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Superposition of an optical vortex and a plane wave with linear polarization states at the tight focus
V.V. Kotlyar 1,2, S.S. Stafeev 1,2, M.A. Telegin 1,2, E.S. Kozlova 1,2

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

 PDF, 850 kB

DOI: 10.18287/2412-6179-CO-1502

Pages: 851-857.

Full text of article: Russian language.

Abstract:
We analyze the sharp focusing of the superposition of a vortex laser beam with topological charge n and linear polarization and a plane wave with the same linear polarization directed along the horizontal axis. Using the Richards-Wolf formalism, analytical expressions are obtained for the intensity distribution and longitudinal projection of the spin angular momentum (SAM) in the focal plane. It is shown that for even and odd numbers n the intensity and SAM have different symmetries: for even n they are symmetric with respect to both Cartesian axes, and for odd n they are symmetric only with respect to the vertical axis. The intensity distribution has 2n local maxima at the focus, and the intensity on the optical axis is nonzero for any n. The distribution of the longitudinal SAM (spin density) in the focal plane has (n+2) subwavelength regions with a positive SAM and (n+2) regions with a negative SAM, the centers of which alternately locate on a circle of a certain radius centered at the optical axis. Such an alternating-spin pattern demonstrates the spin Hall effect at the focus. At the focus, the negative and positive spins are mutually compensated, meaning that the total spin is zero.

Keywords:
spin angular momentum, Richards-Wolf formulas, Hall effect, optical vortex, plane wave, linear polarization.

Citation:
Kotlyar VV, Stafeev SS, Telegin AM, Kozlova ES. Superposition of an optical vortex and a plane wave with linear polarization states at the tight focus. Computer Optics 2024; 48(6): 851-857. DOI: 10.18287/2412-6179-CO-1502.

Acknowledgements:
The work was partly funded by the Russian Science Foundation under grant #23-12-00236 (Theory and Numerical Simulation) and the NRC "Kurchatov Institute" under a government project (Introduction and Conclusion).

References:
  1. Aiello A, Banzer P, Neugebauer M, Leuchs G. From transverse angular momentum to photonic wheels. Nature Photon 2015; 9: 789-795. DOI: 10.1038/nphoton.2015.203.
  2. Bauer T, Banzer P, Karimi E, Orlov S, Rubano A, Marrucci L, Santa Mato E, Boyd RW, Leuchs G. Observation of optical polarization Möbius strips. Science 2015; 347: 964-966. DOI: 10.1126/science.1260635.
  3. Wan C, Zhan Q. Generation of exotic optical polarization Möbius strips. Opt Express 2019; 27(8): 11516-11524. DOI: 10.1364/OE.27.011516.
  4. Leach J, Dennis MR, Courtial J, Padgett MJ. Knotted threads of darkness. Nature 2004; 432: 165. DOI: 10.1038/432165a.
  5. Dennis MR, King RP, Jack B, O’Holleran K, Padgett MJ. Isolated optical vortex knots. Nat Phys 2010; 6: 118-121. DOI: 10.1038/nphys1504.
  6. Sugic D, Dennis MR. Singular knot bundle in light. J Opt Soc Am A 2018; 35(12): 1987-1999. DOI: 10.1364/JOSAA.35.001987.
  7. Kotlyar VV, Stafeev SS, Nalimov AG, Kovalev AA, Porfirev AP. Mechanism of formation of an inverse energy flow in a sharp focus. Phys Rev A 2020; 101(3): 033811. DOI: 10.1103/PhysRevA.101.033811.
  8. Yang X, Mou Y, Zapata R, Reynier B, Gallas B, Mivelle M. An inverse Faraday effect generated by linearly polarized light through a plasmonic nano-antenna. Nanophotonics 2023; 12(4): 687-694. DOI: 10.1515/nanoph-2022-0488.
  9. Zhou S, Rui G, Chen H, Zhan Q. Diffraction-limited optical focusing with arbitrarily oriented magnetic field. J Opt 2019; 21(4): 045610. DOI: 10.1088/2040-8986/ab0f8f.
  10. Zhao K, Zhang Z, Zang H, Du J, Lu Y, Wang P. Generation of pure longitudinal magnetization focal spot with a triplex metalens. Opt Lett 2021; 46(8): 1896-1899. DOI: 10.1364/OL.422351.
  11. Bliokh KY, Ostrovskaya EA, Alonso MA, Rodríguez-Herrera OG, Lara D, Dainty C. Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems. Opt Express 2011; 19(27): 26132-26149. DOI: 10.1364/OE.19.026132.
  12. Kotlyar VV, Nalimov AG, Kovalev AA, Porfirev AP, Stafeev SS. Spin-orbit and orbit-spin conversion in the sharp focus of laser light: Theory and experiment. Phys Rev A 2020; 102(3): 033502. DOI: 10.1103/PhysRevA.102.033502.
  13. Devlin EC, Ambrosio A, Wintz D, Oscurato SL, Zhu AY, Khorasaninejad M, Oh J, Maddalena P, Capasso F. Spin-to-orbital angular momentum conversion in dielectric metasurfaces. Opt Express 2017; 25(1): 377-393. DOI: 10.1364/OE.25.000377.
  14. Leyder C, Romanelli M, Karr JP, Giacobino E, Liew TCH, Glazov MM, Kavokin AV, Malpuech G, Bramati A. Observation of the optical spin Hall effect. Nature Phys 2007; 3(9): 628-631. DOI: 10.1038/nphys676.
  15. Li H, Ma C, Wang J, Tang M, Li X. Spin-orbit Hall effect in the tight focusing of a radially polarized vortex beam. Opt Express 2021; 29(24): 39419-39427. DOI: 10.1364/OE.443271.
  16. Kotlyar VV, Kovalev AA, Kozlova ES, Telegin AM. Hall effect at the focus of an optical vortex with linear polarization. Micromachines 2023; 14(4): 788. DOI: 10.3390/mi14040788.
  17. Kotlyar VV, Stafeev SS, Zaitsev VD, Kovalev AA. Multiple optical spin-orbit Hall effect at the tight focus. Phys Lett A 2023; 458: 128596. DOI: 10.1016/j.physleta.2022.128596.
  18. Richards B, Wolf E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system. Proc R Soc A Math Phys Eng Sci 1959; 253(1274): 358-379. DOI: 10.1098/rspa.1959.0200.
  19. Kovalev AA, Kotlyar VV. Spin hall effect of double-index cylindrical vector beams in a tight focus. Micromachines 2023; 14(2): 494. DOI: 10.3390/mi14020494.
  20. Davidson N, Bokor N. High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens. Opt Lett 2004; 29(12): 1318-1320. DOI: 10.1364/ol.29.001318.
  21. Stafeev SS, Nalimov AG, Kovalev AA, Zaitsev VD, Kotlyar VV. Circular polarization near the tight focus of linearly polarized light. Photonics 2022; 9(3): 196. DOI: 10.3390/photonics9030196.
  22. Zhai Y, Cao L, Liu Y, Tan X. A review of polarization-sensitive materials for polarization holography. Materials 2020; 13(23): 5562. DOI: 10.3390/ma13235562.
  23. Merte M, Freimuth F, Go D, Adamantopoulos T, Lux FR, Plucinski L, Gomonay O, Blügel S, Mokrousov Y. Photocurrents, inverse Faraday effect, and photospin Hall effect in Mn2Au. APL Mater 2023; 11(7): 071106. DOI: 10.1063/5.0149955.

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