Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning
Abstract
:1. Introduction
2. Concept and Principle of the Optical Encoding Model
3. SVMBased Decoding Method for Image Recognition and Classification
Algorithm 1 Pseudocode for decoding processing using an SVM–ECOC model 

4. Case Study
5. Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Support Vector Machine Algorithm
Type of SVM  Kernel  Description 

Base function (Gaussian)  $K\left({x}_{1},{x}_{2}\right)={e}^{\frac{{\u2225{x}_{1}{x}_{2}\u2225}^{2}}{2{\sigma}^{2}}}$  Learning of one class, where $\sigma $ represents the width of the kernel 
Linear  $K\left({x}_{1},{x}_{2}\right)={x}_{1}^{T}{x}_{2}$  Learning of two classes 
Polynomial  $K\left({x}_{1},{x}_{2}\right)={\left({x}_{1}^{T}{x}_{2}+1\right)}^{\rho}$  $\rho $ is the polynomial degree 
Sigmoid  $K\left({x}_{1},{x}_{2}\right)=\phantom{\rule{0ex}{0ex}}tanh\left({\beta}_{0}{x}_{1}^{T}{x}_{2}+{\beta}_{1}\right)$  The kernel is determined by specific ${\beta}_{0}$ and ${\beta}_{1}$ 
References
 Allen, L.; Beijersbergen, M.W.; Spreeuw, R.; Woerdman, J. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 1992, 45, 8185. [Google Scholar] [CrossRef] [PubMed]
 Lian, Y.; Qi, X.; Wang, Y.; Bai, Z.; Wang, Y.; Lu, Z. OAM beam generation in space and its applications: A review. Opt. Lasers Eng. 2022, 151, 106923. [Google Scholar] [CrossRef]
 Zhao, J.; Chremmos, I.D.; Song, D.; Christodoulides, D.N.; Efremidis, N.K.; Chen, Z. Curved singular beams for threedimensional particle manipulation. Sci. Rep. 2015, 5, 12086. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 Liu, K.; Cheng, Y.; Gao, Y.; Li, X.; Qin, Y.; Wang, H. Superresolution radar imaging based on experimental OAM beams. Appl. Phys. Lett. 2017, 110, 164102. [Google Scholar] [CrossRef]
 Wang, J.; Liu, K.; Cheng, Y.; Wang, H. Vortex SAR imaging method based on OAM beams design. IEEE Sensors J. 2019, 19, 11873–11879. [Google Scholar] [CrossRef]
 Wang, J. Twisted optical communications using orbital angular momentum. Sci. China Phys. Mech. Astron. 2019, 62, 34201. [Google Scholar] [CrossRef]
 Trichili, A.; RosalesGuzmán, C.; Dudley, A.; Ndagano, B.; Ben Salem, A.; Zghal, M.; Forbes, A. Optical communication beyond orbital angular momentum. Sci. Rep. 2016, 6, 27674. [Google Scholar] [CrossRef] [Green Version]
 Gong, L.; Zhao, Q.; Zhang, H.; Hu, X.Y.; Huang, K.; Yang, J.M.; Li, Y.M. Optical orbitalangularmomentummultiplexed data transmission under high scattering. Light Sci. Appl. 2019, 8, 27. [Google Scholar] [CrossRef] [Green Version]
 Zhao, Q.; Yu, P.P.; Liu, Y.F.; Wang, Z.Q.; Li, Y.M.; Gong, L. Light field imaging through a single multimode fiber for OAMmultiplexed data transmission. Appl. Phys. Lett. 2020, 116, 181101. [Google Scholar] [CrossRef]
 Kai, C.; Feng, Z.; Dedo, M.I.; Huang, P.; Guo, K.; Shen, F.; Gao, J.; Guo, Z. The performances of different OAM encoding systems. Opt. Commun. 2019, 430, 151–157. [Google Scholar] [CrossRef]
 Willner, A.E.; Pang, K.; Song, H.; Zou, K.; Zhou, H. Orbital angular momentum of light for communications. Appl. Phys. Rev. 2021, 8, 041312. [Google Scholar] [CrossRef]
 Fang, X.; Ren, H.; Gu, M. Orbital angular momentum holography for highsecurity encryption. Nat. Photonics 2020, 14, 102–108. [Google Scholar] [CrossRef]
 Xiao, Q.; Ma, Q.; Yan, T.; Wu, L.W.; Liu, C.; Wang, Z.X.; Wan, X.; Cheng, Q.; Cui, T.J. Orbitalangularmomentumencrypted holography based on coding information metasurface. Adv. Opt. Mater. 2021, 9, 2002155. [Google Scholar] [CrossRef]
 Fu, S.; Zhai, Y.; Zhou, H.; Zhang, J.; Wang, T.; Yin, C.; Gao, C. Demonstration of freespace onetomany multicasting link from orbital angular momentum encoding. Opt. Lett. 2019, 44, 4753–4756. [Google Scholar] [CrossRef]
 Willner, A.J.; Ren, Y.; Xie, G.; Zhao, Z.; Cao, Y.; Li, L.; Ahmed, N.; Wang, Z.; Yan, Y.; Liao, P.; et al. Experimental demonstration of 20 Gbit/s data encoding and 2 ns channel hopping using orbital angular momentum modes. Opt. Lett. 2015, 40, 5810–5813. [Google Scholar] [CrossRef] [Green Version]
 Li, S.; Xu, Z.; Liu, J.; Zhou, N.; Zhao, Y.; Zhu, L.; Xia, F.; Wang, J. Experimental demonstration of freespace optical communications using orbital angular momentum (OAM array encoding/decoding. In Proceedings of the 2015 Conference on Lasers and ElectroOptics (CLEO), Busan, Republic of Korea, 24–28 August 2015; pp. 1–2. [Google Scholar]
 Trichili, A.; Salem, A.B.; Dudley, A.; Zghal, M.; Forbes, A. Encoding information using Laguerre Gaussian modes over free space turbulence media. Opt. Lett. 2016, 41, 3086–3089. [Google Scholar] [CrossRef] [Green Version]
 Wang, J.; Yang, J.Y.; Fazal, I.M.; Ahmed, N.; Yan, Y.; Huang, H.; Ren, Y.; Yue, Y.; Dolinar, S.; Tur, M.; et al. Terabit freespace data transmission employing orbital angular momentum multiplexing. Nat. Photonics 2012, 6, 488–496. [Google Scholar] [CrossRef]
 Zhou, H.; Sain, B.; Wang, Y.; Schlickriede, C.; Zhao, R.; Zhang, X.; Wei, Q.; Li, X.; Huang, L.; Zentgraf, T. Polarizationencrypted orbital angular momentum multiplexed metasurface holography. ACS Nano 2020, 14, 5553–5559. [Google Scholar] [CrossRef]
 Bolduc, E.; Bent, N.; Santamato, E.; Karimi, E.; Boyd, R.W. Exact solution to simultaneous intensity and phase encryption with a single phaseonly hologram. Opt. Lett. 2013, 38, 3546–3549. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 Willner, A.E.; Song, H.; Liu, C.; Zhang, R.; Pang, K.; Zhou, H.; Hu, N.; Song, H.; Su, X.; Zhao, Z.; et al. Causes and mitigation of modal crosstalk in OAM multiplexed optical communication links. In Structured Light for Optical Communication; Elsevier: Amsterdam, The Netherlands, 2021; pp. 259–289. [Google Scholar]
 Ouyang, X.; Xu, Y.; Xian, M.; Feng, Z.; Zhu, L.; Cao, Y.; Lan, S.; Guan, B.O.; Qiu, C.W.; Gu, M.; et al. Synthetic helical dichroism for sixdimensional optical orbital angular momentum multiplexing. Nat. Photonics 2021, 15, 901–907. [Google Scholar] [CrossRef]
 Zhu, F.; Jiang, J.; Li, Y.; Zhou, C.; Tang, L.; Lai, Z. Index Modulation of OAMUCA with LDPC Transmission. In Proceedings of the 2021 IEEE 21st International Conference on Communication Technology (ICCT), Tianjin, China, 13–16 October 2021; pp. 1300–1303. [Google Scholar]
 Li, Y.; Zhang, Z. Image information transfer with petallike beam lattices encoding/decoding. Opt. Commun. 2022, 510, 127931. [Google Scholar] [CrossRef]
 Du, J.; Li, S.; Zhao, Y.; Xu, Z.; Zhu, L.; Zhou, P.; Liu, J.; Wang, J. Demonstration of Mary encoding/decoding using visiblelight Bessel beams carrying orbital angular momentum (OAM) for freespace obstructionfree optical communications. In Proceedings of the Optical Fiber Communication Conference, Los Angeles, CA, USA, 22–26 March 2015; p. M2F4. [Google Scholar]
 Fujita, H.; Sato, M. Encoding orbital angular momentum of light in magnets. Phys. Rev. B 2017, 96, 060407. [Google Scholar] [CrossRef] [Green Version]
 Zhao, N.; Li, X.; Li, G.; Kahn, J.M. Capacity limits of spatially multiplexed freespace communication. Nat. Photonics 2015, 9, 822–826. [Google Scholar] [CrossRef]
 Chen, M.; Dholakia, K.; Mazilu, M. Is there an optimal basis to maximise optical information transfer? Sci. Rep. 2016, 6, 22821. [Google Scholar] [CrossRef]
 Trichili, A.; Park, K.H.; Zghal, M.; Ooi, B.S.; Alouini, M.S. Communicating using spatial mode multiplexing: Potentials, challenges, and perspectives. IEEE Commun. Surv. Tutorials 2019, 21, 3175–3203. [Google Scholar] [CrossRef] [Green Version]
 Bartkiewicz, K.; Gneiting, C.; Černoch, A.; Jiráková, K.; Lemr, K.; Nori, F. Experimental kernelbased quantum machine learning in finite feature space. Sci. Rep. 2020, 10, 12356. [Google Scholar] [CrossRef]
 Zhou, J.; Huang, B.; Yan, Z.; Bünzli, J.C.G. Emerging role of machine learning in lightmatter interaction. Light Sci. Appl. 2019, 8, 84. [Google Scholar] [CrossRef] [Green Version]
 Neary, P.L.; Watnik, A.T.; Judd, K.P.; Lindle, J.R.; Flann, N.S. Machine learningbased signal degradation models for attenuated underwater optical communication OAM beams. Opt. Commun. 2020, 474, 126058. [Google Scholar] [CrossRef]
 Kirchner, T.; Gröhl, J.; MaierHein, L. Context encoding enables machine learningbased quantitative photoacoustics. J. Biomed. Opt. 2018, 23, 056008. [Google Scholar] [CrossRef] [Green Version]
 Zhou, L.; Chen, X.; Chen, W. Deep learning based attack on phasetruncated optical encoding. In Proceedings of the 2020 IEEE MTTS International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), Hangzhou, China, 7–9 December 2020; pp. 1–4. [Google Scholar]
 Doster, T.; Watnik, A.T. Laguerre–Gauss and Bessel–Gauss beams propagation through turbulence: Analysis of channel efficiency. Appl. Opt. 2016, 55, 10239–10246. [Google Scholar] [CrossRef]
 Paufler, W.; Böning, B.; Fritzsche, S. High harmonic generation with Laguerre–Gaussian beams. J. Opt. 2019, 21, 094001. [Google Scholar] [CrossRef]
 Litvin, I.A.; Burger, L.; Forbes, A. Angular selfreconstruction of petallike beams. Opt. Lett. 2013, 38, 3363–3365. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 Guo, Z.; Wang, Z.; Dedo, M.I.; Guo, K. The orbital angular momentum encoding system with radial indices of Laguerre–Gaussian beam. IEEE Photonics J. 2018, 10, 7906511. [Google Scholar] [CrossRef]
 Zetie, K.; Adams, S.; Tocknell, R. How does a Mach–Zehnder interferometer work? Phys. Educ. 2000, 35, 46. [Google Scholar] [CrossRef] [Green Version]
 Schimpf, D.; Barankov, R.; Ramachandran, S. Crosscorrelated (C^{2}) imaging of fiber and waveguide modes. Opt. Express 2011, 19, 13008–13019. [Google Scholar] [CrossRef]
 Beijersbergen, M.W.; Allen, L.; Van der Veen, H.; Woerdman, J. Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun. 1993, 96, 123–132. [Google Scholar] [CrossRef]
 Zheng, G.; Qian, Z.; Yang, Q.; Wei, C.; Xie, L.; Zhu, Y.; Li, Y. The combination approach of SVM and ECOC for powerful identification and classification of transcription factor. BMC Bioinform. 2008, 9, 282. [Google Scholar] [CrossRef] [Green Version]
 Liu, M.; Zhang, D.; Chen, S.; Xue, H. Joint binary classifier learning for ECOCbased multiclass classification. IEEE Trans. Pattern Anal. Mach. Intell. 2015, 38, 2335–2341. [Google Scholar] [CrossRef]
 Binh, L.N. Noises in Optical Communications and Photonic Systems; CRC Press LLC: Boca Raton, FL, USA, 2016. [Google Scholar]
 Kareem, F.Q.; Zeebaree, S.; Dino, H.I.; Sadeeq, M.; Rashid, Z.N.; Hasan, D.A.; Sharif, K.H. A survey of optical fiber communications: Challenges and processing time influences. Asian J. Res. Comput. Sci. 2021, 7, 48–58. [Google Scholar] [CrossRef]
 Sheng, M.; Jiang, P.; Hu, Q.; Su, Q.; Xie, X.X. Endtoend average BER analysis for multihop freespace optical communications with pointing errors. J. Opt. 2013, 15, 055408. [Google Scholar] [CrossRef]
 Freude, W.; Schmogrow, R.; Nebendahl, B.; Winter, M.; Josten, A.; Hillerkuss, D.; Koenig, S.; Meyer, J.; Dreschmann, M.; Huebner, M.; et al. Quality metrics for optical signals: Eye diagram, Qfactor, OSNR, EVM and BER. In Proceedings of the 2012 14th International Conference on Transparent Optical Networks (ICTON), Coventry, UK, 2–5 July 2012; pp. 1–4. [Google Scholar]
 Hayal, M.R.; Yousif, B.B.; Azim, M.A. Performance enhancement of DWDMFSO optical fiber communication systems based on hybrid modulation techniques under atmospheric turbulence channel. Photonics 2021, 8, 464. [Google Scholar] [CrossRef]
 Hernández, J.A.; Martín, I.; Camarillo, P.; de Arcaute, G.M.R. Applications of Machine Learning Techniques for Whatif Analysis and Network Overload Detection. In Proceedings of the 2022 18th International Conference on the Design of Reliable Communication Networks (DRCN), Vilanova i la Gelrú, Spain, 28–31 March 2022; pp. 1–7. [Google Scholar]
 Zhang, L.; Li, X.; Tang, Y.; Xin, J.; Huang, S. A survey on QoT prediction using machine learning in optical networks. Opt. Fiber Technol. 2022, 68, 102804. [Google Scholar] [CrossRef]
 Walsh, D.; Moodie, D.; Mauchline, I.; Conner, S.; Johnstone, W.; Culshaw, B. Practical bit error rate measurements on fibre optic communications links in student teaching laboratories. In Proceedings of the 9th International Conference on Education and Training in Optics and Photonics (ETOP), Marseille, France, 24–27 October 2005. [Google Scholar]
 Balsells, J.M.G.; LópezGonzález, F.J.; JuradoNavas, A.; CastilloVázquez, M.; Notario, A.P. General closedform biterror rate expressions for coded Mdistributed atmospheric optical communications. Opt. Lett. 2015, 40, 2937–2940. [Google Scholar] [CrossRef]
 Keiser, G. Fiber Optic Communications; Springer: Berlin/Heidelberg, Germany, 2021. [Google Scholar]
 Chan, V.W. Freespace optical communications. J. Light. Technol. 2006, 24, 4750–4762. [Google Scholar] [CrossRef]
 Andrews, L.C.; Phillips, R.L. Laser beam propagation through random media. In Laser Beam Propagation Through Random Media: Second Edition; SPIE Publications: Bellingham, WA, USA, 2005. [Google Scholar]
 Bhatnagar, M.R.; Ghassemlooy, Z. Performance analysis of gamma–gamma fading FSO MIMO links with pointing errors. J. Light. Technol. 2016, 34, 2158–2169. [Google Scholar] [CrossRef]
 Li, L.; Xie, G.; Ren, Y.; Ahmed, N.; Huang, H.; Zhao, Z.; Liao, P.; Lavery, M.P.; Yan, Y.; Bao, C.; et al. Orbitalangularmomentummultiplexed freespace optical communication link using transmitter lenses. Appl. Opt. 2016, 55, 2098–2103. [Google Scholar] [CrossRef] [Green Version]
 Cervantes, J.; GarciaLamont, F.; Rodriguez, L.; López, A.; Castilla, J.R.; Trueba, A. PSObased method for SVM classification on skewed data sets. Neurocomputing 2017, 228, 187–197. [Google Scholar] [CrossRef] [Green Version]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. 
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Lamilla, E.; Sacarelo, C.; AlvarezAlvarado, M.S.; Pazmino, A.; Iza, P. Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning. Sensors 2023, 23, 2755. https://doi.org/10.3390/s23052755
Lamilla E, Sacarelo C, AlvarezAlvarado MS, Pazmino A, Iza P. Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning. Sensors. 2023; 23(5):2755. https://doi.org/10.3390/s23052755
Chicago/Turabian StyleLamilla, Erick, Christian Sacarelo, Manuel S. AlvarezAlvarado, Arturo Pazmino, and Peter Iza. 2023. "Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning" Sensors 23, no. 5: 2755. https://doi.org/10.3390/s23052755