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Topological charge of a geometric progression of optical vortices in a turbulent medium
D.O. Shilov1, E.S. Kozlova1,2

1 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34;
2 Image Processing Systems Institute, NRC "Kurchatov Institute", 443001, Samara, Russia, Molodogvardeyskaya 151

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DOI: 10.18287/COJ1737

Article ID: 1737

Language: Russian

Abstract:
The paper considers beams in the form of a geometric progression of optical vortices. Numerical modelling of the propagation of such optical fields in turbulent media is conducted using a Fresnel integral. Topological charges of the initial and resulting fields are calculated. As one would expect, an analysis of the obtained results shows that superpositions with a smaller number of beams are more resistant to distortions by strongly turbulent media. It is shown that the stability of the propagation of a superposition of optical vortices in the form of a geometric progression through turbulence is affected not only by the parameters of the medium, but also by the parameters of the geometric progression.

Keywords:
optical vortices, topological charge, superposition, geometric progression, turbulence, Fresnel transform, Berry formula.

Acknowledgements:
This work was financially supported by the RF Ministry of Science and Higher Education under a government project of the FSRC "Crystallography and Photonics" RAS (Numerical Simulation) and the Russian Science Foundation under project No. 22-12-00137 (Theoretical analysis).

Citation:
Shilov DO, Kozlova ES. Topological charge of a geometric progression of optical vortices in a turbulent medium. Computer Optics 2026; 50(3): 1737. DOI: 10.18287/COJ1737.

References:

  1. Das BK, Granados C, Ciappina MF. Generation of elliptical perfect optical vortex beams and their propagation in free-space. Appl Opt 2024; 63(10): 2737-2745. doi:10.1364/AO.521826.
  2. Hyde MW IV, Porras MA. Propagation of spatiotemporal optical vortex beams in linear, second-order dispersive media. Phys Rev A 2023; 108(1): 013519. doi:10.1103/PhysRevA.108.013519.
  3. Kotlyar VV, Kovalev AA, Kozlova ES, Savelyeva AA, Stafeev SS. A new type of vortex laser beams: Squared Laguerre-Gaussian beam. Optik 2022; 270: 169916. doi:10.1016/j.ijleo.2022.169916.
  4. Acevedo CH, Eshaghi M, Dogariu A. Propagation of asymmetric optical vortex beams through turbulence and evolution of their OAM spectra. J Opt Soc Am A 2023; 40(12): 2135-2145. doi:10.1364/JOSAA.500239.
  5. Weng X, Yu M, Wang G, Zhan Q, Dong X, Qu J, Gao X, Zhuang S. Propagable optical vortices with natural noninteger orbital angular momentum in free space. Adv Photonics Res 2023; 4(1): 2200094. doi:10.1002/adpr.202200094.
  6. Kotlyar VV, Kovalev AA, Nalimov AG. Topological charge of optical vortices. Boca Raton, FL: CRC Press; 2022. 320 p. doi:10.1201/9781003326304.
  7. Shen Y, Wang X, Xie Z, Min C, Fu X, Liu Q, Gong M, Yuan X. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. Light Sci Appl 2019; 8: 90. doi:10.1038/s41377-019-0194-2.
  8. Moradi H, Mahmoudi M. Direct determination of topological charge of structured light via phase-shift interference. Optik 2024; 311: 171943. doi:10.1016/j.ijleo.2024.171943.
  9. Dev V, Pal V. Probing topological charge of discrete vortices. Phys Rev Appl 2023; 20(3): 034071. doi:10.1103/PhysRevApplied.20.034071.
  10. Anufriyev EG. Determination of the orbital angular momentum state of a radio wave beam based on quantitative characteristics of a radio communication system. Computer Optics 2022; 46(1): 22-29. doi:10.18287/2412-6179-CO-907.
  11. Shang Y, Wang W, Mi Z, Wang B, Zhang L, Han K, Lei C, Man Z, Ge X. Determining the topological charge of optical vortex by intensity distribution of a quasi-Airy vortex beam. Opt Commun 2023; 529: 129075. doi:10.1016/j.optcom.2022.129075.
  12. Kotlyar VV, Kovalev AA, Porfirev AP. Determination of an optical vortex topological charge using an astigmatic transform. Computer Optics 2016; 40(6): 781-792. doi:10.18287/2412-6179-2016-40-6-781-792.
  13. Han Y, Zhao G. Measuring the topological charge of optical vortices with an axicon. Opt Lett 2011; 36(11): 2017-2019. doi:10.1364/OL.36.002017.
  14. Zhang B, Hu ZJ, Wu D, Wang J, Nie Y, Zhang F, Li M, Khakhomov S. Metasurface-based perfect vortex beams with trigonometric-function topological charge for OAM manipulation. Opt Lett 2023; 48(9): 2409-2412. doi:10.1364/OL.488701.
  15. Guo M, Le W, Wang C, Rui G, Zhu Z, He J, Gu B. Generation, topological charge, and orbital angular momentum of off-axis double vortex beams. Photonics 2023; 10(4): 368. doi:10.3390/photonics10040368.
  16. Kovalev AA, Kotlyar VV. Optical vortex beams with the infinite topological charge. J Opt 2021; 23(5): 055601. doi:10.1088/2040-8986/abf172.
  17. Kotlyar VV, Kovalev AA. Topological charge of asymmetric optical vortices. Opt Express 2020; 28(14): 20449-20460. doi:10.1364/OE.394273.
  18. Kotlyar VV, Kovalev AA. Topological charge of a superposition of optical vortices described by a geometric sequence. Computer Optics 2022; 46(6): 864-871. doi:10.18287/2412-6179-CO-1152.
  19. Kotlyar VV, Kovalev AA, Savelyeva AA. Coherent superposition of the Laguerre-Gaussian beams with different wavelengths: colored optical vortices. Computer Optics 2022; 46(5): 692-700. doi:10.18287/2412-6179-CO-1106.
  20. Kotlyar VV, Kovalev AA, Savelyeva AA. Topological charge of a superposition of identical parallel single-ringed Laguerre-Gaussian beams. Computer Optics 2022; 46(2): 184-188. doi:10.18287/2412-6179-CO-1086.
  21. Kotlyar VV, Kovalev AA. Topological charge of a superposition of two Bessel-Gaussian beams. Computer Optics 2021; 45(1): 19-28. doi:10.18287/2412-6179-CO-816.
  22. Prentice PA, MacDonald MP, Frank TG, Cuschieri A, Spalding GC, Sibbett W, Campbell PA, Dholakia K. Manipulation and filtration of low index particles with holographic Laguerre-Gaussian optical trap arrays. Opt Express 2004; 12(4): 593-600. doi:10.1364/OPEX.12.000593.
  23. Willner AE, Song H, Zou K, Zhou H, Su X. Orbital angular momentum beams for high-capacity communications. J Lightwave Technol 2023; 41(7): 1918-1933. doi:10.1109/JLT.2022.3224413.
  24. Goncharov RK, Kiselev AD, Samsonov EO, Egorov VI. Subcarrier wave continuous-variable quantum key distribution with Gaussian modulation: composable security analysis. Computer Optics 2023; 47(3): 374-380. doi:10.18287/2412-6179-CO-1225.
  25. Lu W, Liu L, Sun J. Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence. J Opt A Pure Appl Opt 2006; 8(12): 1052-1058. doi:10.1088/1464-4258/8/12/004.
  26. Fu S, Gao C. Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams. Photon Res 2016; 4(5): B1-B4. doi:10.1364/PRJ.4.000B1.
  27. Falits AV, Kuskov VV, Banakh VA. Propagation of vortex optical beams through artificial convective turbulence. J Quant Spectrosc Radiat Transf 2023; 302: 108568. doi:10.1016/j.jqsrt.2023.108568.
  28. Wang S, Cheng M, Yang X, Xu J, Yang Y. Self-focusing effect analysis of a perfect optical vortex beam in atmospheric turbulence. Opt Express 2023; 31(13): 20861-20871. doi:10.1364/OE.492275.
  29. Zhu D, Li C, Sun X, Liu Y, Zhang Y, Gao H. The effect of air turbulence on vortex beams in nonlinear propagation. Sensors 2023; 23(4): 1772. doi:10.3390/s23041772.
  30. Lukin VP. Outer scale of turbulence and its influence on fluctuations of optical waves. Phys Usp 2021; 64(3): 292-317. doi:10.3367/UFNe.2020.10.038849.
  31. Lukin VP, Lukin IP. Overview of modern technologies for measuring, predicting and correcting turbulent distortions in optical waves. Computer Optics 2024; 48(1): 68-80. doi:10.18287/2412-6179-CO-1355.
  32. Lukin VP. Prediction of optical wave phase fluctuations in a turbulent atmosphere based on current database. Russ Phys J 2024; 67(3): 217-228. doi:10.1007/s11182-024-03112-5.
  33. Tripathi S, Paxman R, Bifano T, Toussaint KC. Vector transmission matrix for the polarization behavior of light propagation in highly scattering media. Opt Express 2012; 20(14): 16067-16076. doi:10.1364/OE.20.016067.
  34. Schmidt S, Thiele S, Herkommer A, Tünnermann A, Gross H. Rotationally symmetric formulation of the wave propagation method: application to the straylight analysis of diffractive lenses. Opt Lett 2017; 42(8): 1612-1615. doi:10.1364/OL.42.001612.
  35. Poggiolini P, Bosco G, Carena A, Curri V, Jiang Y, Forghieri F. The GN-model of fiber nonlinear propagation and its applications. J Lightwave Technol 2014; 32(4): 694-721. doi:10.1109/JLT.2013.2295208.
  36. Kotlyar VV, Kovalev AA, Porfirev AP. Birth of optical vortices in propagating fields with an original fractional topological charge. Computer Optics 2020; 44(4): 493-500. doi:10.18287/2412-6179-CO-715.
  37. Kotlyar VV, Stafeev SS. Modeling sharp focus radially-polarized laser mode with conical and binary microaxicons. Computer Optics 2009; 33(1): 52-60.
  38. Lukin VP, Konyaev PA, Sennikov VA. Beam spreading of vortex beams propagating in turbulent atmosphere. Appl Opt 2012; 51(1): C84-C87. doi:10.1364/AO.51.000C84.
  39. Tinin MV. Integral representation of the field of the wave propagating in a medium with large-scale irregularities. Radiophys Quantum El 2012; 55(6): 391-398. doi:10.1007/s11141-012-9376-y.
  40. Banakh VA, Falits AV. Numerical simulation of propagation of laser beams formed by multielement apertures in a turbulent atmosphere under thermal blooming. Atmos Ocean Opt 2013; 26(6): 455-465. doi:10.1134/S102485601306002X.
  41. Konyaev PA, Lukin VP. Computational algorithms for simulations in atmospheric optics. Appl Opt 2016; 55(12): B107-B112. doi:10.1364/AO.55.00B107.
  42. Vasilyev VS, Kapustin AI, Skidanov RV, Podlipnov VV, Ivliev NA, Ganchevskaya SV. Experimental investigation of the stability of Bessel beams in the atmosphere. Computer Optics 2019; 43(3): 376-384. doi:10.18287/2412-6179-2019-43-3-376-384.
  43. Soifer VA, Korotkova O, Khonina SN, Shchepakina EA. Vortex beams in turbulent media: review. Computer Optics 2016; 40(5): 605-624. doi:10.18287/2412-6179-2016-40-5-605-624.
  44. Zuev VE, Zemlyanov AA, Kopytin YD, Kuzikovskii AV. High-power laser radiation in atmospheric aerosols. In: Nonlinear optics of aerodispersed media. Atmospheric and Oceanographic Sciences Library. Vol. 4. Dordrecht: Springer; 1985. 292 p. doi:10.1007/978-94-009-5219-5.
  45. Porfirev AP, Kirilenko MS, Khonina SN, Skidanov RV, Soifer VA. Study of propagation of vortex beams in aerosol optical medium. Appl Opt 2017; 56(11): E8-E15. doi:10.1364/AO.56.000E8.
  46. Khonina SN, Volotovskiy SG, Kirilenko MS. A method of generating a random optical field using the Karhunen-Loeve expansion to simulate atmospheric turbulence. Computer Optics 2020; 44(1): 53-59. doi:10.18287/2412-6179-CO-680.
  47. Kovalev AA, Kotlyar VV, Porfirev AP. Orbital angular momentum and topological charge of a multi-vortex Gaussian beam. J Opt Soc Am A 2020; 37(11): 1740-1747. doi:10.1364/JOSAA.401561.
  48. Goodman JW. Introduction to Fourier Optics. 4th ed. Englewood, CO: Roberts and Company Publishers; 2017.
  49. Iroshnikov NG, Larichev AV, Koryabin AV, Shmalgauzen VI. Express analysis of turbulence parameters. Moscow Univ Phys Bull 2009; 64(5): 550-554. doi:10.3103/S0027134909050178.
  50. Fried DL. Scaling laws for propagation through turbulence. Atmos Ocean Opt 1998; 11(11): 982-990.
  51. Feizulin ZI, Kravtsov YA. Broadening of a laser beam in a turbulent medium. Radiophys Quantum El 1967; 10(1): 33-35. doi:10.1007/BF01038157.
  52. Berry MV. Optical vortices evolving from helicoidal integer and fractional phase steps. J Opt A Pure Appl Opt 2004; 6(2): 259-268. doi:10.1088/1464-4258/6/2/018.

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