(49-5) 01 * << * >> * Russian * English * Content * All Issues

Singularity index and orbital angular momentum of a beam with a hybrid polarization singularity
V.V. Kotlyar 1,2, A.A. Kovalev 1,2, S.S. Stafeev 1,2

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

 PDF, 1302 kB

DOI: 10.18287/2412-6179-CO-1624

Pages: 707-714.

Full text of article: Russian language.

Abstract:
Alongside scalar optical vortex beams, which have a topological charge (TC), a spiral wave front and carry an orbital angular momentum (OAM) that can be transferred to microparticles and rotate them along circular trajectories, polarization optical vortices are also known, in which the polarization state in the beam cross section changes with a change in the azimuthal angle. Such vortices have points of polarization singularity, which are described by indices similar to TZ. However, polarization OAMs for polarization vortices have not yet been considered. Meanwhile, laser beams with inhomogeneous polarization can perform spiral transfer of matter in polarization-sensitive media. In this paper, two possible definitions of polarization OAMs are considered. One OAM is proportional to the azimuthal rate of change of the linear polarization vector direction, and the second (hybrid OAM) is proportional to the azimuthal rate of change of the degree of ellipticity of the polarization ellipse. For example, the normalized polarization OAM is equal to the order of a cylindrical vector beam and is also equal to the order of a Poincaré beam.

Keywords:
orbital angular momentum, polarization singularity index, Stokes vector, non-uniform polarization.

Citation:
Kotlyar VV, Kovalev AA, Stafeev SS. Singularity index and orbital angular momentum of a beam with a hybrid polarization singularity. Computer Optics 2025; 49(5): 707-714. DOI: 10.18287/2412-6179-CO-1624.

Acknowledgements:
This work was financially supported by the Russian Science Foundation under grant 23-12-00236 ("Theory" Section) and the government project of the NRC "Kurchatov Institute" ("Numerical Simulation" Section).

References:
  1. Berry MV. Optical vortices evolving from helicoidal integer and fractional phase steps. J Opt A 2004; 6(2): 259-268. DOI: 10.1088/1464-4258/6/2/018.
  2. Allen L, Beijersbergen MW, Spreeuw RJC, Woerdman JP. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A 1992; 45(11): 8185-8189. DOI: 10.1103/PhysRevA.45.8185.
  3. Berry MV. Index formulae for singular lines of polarization. J Opt A 2004; 6(7): 675-678. DOI: 10.1088/1464-4258/6/7/003.
  4. Freund I. Polarization singularity indices in Gaussian laser beams. Opt Commun 2002; 201(4-6): 251-270. DOI: 10.1016/S0030-4018(01)01725-4.
  5. Zhan Q. Cylindrical vector beams: from mathematical concepts to applications. Adv Opt Photonics 2009; 1(1): 1-57. DOI: 10.1364/AOP.1.000001.
  6. He H, Friese MEJ, Heckenberg NR, Rubinsztein-Dunlop H. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys Rev Lett 1995; 75(5): 826-829. DOI: 10.1103/PhysRevLett.75.826
  7. Ambrosio A, Maddalena P, Marrucci L. Molecular model for light-driven spiral mass transport in azopolymer films. Phys Rev Lett 2013; 110(14): 146102. DOI: 10.1103/PhysRevLett.110.146102.
  8. 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.
  9. Porfirev A, Khonina S, Porfirev D, Ivliev N. Structured polarized laser beams for controlled spiral-shaped mass transfer in azopolymer thin films. Appl Opt 2024; 63(14): 3779-3784. DOI: 10.1364/AO.521196.
  10. Poynting JH. The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light. Proc R Soc London A 1909; 82(557): 560-567. DOI: 10.1098/rspa.1909.0060.
  11. Beth RA. Mechanical detection and measurement of the angular momentum of light. Phys Rev 1936; 50(2): 115-125. DOI: 10.1103/PhysRev.50.115.
  12. Friese MEJ, Enger J, Rubinsztein-Dunlop H, Heckenberg NR. Optical angular-momentum transfer to trapped absorbing particles. Phys Rev A 1996; 54(2): 1593-1596. DOI: 10.1103/PhysRevA.54.1593.
  13. Zhao Y, Zhou L, Jiang X, Zhu L, Shi Q. Optical force effects of Rayleigh particles by cylindrical vector beams. Nanomaterials 2024; 14(8): 691. DOI: 10.3390/nano14080691.
  14. Albaladejo S, Marqués MI, Laroche M, Sáenz JJ. Scattering forces from the curl of the spin angular momentum of a light field. Phys Rev Lett 2009; 102(11): 113602. DOI: 10.1103/PhysRevLett.102.113602.
  15. Baranova NB, Zel’dovich BY, Scully MO. Acceleration of charged particles by laser beams. JETP 1994; 78(3): 249-258.
  16. Mellado VH, Hacyan S, Jauregui R. Trapping and acceleration of charged particles in Bessel beams. Laser Part Beams 2006; 24(4): 559-566. DOI: 10.1017/S0263034606060745.
  17. Polak K, Gayde J-C, Sulc M. 3D Polarisation of a structured laser beam and prospects for its application to charged particle acceleration. J Phys Conf Ser 2024; 2687(4): 042003. DOI: 10.1088/1742-6596/2687/4/042003.
  18. Maragò OM, Jones PH, Gucciardi PG, Volpe G, Ferrari AC. Optical trapping and manipulation of nanostructures. Nat Nanotechnol 2013; 8(11): 807-819. DOI: 10.1038/nnano.2013.208.
  19. Meng P, Man Z, Konijnenberg AP, Urbach HP. Angular momentum properties of hybrid cylindrical vector vortex beams in tightly focused optical systems. Opt Express 2019; 27(24): 35336-35348. DOI: 10.1364/OE.27.035336.
  20. Yang R, Li R, Qin S, Ding C, Mitri FG. Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams. J Opt 2017; 19(2): 025602. DOI: 10.1088/2040-8986/19/2/025602.
  21. 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. Nat Phys 2007; 3(9): 628–631. DOI: 10.1038/nphys676.
  22. 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.
  23. Bauer T, Banzer P, Karimi E, Orlov S, Rubano A, Marrucci L, Santamato E, Boyd RW, Leuchs G. Observation of optical polarization Möbius strips. Science 2015; 347(6225): 964-966. DOI: 10.1126/science.1260635.
  24. Graydon O. Photonic wheel. Nat Photonics 2013; 7(9): 672-672. DOI: 10.1038/nphoton.2013.229.
  25. Aiello A, Banzer P, Neugebauer M, Leuchs G. From transverse angular momentum to photonic wheels. Nat Photonics 2015; 9(12): 789-795. DOI: 10.1038/nphoton.2015.203.
  26. Zhao Y, Edgar JS, Jeffries GDM, McGloin D, Chiu DT. Spin-to-orbital angular momentum conversion in a strongly focused optical beam. Phys Rev Lett 2007; 99(7): 073901. DOI: 10.1103/PhysRevLett.99.073901.
  27. Nieminen TA, Stilgoe AB, Heckenberg NR, Rubinsztein-Dunlop H. Angular momentum of a strongly focused Gaussian beam. J Opt A 2008; 10(11): 115005. DOI: 10.1088/1464-4258/10/11/115005.
  28. Kotlyar VV, Nalimov AG, Stafeev SS. Exploiting the circular polarization of light to obtain a spiral energy flow at the subwavelength focus. J Opt Soc Am B. 2019; 36(10): 2850-2855. DOI: 10.1364/JOSAB.36.002850.
  29. Kotlyar VV, Stafeev SS, Kozlova ES, Butt MA. High-order orbital and spin Hall effects at the tight focus of laser beams. Photonics 2022; 9(12): 970. DOI: 10.3390/photonics9120970.
  30. Kotlyar VV, Stafeev SS. Orbital and spin energy flows in tight focus. Optik 2021; 245: 167703. DOI: 10.1016/j.ijleo.2021.167703.
  31. Bansal S, Senthilkumaran P. Stokes polarimetry with Poincaré–Hopf index beams. Opt Lasers Eng 2023; 160: 107295. DOI: 10.1016/j.optlaseng.2022.107295.
  32. Ruchi, Senthilkumaran P, Pal SK. Phase Singularities to Polarization Singularities. Int J Opt 2020; 2020: 2812803. DOI: 10.1155/2020/2812803.
  33. Kotlyar VV, Kovalev AA, Zaitsev VD. Topological charge of light fields with a polarization singularity. Photonics 2022; 9(5): 298. DOI: 10.3390/photonics9050298.
  34. Fang L, Wang J. Optical angular momentum derivation and evolution from vector field superposition. Opt Express 2017; 25(19): 23364-23375. DOI: 10.1364/OE.25.023364.
  35. Kotlyar VV, Kovalev AA, Porfirev AP. Astigmatic transforms of an optical vortex for measurement of its topological charge. Appl Opt 2017; 56(14): 4095-4104. DOI: 10.1364/AO.56.004095.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20