Vol. 38, issue 04, article # 1

Abstract:

Currently, many studies are aimed at increasing the information capacity of data transmission channels by using the orbital angular momentum (OAM) of laser beams to encode information. The use of this approach in atmospheric optical communication systems is limited by the distorting effect of atmospheric turbulence, which makes decoding difficult and reduces the data transfer rate. In addition, the intensity distributions of vortex beams with opposite in sign OAM values are identical in the case of homogeneous media, which limits the use of the OAM sign for encoding information. The main goal of the study was to evaluate the fundamental possibility of using neural networks to recognize opposite in sign OAM values of vortex beams in a turbulent atmosphere only through intensity images. The study is based on numerical simulation of the Laguerre-Gauss beam propagation in a turbulent atmosphere and further use of the obtained intensity images for training and testing neural networks. It has been shown for the first time that the use of neural networks makes it possible to recognize opposite in sign OAM values of Laguerre-Gauss beam through intensity images in case of propagation in a turbulent atmosphere with an accuracy of more than 90%. The obtained results can be useful for developers and researchers of atmospheric optical communication systems using OAM of vortex beam.

Keywords:

orbital angular momentum, topological charge, vortex beam, turbulent atmosphere, optical vortex, neural network

References:

1. Agrell E., Karlsson M., Chraplyvy A.R., Richardson D.J., Krummrich P.M., Winzer P., Roberts K., Fischer J.K., Savory S.J., Eggleton B.J., Secondini M., Kschischang F.R., Lord A., Prat J., Tomkos I., Bowers J.E., Srinivasan S., Brandt-Pearce M., Gisin N. Roadmap of optical communications // J. Opt. UK. 2016. V. 18, N. 6. DOI: 10.1088/2040-8978/18/6/063002.
2. Wang J. Advances in communications using optical vortices // Photonics Res. 2016. V. 4, N 5. P. B14–B28. DOI: 10.1364/prj.4.000b14.
3. Liu Z., Huang Y., Liu H., Chen X. Non-line-of-sight optical communication based on orbital angular momentum // Opt. Lett. 2021. V. 46, N 20. P. 5112–5115. DOI: 10.1364/ol.441441.
4. Wang J., Yang J.Y., Fazal I.M., Ahmed N., Yan Y., Huang H., Ren Y., Yue Y., Dolinar S., Tur M., Willner A.E. Terabit free-space data transmission employing orbital angular momentum multiplexing // Nat. Photonics. V. 6, N 7. P. 488–496. DOI: 10.1038/nphoton.2012.138.
5. 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. V. 16. DOI: 10.1088/1367-2630/16/11/113028.
6. Adamov E.V., Aksenov V.P., Atuchin V.V., Dudorov V.V., Kolosov V.V., Levitsky M.E. Laser beam shaping based on amplitude-phase control of a fiber laser array // OSA Continuum. 2021. V. 4, N 1. P. 182–192. DOI: 10.1364/osac.413956.
7. Huang H., Xie G., Yan Y., Ahmed N., Ren Y., Yue Y., Rogawski D., Willner M.J., Erkmen B.I., Birnbaum K.M., Dolinar S.J., Lavery M.P.J., Padgett M.J., Tur M., Willner A.E. 100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength // Opt. Lett. 2014. V. 39, N 2. P. 197 –200. DOI: 10.1364/ol.39.000197.
8. Adamov E.V., Bogach E.A., Dudorov V.V., Kolosov V.V., Levitskii M.E. Controlling the polarization structure of vector beams synthesized by a fiber laser array // Opt. Commun. 2024. V. 559. DOI: 10.1016/j.optcom.2024.130399.
9. Willner A.E., Huang H., Yan Y., Ren Y., Ahmed N., Xie G., Bao C., Li L., Cao Y., Zhao Z., Wang J., Lavery M.P.J., Tur M., Ramachandran S., Molisch A.F., Ashrafi N., Ashrafi S. Optical communications using orbital angular momentum beams // Adv. Opt. Photonics. 2015. V. 7, N 1. P. 66–106. DOI: 10.1364/aop.7.000066.
10. Aksenov V.P., Dudorov V.V., Kolosov V.V., Pogutsa Ch.E. Optical communication in a turbulent atmosphere via the orbital angular momentum of a laser beam. I. Mode purity of OAM transmission // Appl. Opt. 2024. V. 63, N 28. P. 7475–7484. DOI: 10.1364/AO.530512.
11. Yan Y., Xie G., Lavery M.P.J., Huang H., Ahmed N., Bao C., Ren Y., Cao Y., Li L., Zhao Z., Molisch A.F., Tur M., Padgett M.J., Willner A.E. High‑capacity millimetre‑wave communications with orbital angular momentum multiplexing // Nat. Commun. 2014. V. 5. DOI: 10.1038/ncomms5876.
12. Kovalyov A.A., Kotlyar V.V., Kalinkina D.S. Orbital'nyj uglovoj moment i topologicheskij zaryad Gaussova puchka s neskol'kimi opticheskimi vihryami // Komp'yuternaya optika. 2020. V. 44, N 1. P. 34 –39. DOI: 10.18287/2412-6179-CO-632.
13. 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. Lett. 1992. V 45, N 11. P. 8185– 8189. DOI: 10.1103/PhysRevA.45.8185.
14. Berkhout G.C.G., Beijersbergen M.W. Method for probing the oirbital angular momentum of optical vortices in electromagnetic waves from astronomical objects // Phys. Rev. Lett. 2008. V. 101, N 10. P. 100801-1–100801-4. DOI: 10.1103/PhysRevLett.101.100801.
15. Gavril’eva K.N., Mermoul A., Sevryugin A.A., Shubenkova E.V., Touil M., Tursunov I.M., Efremova E.A., Venediktov V.Y. Detection of optical vortices using cyclic, rotational and reversal shearing interferometers // Opt. Laser Technol. 2019. V. 113. P. 374–378. DOI: 10.1016/j.optlastec.2019.01.006.
16. Kanev F.Yu., Aksenov V.P., Starikov F.A., Dolgopolov Yu.V., Kopalkin A.V., Veretekhin I.D. Algoritm opredeleniya topologicheskih zaryadov i chisla opticheskih vihrej po vetvleniyu polos interferencionnoj kartiny // Optika atmosf. i okeana. 2019. V. 32, N 8. P. 620‑627. DOI: 10.15372/AOO20190803.
17. Zhang N., Davis J.A., Moreno I., Lin J., Moh K.-J., Cottrell D.M., Yuan X. Analysis of fractional vortex beams using a vortex grating spectrum analyzer // Appl. Opt. 2010. V. 49, N 13. P. 2456–2462. DOI: 10.1364/AO.49.002456.
18. Khonina S.N., Kotlyar V.V., Soifer V.A., Pääkkönen P., Simonen J., Turunen J. An analysis of the angular momentum of a light field in terms of angular harmonics // J. Mod. Opt. 2001. V. 48, N 10. P. 1543–1557. DOI: 10.1080/09500340108231783.
19. Guo C.-S., Lu L.-L., Wang H.-T. Characterizing topological charge of optical vortices by using an annular aperture // Opt. Lett. 2009. V. 34, N 23. P. 3686–3688. DOI: 10.1364/OL.34.003686.
20. Ferreira Q.S., Jesus-Silva A.J., Fonseca E.J.S., Hickmann J.M. Fraunhofer diffraction of light with orbital angular momentum by a slit // Opt. Lett. 2011. V. 36, N 16. P. 3106–3108. DOI: 10.1364/ol.36.003106
21. Mirhosseini M., Malik M., Shi Z., Boyd R.W. Efficient separation of the orbital angular momentum eigenstates of light // Nat. Commun. 2013. V. 4. Article № 2781. DOI: 10.1038/ncomms3781.
22. Wen Y., Chremmos I., Chen Y., Zhu J., Zhang Y., Yu S. Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes // Phys. Rev. Lett. 2018. V. 120, N 19. P. 193904-1–193904-6. DOI: 10.1103/PhysRevLett.120.193904.
23. Aksenov V.P., Kolosov V.V., Pogutsa C.E. The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: A numerical experiment // J. Opt. UK. 2013. V. 15, N 4. DOI: 10.1088/2040-8978/15/4/044007.
24. Andrews L., Phillips R. Laser Beam Propagation through Random Media. Belingham, WA: SPIE Opt. Eng. Press, 2005. 820 p. DOI: 10.1117/3.626196.
25. Aksenov V.P., Pogutsa Ch.E. Vliyanie opticheskogo vihrya na sluchajnye smeshcheniya Lagerra-Gaussova lazernogo puchka, rasprostranyayushchegosya v turbulentnoj atmosfere // Optika atmosf. i okeana. 2012. V. 25, N 7. P. 561‑565; Aksenov V.P., Pogutsa Ch.E. The effect of optical vortex on random Laguerre–Gauss shifts of a laser beam propagating in a turbulent atmosphere // Atmos. Ocean. Opt. 2013. V. 26, N 1. P. 13–17.
26. Konyaev P.A., Lukin V.P. Adaptivnaya fazovaya korrekciya vihrevyh lazernyh puchkov v turbulentnoj atmosfere // Kvant. Elektron. 2022. V. 52, N 12. P. 1146–1151.
27. Adamov E.V., Aksenov V.P., Bogach E.A., Dudorov V.V., Kolosov V.V., Levitskii M.E. Adaptive formation of the orbital angular momentum of synthesized beams in a turbulent atmosphere // Proc. SPIE. 2022. V. 12341. P. 1234114-1–1234114-7. DOI: 10.1117/12.2644915.
28. Ren Y., Xie G., Huang H., Bao C., Yan Y., Ahmed N., Lavery M.P.J., Erkmen B.I., Dolinar S., Tur M., Neifeld M.A., Padgett M.J., Boyd R.W., Shapiro J.H., Willner A.E. Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence // Opt. Lett. 2014. V. 39, N 10. P. 2845–2848. DOI: 10.1364/ol.39. 002845.
29. Galaktionov I., Sheldakova J., Samarkin V., Toporovsky V., Kudryashov A. Atmospheric turbulence with Kolmogorov spectra: Software simulation, real-time reconstruction and compensation by means of adaptive optical system with bimorph and stacked-actuator deformable mirrors // Photonics. 2023. V. 10, N 10. P. 1147. DOI: 10.3390/photonics10101147.
30. 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. V. 27, N 12. P. 16671–16688. DOI: 10.1364/oe.27.016671.
31. Guo J., Shi H., Yang T., Lv C., Qiao Z. Atmospheric turbulence compensation for OAM-carrying vortex waves based on convolutional neural network // Adv. Space Res. 2022. V. 69, N 5. P. 1949–1959. DOI: 10.1016/j.asr.2021.11.039.
32. Wang B., Zhang X., Shah S.A.A., Merabet B., Kovalev A.A., Stafeev S.S., Kozlova E.S., Kotlyar V.V., Guo Z. Top three intelligent algorithms for OAM mode recognitions in optical communications // Eng. Res. Express. 2024. V. 6, N 3. DOI: 10.1088/2631-8695/ad61bc.
33. Wang Z., Dedo M.I., Guo K., Zhou K., Shen F., Sun Y., Liu S., Guo Z. Efficient recognition of the propagated orbital angular momentum modes in turbulences with the convolutional neural network // IEEE Photonics J. 2019. V. 11, N 3. DOI: 10.1109/ JPHOT.2019.2916207.
34. Cox M.A., Celik T., Genga Y., Drozdov A.V. Interferometric orbital angular momentum mode detection in turbulence with deep learning // Appl. Opt. 2022. V. 61, N 7. P. D1–D6. DOI: 10.1364/ao.444954.
35. Jing G., Chen L., Wang P., Xiong W., Huang Z., Liu J., Chen Y., Li Y., Fan D., Chen S. Recognizing fractional orbital angular momentum using feed forward neural network // Results Phys. 2021. V. 28. DOI: 10.1016/j.rinp.2021.104619.
36. Hu J., Guo Z., Fu Y., Gan J.A., Chen P.F., Chen G., Min C., Yuan X., Feng F. How convolutional-neural-network detects optical vortex scattering fields // Opt. Laser Eng. 2023 V. 160. DOI: 10.1016/j.optlaseng.2022.107246.
37. Fleck J.A., Morris J.R., Feit M.D. Time-dependent propagation of high energy laser beams through the atmosphere // Appl. Phys. 1976. V. 10. P. 129–160. DOI: 10.1007/BF00896333.
38. Konyaev P.A., Lukin V.P. Thermal distortions of focused laser beams in the atmosphere // Appl. Opt. 1985. V. 24, N 4. P. 415–421. DOI: 10.1364/AO.24.000415.
39. Zhao X., Wang L., Zhang Y., Han X., Deveci M., Parmar M. A review of convolutional neural networks in computer vision // Artif. Intell. Rev. 2024. V. 57, N 99. DOI: 10.1007/s10462-024-10721-6.
40. Krizhevsky A., Sutskever I., Hinton G.E. ImageNet classification with deep convolutional neural networks // Commun. ACM. 2017. V. 60, N 6. P. 84–90. DOI: 10.1145/3065386.
41. Nikolenko S., Kadurin A., Arkhangel'skaya E. Glubokoe obuchenie. SPb.: Piter, 2018. 480 p.