12(22): 5448 https://doi.org/10.1364/OPEX.12.005448
29
Doster T. , T. Watnik A. . Machine learning approach to OAM beam demultiplexing via convolutional neural networks. Appl. Opt., 2017, 56(12): 3386 https://doi.org/10.1364/AO.56.003386
30
Lohani S. , M. Knutson E. , O’Donnell M. , D. Huver S. , T. Glasser R. . On the use of deep neural networks in optical communications. Appl. Opt., 2018, 57(15): 4180 https://doi.org/10.1364/AO.57.004180
31
Park S. , Cattell L. , Nichols J. , Watnik A. , Doster T. , Rohde G. . De-multiplexing vortex modes in optical communications using transport-based pattern recognition. Opt. Express, 2018, 26(4): 4004 https://doi.org/10.1364/OE.26.004004
32
Li J. , Zhang M. , S. Wang D. . Adaptive demodulator using machine learning for orbital angular momentum shift keying. IEEE Photonics Technol. Lett., 2017, 29(17): 1455 https://doi.org/10.1109/LPT.2017.2726139
33
S. Zhao Q. , Q. Hao S. , Wang Y. , Wang L. , F. Wan X. , L. Xu C. . Mode detection of misaligned orbital angular momentum beams based on convolutional neural network. Appl. Opt., 2018, 57(35): 10152 https://doi.org/10.1364/AO.57.010152
34
Lohani S. , T. Glasser R. . Turbulence correction with artificial neural networks. Opt. Lett., 2018, 43(11): 2611 https://doi.org/10.1364/OL.43.002611
35
H. Tian Q. , Li Z. , Hu K. , Zhu L. , L. Pan X. , Zhang Q. , J. Wang Y. , Tian F. , L. Yin X. , J. Xin X. . Turbo-coded 16-ary OAM shift keying FSO communication system combining the CNN-based adaptive demodulator. Opt. Express, 2018, 26(21): 27849 https://doi.org/10.1364/OE.26.027849
36
Li J. , Zhang M. , S. Wang D. , J. Wu S. , Y. Zhan Y. . Joint atmospheric turbulence detection and adaptive demodulation technique using the CNN for the OAM‒FSO communication. Opt. Express, 2018, 26(8): 10494 https://doi.org/10.1364/OE.26.010494
37
Z. Shi Y. , H. Ma Z. , Y. Chen H. , G. Ke Y. , Chen Y. , X. Zhou X. . High-resolution recognition of FOAM modes via an improved EfficientNet V2 based convolutional neural network. Front. Phys., 2024, 19(3): 32205 https://doi.org/10.1007/s11467-023-1373-4
38
Luan H.Lin D.Li K.Meng W.Gu M.Fang X., 768-ary Laguerre‒Gaussian-mode shift keying free-space optical communication based on convolutional neural networks, Opt. Express 29(13), 19807 (2021)
39
Maurer A. , Pontil M. , Paredes B. . The benefit of multitask representation learning. J. Mach. Learn. Res., 2016, 17(1): 2853 https://doi.org/10.5555/2946645.3007034
40
X. Mao Z. , Y. Yu H. , Xia M. , Z. Pan S. , Wu D. , L. Yin Y. , Xia Y. , P. Yin J. . Broad bandwidth and highly efficient recognition of optical vortex modes achieved by the neural-network approach. Phys. Rev. Appl., 2020, 13(3): 034063 https://doi.org/10.1103/PhysRevApplied.13.034063
41
Davis J. , Cottrell D. , Campos J. , Yzuel M. , Moreno I. . Encoding amplitude information onto phase-only filters. Appl. Opt., 1999, 38(23): 5004 https://doi.org/10.1364/AO.38.005004
42
Bolduc E. , Bent N. , Santamato E. , Karimi E. , W. Boyd R. . Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram. Opt. Lett., 2013, 38(18): 3546 https://doi.org/10.1364/OL.38.003546
43
Thung K.Wee C., A brief review on multi-task learning, Multimedia Tools Appl. 77(22), 29705 (2018)
Szegedy C.Wei L.Yangqing J.Sermanet P.Reed S.Anguelov D.Erhan D.Vanhoucke V.Rabinovich A., Going deeper with convolutions, in: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA, 1 (2015)
46
Xie S.B. Girshick R.Dollár P.Tu Z.He K., Aggregated residual transformations for deep neural networks, in: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA, 5987 (2017)
47
Collobert R.Weston J., A unified architecture for natural language processing: deep neural networks with multitask learning, in: Proceedings of the 25th International Conference on Machine Learning, Association for Computing Machinery: Helsinki, Finland, 160–167 (2008)
48
Cui X. , Zhang W. , Finkler U. , Saon G. , Picheny M. , Kung D. . Distributed training of deep neural network acoustic models for automatic speech recognition: A comparison of current training strategies. IEEE Signal Process. Mag., 2020, 37(3): 39 https://doi.org/10.1109/MSP.2020.2969859
49
B. Girshick R.C. N. N. Fast R., IEEE International Conference on Computer Vision (ICCV), 1440 (2015)
50
L. Li B. , T. Luan H. , Y. Li K. , Y. Chen Q. , J. Meng W. , Cheng K. , Gu M. , Y. Fang X. . Orbital angular momentum optical communications enhanced by artificial intelligence. J. Opt., 2022, 24(9): 094003 https://doi.org/10.1088/2040-8986/ac8108
51
S. Wan Z. , Wang H. , Liu Q. , Fu X. , J. Shen Y. . Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics, 2023, 10(7): 2149 https://doi.org/10.1021/acsphotonics.2c01640
