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Measuring Singularities of Vector Structured LG Beams and Stokes Vortices via Intensity Moments Technique

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Abstract

We theoretically and experimentally investigated the transformation processes of polarization singularities (C-points, L-lines, V-points and rings, as well as the Stokes vortices) in vector structured Laguerre–Gaussian (sLG) beams with varying their controllable phase parameters. It was shown that all the Stokes vortices simultaneously turn to zero only in V-points and rings, in other polarization singularities only a part of the Stokes vortices vanish. On the basis of our computer simulation, the process of the birth and annihilation of polarization singularities has been studied. In the experiment, we used the intensity moments technique for the first time to measure the spectrum of vector modes and their digital multiplexing of a simple vector sLG12 beam. The amplitude and phase spectra were measured in each linear polarized component of the space-variant polarization field. Then scalar fields of the polarization components were formed, which was the digital demultiplexing of the vector sLG field. The combination of the vector modes made it possible to restore the vector sLG beam again, that is the digital multiplexing the vector field.

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REFERENCES

  1. Kotlyar, V.V., Kovalev, A.A., Kozlova, E.S., and Porfirev, A.P., Spiral phase plate with multiple singularity centers, Comput. Opt., 2020, vol. 44, no. 6, pp. 901–908. https://doi.org/10.18287/2412-6179-CO-774

    Article  Google Scholar 

  2. Kotlyar, V.V., Kovalev, A.A., Kalinkina, D.S., and Kozlova, E.S., Fourier-Bessel beams of finite energy, Comput. Opt., 2021, vol. 45, no. 4, pp. 506–511. https://doi.org/10.18287/2412-6179-CO-864

    Article  Google Scholar 

  3. Karpeev, S.V., Podlipnov, V.V., Ivliev, N.A., and Khonina, S.N., High-speed format 1000BASE-SX/LX transmission through the atmosphere by vortex beams near IR range with help modified SFP-transmers DEM-310GT, Comput. Opt., 2020, vol. 44, no. 4, pp. 578–581. https://doi.org/10.18287/2412-6179-CO-772

    Article  Google Scholar 

  4. Volyar, A.V., Abramochkin, E.G., Bretsko, M.V., Akimova, Y.E., and Egorov, Y.A., Can the radial number of vortex modes control the orbital angular momentum?, Comput. Opt., 2022, vol. 46, no. 6, pp. 853–863. https://doi.org/10.18287/2412-6179-CO-1169

    Article  Google Scholar 

  5. Porfirev, A., Khonina, S., and Kuchmizhak, A., Light–matter interaction empowered by orbital angular momentum: Control of matter at the micro- and nanoscale, Prog. Quantum Electron., 2023, vol. 88, 100459. https://doi.org/10.1016/j.pquantelec.2023.100459

    Article  Google Scholar 

  6. Kotlyar, V.V., Kovalev, A.A., and Savelyeva, A.A., Coherent superposition of the Laguerre-Gaussian beams with different wavelengths: colored optical vortices, Comput. Opt., 2022, vol. 46, no. 5, pp. 692–700. https://doi.org/10.18287/2412-6179-CO-1106

    Article  Google Scholar 

  7. Kotlyar, V.V., Optical beams with an infinite number of vortices, Comput. Opt., 2021, vol. 45, no. 4, pp. 490–496. https://doi.org/10.18287/2412-6179-CO-858

    Article  Google Scholar 

  8. Kovalev, A.A., Optical vortex beams with an infinite number of screw dislocations, Comput. Opt., 2021, vol. 45, no. 4, pp. 497–505. https://doi.org/10.18287/2412-6179-CO-866

    Article  Google Scholar 

  9. Kotlyar, V.V., Abramochkin, E.G., Kovalev, A.A., and Nalimov, A.G., Astigmatic transformation of a fractional-order edge dislocation, Comput. Opt., 2022, vol. 46, no. 4, pp. 522–530. https://doi.org/10.18287/2412-6179-CO-1084

    Article  Google Scholar 

  10. Nalimov, A.G. and Kotlyar, V.V., Topological charge of optical vortices in the far field with an initial fractional charge: optical “dipoles”, Comput. Opt., 2022, vol. 46, no. 2, pp. 189–195. https://doi.org/10.18287/2412-6179-CO-1073

    Article  Google Scholar 

  11. Litchinitser, N.M., Sun, J., Shalaev, M.I., Xu, T., Xu, Y., and Pandey, A., Structured light-matter interactions in optical nanostructures (Presentation Recording), Proc. SPIE. Plasmonics: Metallic Nanostructures and Their Optical Properties XIII, 2015, vol. 9547, 954727. https://doi.org/10.1117/12.2190277.

  12. Wang, J., Cast ellucci, F., and Franke-Arnold, S., Vectorial light–matter interaction: Exploring spatially structured complex light fields, AVS Quantum Sci., 2020, vol. 2, 031702. https://doi.org/10.1116/5.0016007

    Article  Google Scholar 

  13. Nye, J.F., Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, Bristol and Philadelphia: Inst. of Physics Publ., 1999.

    MATH  Google Scholar 

  14. Nye, J.F., Polarizations effects in the diffraction of electromagnetic waves: The role of disclinations, Proc. R. Soc. London, Ser. A, 1983, vol. 387, pp. 105–132. https://doi.org/10.1098/rspa.1983.0053

    Article  MathSciNet  Google Scholar 

  15. Frank, F.C., Liquid crystals. On the theory of liquid crystals, Discuss. Faraday Soc., 1958, vol. 25, pp. 19–28. https://doi.org/10.1039/DF9582500019

    Article  Google Scholar 

  16. Nye, J.F., Hajnal, J.V., and Hannay, J.H., Phase saddles and dislocations in two-dimensional waves such as the tides, Proc. R. Soc. London, Ser. A, 1988, vol. 417, pp. 7–20. https://doi.org/10.1098/rspa.1988.0047

    Article  MathSciNet  MATH  Google Scholar 

  17. Penrose, R., The topology of ridge systems, Ann. Hum. Genet., 1979, vol. 42, no. 4, pp. 435–444. https://doi.org/10.1111/j.1469-1809.1979.tb00677.x

    Article  Google Scholar 

  18. Volyar, A.V., Shvedov, V.G., and Fadeeva, T.A., Structure of a nonparaxial gaussian beam near the focus: III. Stability, eigenmodes, and vortices, Opt. Spectrosc., 2001, vol. 91, pp. 235–245. https://doi.org/10.1134/1.1397845

    Article  Google Scholar 

  19. Kotlyar, V.V., Kovalev, A.A., Stafeev, S.S., Nalimov, A.G., and Rasouli, S., Tightly focusing vector beams containing V-point polarization singularities, Opt. Laser Technol., 2022, vol. 145, 107479. https://doi.org/10.1016/j.optlastec.2021.107479

    Article  Google Scholar 

  20. Rosales-Guzmán, C., Ndagano, B., and Forbes, A., A review of complex vector light fields and their applications, J. Opt., 2018, vol. 20, no. 12, 123001. https://doi.org/10.1088/2040-8986/aaeb7d

    Article  Google Scholar 

  21. Hu, X-B., Perez-Garcia, B., Rodríguez-Fajardo, V., Hernandez-Aranda, T.I., Forbes, A., and Rosales-Guzmán, C., Free-space local non-separability dynamics of vector modes, Photonics Res., 2021, vol. 9, no. 4, pp. 439–445. https://doi.org/10.1364/PRJ.416342

    Article  Google Scholar 

  22. Dennis, M.R., Polarization singularities in paraxial vector fields: morphology and statistics, Opt. Commun., 2002, vol. 213, pp. 201–221. https://doi.org/10.1016/S0030-4018(02)02088-6

    Article  Google Scholar 

  23. Beckley, A.M., Brown, T.G., and Alonso, M.A., Full Poincare´ beams, Opt. Express, 2010, vol. 18, no. 10, pp. 10777–10785. https://doi.org/10.1364/OE.18.010777

    Article  Google Scholar 

  24. Kotlyar, V.V., Stafeev, S.S., Zaitsev, V.D., and Telegin, A.M., Poincare beams at the tight focus: Inseparability, radial spin Hall effect, and reverse energy flow, Photonics, 2022, vol. 9, no. 12, 969. https://doi.org/10.3390/photonics9120969

    Article  Google Scholar 

  25. Wang, J., Advances in communications using optical vortices, Photonics Res., 2016, vol. 4, no. 5, pp. B14–B28. https://doi.org/10.1364/PRJ.4.000B14

    Article  Google Scholar 

  26. Volyar, A., Abramochkin, E., Akimova, Y., Bretsko, M., and Egorov, Y., Fast oscillations of orbital angular momentum and Shannon entropy caused by radial numbers of structured vortex beams, Appl. Opt., 2022, vol. 61, no. 21, pp. 6398–6407. https://doi.org/10.1364/AO.464178

    Article  Google Scholar 

  27. Kumar Pal, S. and Senthilkumaran, P., Synthesis of stokes vortices, Opt. Lett., 2019, vol. 44, no. 1, pp. 130–133. https://doi.org/10.1364/OL.44.000130

    Article  Google Scholar 

  28. Kumar Pal, S., Bansal, S., and Senthilkumaran, P., Generation of Stokes vortices in three, four and six circularly polarized beam interference, Asian J. Phys., 2019, vol. 28, pp. 867–876.

    Google Scholar 

  29. Volyar, A.V., Abramochkin, E.G., Egorov, Yu.A., Bretsko, M.V., and Akimova, Ya.E., Digital sorting of Hermite-Gauss beams: mode spectra and topological charge of a perturbed Laguerre-Gauss beam, Comput. Opt., 2020, vol. 44, no. 4, pp. 501–509. https://doi.org/10.18287/2412-6179-CO-747

    Article  Google Scholar 

  30. Freund, I., Polarization singularity indices in Gaussian laser beams, Opt. Commun., 2002, vol. 201, no. 4, pp. 251–270. https://doi.org/10.1016/S0030-4018(01)01725-4

    Article  Google Scholar 

  31. Born, M. and Wolf, E., Principles of Optics, Oxford: Pergamon Press, 1959.

    MATH  Google Scholar 

  32. Bekshaev, A.Y. and Soskin, M.S., Transverse energy flows in vectorial fields of paraxial beams with singularities, Opt. Commun., 2007, vol. 271, pp. 332–348. https://doi.org/10.1016/J.OPTCOM.2006.10.057

    Article  Google Scholar 

  33. Berry, M.V., Optical currents, J. Opt. A: Pure Appl. Opt., 2009, vol. 11, 094001. 697.https://doi.org/10.1088/1464-4258/11/9/094001

  34. Kumar, V. and Viswanathan, N.K., Topological structures in vector-vortex beam fields, J. Opt. Soc. Am. B, 2014, vol. 31, no. 6, pp. A40–A45. https://doi.org/10.1364/JOSAB.31.000A40

    Article  Google Scholar 

  35. Freund, I., Polarization flowers, Opt. Commun., 2001, vol. 199, pp. 47–63. https://doi.org/10.1016/S0030-4018(01)01533-4

    Article  Google Scholar 

  36. Kumar, V. and Viswanathan, N.K., C-point and V-point singularity lattice formation and index sign conversion methods, Opt. Commun., 2017, vol. 393, pp. 156–168. https://doi.org/10.1016/j.optcom.2017.02.048

    Article  Google Scholar 

  37. Rosales-Guzmán, C., Bhebhe, N., and Forbes, A., Simultaneous generation of multiple vector beams on a single SLM, Opt. Express., 2017, vol. 25, no. 21, pp. 25697–25706. https://doi.org/10.1364/OE.25.025697

    Article  Google Scholar 

  38. Chen, S., Xie, Z., Ye, H., Wang, X., Guo, Z., He, Y., Li, Y., Yuan, X., and Fan, D., Cylindrical vector beam multiplexer/demultiplexer using off-axis polarization control, Light: Sci. Appl., 2021, vol. 10, no. 222. https://doi.org/10.1038/s41377-021-00667-7

  39. Fadeyeva, T.A. and Volyar, A.V., Vector singularities analysis by the computer differential polarimeter, Proc. of SPIE—9th International Conference on Nonlinear Optics of Liquid and Photorefractive Crystals, 2003, vol. 5257, pp. 286–289. https://doi.org/10.1117/12.545886

  40. Snyder, A.W. and Love, J.D., Optical Waveguide Theory, London, New-York: Chapman and Hall, 1985.

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Volyar, A.V., Khalilov, S.I., Bretsko, M.V. et al. Measuring Singularities of Vector Structured LG Beams and Stokes Vortices via Intensity Moments Technique. Opt. Mem. Neural Networks 32 (Suppl 1), S63–S74 (2023). https://doi.org/10.3103/S1060992X23050193

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