(48-5) 02 * << * >> * Russian * English * Content * All Issues

Sharp focusing of a hybridly polarized optical vortex
S.S. Stafeev 1,2, V.D. Zaitcev 1,2, V.V. Kotlyar 1,2

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

 PDF, 834 kB

DOI: 10.18287/2412-6179-CO-1496

Pages: 655-661.

Full text of article: Russian language.

Abstract:
In this work, using the Richards-Wolf formalism, we consider the sharp focusing of optical vortices with hybrid polarization, which combines the properties of azimuthal and circular polarizations. It is shown that these beams have a number of unique properties: the intensity pattern in such beams is rotating with distance from the focal spot and the longitudinal component of the spin angular momentum is asymmetrically shaped.

Keywords:
sharp focusing, optical vortex, inhomogeneous polarization, spin angular momentum.

Citation:
Stafeev SS, Zaitsev VD, Kotlyar VV. Sharp focusing of a hybridly polarized optical vortex. Computer Optics 2024; 48(5): 655-661. DOI: 10.18287/2412-6179-CO-1496.

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

References:

  1. D'Errico A, Maffei M, Piccirillo B, de Lisio C, Cardano F, Marrucci L. Topological features of vector vortex beams perturbed with uniformly polarized light. Sci Rep 2017; 7: 40195. DOI: 10.1038/srep40195.
  2. Gao XZ, Pan Y, Zhang GL, Zhao MD, Ren ZC, Tu CG, Li YN, Wang HT. Redistributing the energy flow of tightly focused ellipticity-variant vector optical fields. Photonics Res 2017; 5: 640. DOI: 10.1364/PRJ.5.000640.
  3. Khonina SN, Ustinov AV, Porfirev AP. Vector Lissajous laser beams. Opt Lett 2020; 45(15): 4112-4115. DOI: 10.1364/OL.398209.
  4. Lyu Y, Man Z, Zhao R, Meng P, Zhang W, Ge X, Fu S. Hybrid polarization induced transverse energy flow. Opt Commun 2021; 485: 126704. DOI: 10.1016/j.optcom.2020.126704.
  5. Wang X-L, Li Y, Chen J, Guo C-S, Ding J, Wang H-T. A new type of vector fields with hybrid states of polarization. Opt Express 2010; 18(10): 10786-10795. DOI: 10.1364/OE.18.010786.
  6. Lerman GM, Stern L, Levy U. Generation and tight focusing of hybridly polarized vector beams. Opt Express 2010; 18(26): 27650-27657. DOI: 10.1364/OE.18.027650.
  7. Hu K, Chen Z, Pu J. Tight focusing properties of hybridly polarized vector beams. J Opt Soc Am A 2012; 29(6): 1099-1104. DOI: 10.1364/JOSAA.29.001099.
  8. Ji K, Qin Y, Liu X, Zheng H, Ren H, Hu Y. Tight focusing of the centrosymmetric shape of hybrid polarized beams by adjustable multi-vortex phases. Laser Phys 2021; 31: 045001. DOI:10.1088/1555-6611/abe7db.
  9. Khonina SN. Vortex beams with high-order cylindrical polarization: features of focal distributions. Appl Phys B 2019; 125: 100. DOI: 10.1007/s00340-019-7212-1.
  10. Khonina SN, Ustinov AV, Fomchenkov SA, Porfirev AP. Formation of hybrid higher-order cylindrical vector beams using binary multi-sector phase plates. Sci Rep 2018; 8: 14320. DOI: 10.1038/s41598-018-32469-0.
  11. Chen S, Zhou X, Liu Y, Ling X, Luo H, Wen S. Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere. Opt Lett 2014; 39(18): 5274-5276. DOI: 10.1364/OL.39.005274.
  12. Holmes BM, Galvez EJ. Poincaré Bessel beams: structure and propagation. J Opt 2019; 21: 104001. DOI: 10.1088/2040-8986/ab3d7d.
  13. Shen Y, Wang Z, Fu X, Naidoo D, Forbes A. SU(2) Poincaré sphere: A generalized representation for multidimensional structured light. Phys Rev A 2020; 102: 031501. DOI: 10.1103/PhysRevA.102.031501.
  14. Milione G, Sztul HI, Nolan DA, Alfano RR. Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light. Phys Rev Lett 2011; 107: 053601. DOI: 10.1103/PhysRevLett.107.053601.
  15. Zhang X, Han L, Wu X, Du J, Xin Y, Wei BB, Liu S, Li P, Zhao J. Spin-orbit coupling induced polarization transform in the autofocusing of ring Airy beams with hybrid polarizations. Opt Express 2023, 31(26): 44019-44027. DOI: 10.1364/OE.506967.
  16. Liu Z, Liu Y, Ke Y, Liu Y, Shu W, Luo H, Wen S. Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere. Photonics Res 2017; 5: 15. DOI: 10.1364/PRJ.5.000015.
  17. Kovalev AA, Kotlyar VV, Stafeev SS. Spin Hall effect in the paraxial light beams with multiple polarization singularities. Micromachines 2023, 14(4): 777. DOI: 10.3390/mi14040777.
  18. Kovalev AA, Kotlyar VV. Gaussian beams with multiple polarization singularities. Opt Commun 2018; 423: 111-120. DOI: 10.1016/j.optcom.2018.04.023.
  19. 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: 073901. DOI: 10.1103/PhysRevLett.99.073901.
  20. Yu P, Zhao Q, Hu X, Li Y, Gong L. Orbit-induced localized spin angular momentum in the tight focusing of linearly polarized vortex beams. Opt Lett 2018, 43(22): 5677-5680. DOI: 10.1364/OL.43.005677.
  21. Li M, Cai Y, Yan S, Liang Y, Zhang P, Yao B. Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams. Phys Rev A 2018; 97: 053842. DOI: 10.1103/PhysRevA.97.053842.
  22. Kotlyar VV, Stafeev SS, Kozlova ES, Nalimov AG. Spin-orbital conversion of a strongly focused light wave with high-order cylindrical–circular polarization. Sensors 2021; 21(19): 6424. DOI: 10.3390/s21196424.
  23. Richards B, Wolf E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system. Proc R Soc A 1959, 253(1274): 358-379. DOI: 10.1098/rspa.1959.0200.
  24. Pereira SF, van de Nes AS. Superresolution by means of polarisation, phase and amplitude pupil masks. Opt Commun 2004; 234: 119-124. DOI: 10.1016/j.optcom.2004.02.020.
  25. 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.
  26. Abramochkin E, Volostnikov V. Spiral-type beams. Opt Commun 1993; 102(3-4): 336-350. DOI: 10.1016/0030-4018(93)90406-U.
  27. Abramochkin E, Losevsky N, Volostnikov V. Generation of spiral-type laser beams. Opt Commun 1997; 141(1-2): 59-64. DOI: 10.1016/S0030-4018(97)00215-0.
  28. Schechner YY, Piestun R, Shamir J. Wave propagation with rotating intensity distributions. Phys Rev E 1996; 54(1): R50. DOI: 10.1103/PhysRevE.54.R50.
  29. Paakkonen P, Lautanen J, Honkanen M, Kuittinen M, Turunen J, Khonina SN, Kotlyar VV, Soifer VA, Friberg AT. Rotating optical fields: Experimental demonstration with diffractive optics. J Mod Opt 1998; 45(11): 2355-2369. DOI: 10.1080/09500349808231245.
  30. Kotlyar VV, Stafeev SS, Nalimov AG, Schulz S, O'Faolain L. Two-petal laser beam near a binary spiral axicon with topological charge 2. Opt Laser Technol 2019; 119: 105649. DOI: 10.1016/j.optlastec.2019.105649.
  31. Degtyarev SA, Porfirev AP, Khonina SN. Photonic nanohelix generated by a binary spiral axicon. Appl Opt 2016; 55(12): B44-B48. DOI: 10.1364/AO.55.000B44.

© 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