Dual-Output Mode Analysis of Multimode Laguerre-Gaussian Beams via Deep Learning
Abstract
:1. Introduction
2. Materials and Methods
3. Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Service, R.F. Light Beams With a Twist Could Give a Turbo Boost to Fiber-Optic Cables. Science 2013, 340, 1513. [Google Scholar] [CrossRef]
- Allen, L.; Beijersbergen, M.W.; Spreeuw, R.J.C.; Woerdman, J.P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 1992, 45, 8185–8189. [Google Scholar] [CrossRef]
- Peng, J.; Zhang, L.; Zhang, K.; Ma, J. Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence. Opt. Commun. 2018, 418, 32–36. [Google Scholar] [CrossRef]
- Du, J.; Wang, J. High-dimensional structured light coding/decoding for free-space optical communications free of obstructions. Opt. Lett. 2015, 40, 4827–4830. [Google Scholar] [CrossRef] [PubMed]
- Wang, A.; Zhu, L.; Chen, S.; Du, C.; Mo, Q.; Wang, J. Characterization of LDPC-coded orbital angular momentum modes transmission and multiplexing over a 50-km fiber. Opt. Express 2016, 24, 11716–11726. [Google Scholar] [CrossRef] [PubMed]
- Gu, B.; Hu, Y.; Zhang, X.; Li, M.; Zhu, Z.; Rui, G.; He, J.; Cui, Y. Angular momentum separation in focused fractional vector beams for optical manipulation. Opt. Express 2021, 29, 14705–14719. [Google Scholar] [CrossRef]
- Bobkova, V.; Stegemann, J.; Droop, R.; Otte, E.; Denz, C. Optical grinder: Sorting of trapped particles by orbital angular momentum. Opt. Express 2021, 29, 12967–12975. [Google Scholar] [CrossRef] [PubMed]
- 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, 060503. [Google Scholar] [CrossRef] [Green Version]
- Cozzolino, D.; Bacco, D.; Da Lio, B.; Ingerslev, K.; Ding, Y.; Dalgaard, K.; Kristensen, P.; Galili, M.; Rottwitt, K.; Ramachandran, S.; et al. Orbital Angular Momentum States Enabling Fiber-based High-dimensional Quantum Communication. Phys. Rev. Appl. 2019, 11, 064058. [Google Scholar] [CrossRef] [Green Version]
- Bozinovic, N.; Yue, Y.; Ren, Y.; Tur, M.; Kristensen, P.; Huang, H.; Willner, A.E.; Ramachandran, S. Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers. Science 2013, 340, 1545–1548. [Google Scholar] [CrossRef] [Green Version]
- Willner, A.E.; Li, L.; Xie, G.; Ren, Y.; Huang, H.; Yue, Y.; Ahmed, N.; Willner, M.J.; Willner, A.J.; Yan, Y.; et al. Orbital-angular-momentum-based reconfigurable optical switching and routing. Photon Res. 2016, 4, B5–B8. [Google Scholar] [CrossRef] [Green Version]
- Wang, A.; Zhu, L.; Wang, L.; Ai, J.; Chen, S.; Wang, J. Directly using 8.8-km conventional multi-mode fiber for 6-mode orbital angular momentum multiplexing transmission. Opt. Express 2018, 26, 10038–10047. [Google Scholar] [CrossRef] [PubMed]
- Turunen, J.; Tervonen, E.; Friberg, A.T. Coherence theoretic algorithm to determine the transverse-mode structure of lasers. Opt. Lett. 1989, 14, 627–629. [Google Scholar] [CrossRef]
- Tervonen, E.; Turunen, J.; Friberg, A.T. Transverse laser-mode structure determination from spatial coherence measurements: Experimental results. Appl. Phys. B 1989, 49, 409–414. [Google Scholar] [CrossRef]
- Cutolo, A.; Isernia, T.; Izzo, I.; Pierri, R.; Zeni, L. Transverse mode analysis of a laser beam by near- and far-field intensity measurements. Appl. Opt. 1995, 34, 7974–7978. [Google Scholar] [CrossRef] [PubMed]
- Xue, X.; Wei, H.; Kirk, A.G. Intensity-based modal decomposition of optical beams in terms of Hermite–Gaussian functions. J. Opt. Soc. Am. A 2000, 17, 1086–1091. [Google Scholar] [CrossRef]
- Wang, K.; Dou, J.; Kemao, Q.; Di, J.; Zhao, J. Y-Net: A one-to-two deep learning framework for digital holographic reconstruction. Opt. Lett. 2019, 44, 4765–4768. [Google Scholar] [CrossRef]
- Liu, A.; Lin, T.; Han, H.; Zhang, X.; Chen, Z.; Gan, F.; Lv, H.; Liu, X. Analyzing modal power in multi-mode waveguide via machine learning. Opt. Express 2018, 26, 22100–22109. [Google Scholar] [CrossRef]
- Wang, H.; Lyu, M.; Situ, G. eHoloNet: A learning-based end-to-end approach for in-line digital holographic reconstruction. Opt. Express 2018, 26, 22603–22614. [Google Scholar] [CrossRef]
- Lyu, M.; Wang, W.; Wang, H.; Wang, H.; Li, G.; Chen, N.; Situ, G. Deep-learning-based ghost imaging. Sci. Rep. 2017, 7, 17865. [Google Scholar] [CrossRef]
- Lohani, S.; Knutson, E.M.; O’donnell, M.; Huver, S.D.; Glasser, R.T. On the use of deep neural networks in optical communications. Appl. Opt. 2018, 57, 4180–4190. [Google Scholar] [CrossRef]
- Liu, Z.; Yan, S.; Liu, H.; Chen, X. Superhigh-Resolution Recognition of Optical Vortex Modes Assisted by a Deep-Learning Method. Phys. Rev. Lett. 2019, 123, 183902. [Google Scholar] [CrossRef] [PubMed]
- Park, S.R.; Cattell, L.; Nichols, J.M.; Watnik, A.; Doster, T.; Rohde, G.K. De-multiplexing vortex modes in optical communications using transport-based pattern recognition. Opt. Express 2018, 26, 4004–4022. [Google Scholar] [CrossRef]
- Doster, T.; Watnik, A.T. Machine learning approach to OAM beam demultiplexing via convolutional neural networks. Appl. Opt. 2017, 56, 3386–3396. [Google Scholar] [CrossRef] [PubMed]
- Bekerman, A.; Froim, S.; Hadad, B.; Bahabad, A. Beam profiler network (BPNet): A deep learning approach to mode demultiplexing of Laguerre–Gaussian optical beams. Opt. Lett. 2019, 44, 3629–3632. [Google Scholar] [CrossRef]
- Zhao, Q.; Hao, S.; Wang, Y.; Wang, L.; Wan, X.; Xu, C. Mode detection of misaligned orbital angular momentum beams based on convolutional neural network. Appl. Opt. 2018, 57, 10152–10158. [Google Scholar] [CrossRef] [PubMed]
- Li, J.; Zhang, M.; Wang, D.; Wu, S.; Zhan, Y. Joint atmospheric turbulence detection and adaptive demodulation technique using the CNN for the OAM-FSO communication. Opt. Express 2018, 26, 10494–10508. [Google Scholar] [CrossRef] [PubMed]
- Liu, J.; Wang, P.; Zhang, X.; He, Y.; Zhou, X.; Ye, H.; Li, Y.; Xu, S.; Chen, S.; Fan, D. Deep learning based atmospheric turbulence compensation for orbital angular momentum beam distortion and communication. Opt. Express 2019, 27, 16671–16688. [Google Scholar] [CrossRef]
- Cui, X.; Yin, X.; Chang, H.; Liao, H.; Chen, X.; Xin, X.; Wang, Y. Experimental study of machine-learning-based orbital angular momentum shift keying decoders in optical underwater channels. Opt. Commun. 2019, 452, 116–123. [Google Scholar] [CrossRef]
- Courtial, J.; Padgett, M.J. Performance of a cylindrical lens mode converter for producing Laguerre–Gaussian laser modes. Opt. Commun. 1999, 159, 13–18. [Google Scholar] [CrossRef]
- Hall, D.G. Vector-beam solutions of Maxwell’s wave equation. Opt. Lett. 1996, 21, 9–11. [Google Scholar] [CrossRef] [PubMed]
- Krizhevsky, A.; Sutskever, I.; Hinton, G.E. ImageNet classification with deep convolutional neural networks. Commun. ACM 2017, 60, 84–90. [Google Scholar] [CrossRef]
- Kwan, H.K. Simple sigmoid-like activation function suitable for digital hardware implementation. Electron. Lett. 1992, 28, 1379–1380. [Google Scholar] [CrossRef]
- Lee Rodgers, J.; Nicewander, W.A. Thirteen Ways to Look at the Correlation Coefficient. Am. Stat. 1988, 42, 59–66. [Google Scholar] [CrossRef]
- An, Y.; Huang, L.; Li, J.; Leng, J.; Yang, L.; Zhou, P. Learning to decompose the modes in few-mode fibers with deep convolutional neural network. Opt. Express 2019, 27, 10127–10137. [Google Scholar] [CrossRef] [PubMed]
- Brüning, R.; Gelszinnis, P.; Schulze, C.; Flamm, D.; Duparré, M. Comparative analysis of numerical methods for the mode analysis of laser beams. Appl. Opt. 2013, 52, 7769–7777. [Google Scholar] [CrossRef] [PubMed]
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Yuan, X.; Xu, Y.; Zhao, R.; Hong, X.; Lu, R.; Feng, X.; Chen, Y.; Zou, J.; Zhang, C.; Qin, Y.; et al. Dual-Output Mode Analysis of Multimode Laguerre-Gaussian Beams via Deep Learning. Optics 2021, 2, 87-95. https://0-doi-org.brum.beds.ac.uk/10.3390/opt2020009
Yuan X, Xu Y, Zhao R, Hong X, Lu R, Feng X, Chen Y, Zou J, Zhang C, Qin Y, et al. Dual-Output Mode Analysis of Multimode Laguerre-Gaussian Beams via Deep Learning. Optics. 2021; 2(2):87-95. https://0-doi-org.brum.beds.ac.uk/10.3390/opt2020009
Chicago/Turabian StyleYuan, Xudong, Yaguang Xu, Ruizhi Zhao, Xuhao Hong, Ronger Lu, Xia Feng, Yongchuang Chen, Jincheng Zou, Chao Zhang, Yiqiang Qin, and et al. 2021. "Dual-Output Mode Analysis of Multimode Laguerre-Gaussian Beams via Deep Learning" Optics 2, no. 2: 87-95. https://0-doi-org.brum.beds.ac.uk/10.3390/opt2020009