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.
Similar content being viewed by others
REFERENCES
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
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
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
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
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
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
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
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
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
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
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.
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
Nye, J.F., Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, Bristol and Philadelphia: Inst. of Physics Publ., 1999.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
Born, M. and Wolf, E., Principles of Optics, Oxford: Pergamon Press, 1959.
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
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
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
Freund, I., Polarization flowers, Opt. Commun., 2001, vol. 199, pp. 47–63. https://doi.org/10.1016/S0030-4018(01)01533-4
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
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
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
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
Snyder, A.W. and Love, J.D., Optical Waveguide Theory, London, New-York: Chapman and Hall, 1985.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1060992X23050193