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Asymmetry of hybrid-polarized beams in the sharp focus
V.D. Zaitsev 1, S.S. Stafeev 1, E. S. Kozlova 1

1 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

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DOI: 10.18287/COJ1977

Article ID: 1977

Language: Russian

Abstract:
In this paper, using the Richards-Wolf formalism, we investigate the helicity density and Poynting vector of hybrid vector vortex beams, which are beams with various combinations of topological charges (vortex orders) and polarization orders. It is shown that when focusing an optical vortex with hybrid polarization, neither the intensity nor helicity density exhibit radial symmetry, while showing central symmetry. Unlike non-vortex beams with hybrid polarization, asymmetry is observed in the zones with negative and positive helicity density values. For example, for a beam with a unit polarization order and a unit topological charge, the maximum positive helicity density values are approximately equal to half the absolute value of the minimum negative values. Such asymmetry in the helicity density zones has not previously been observed in the beams. Also, as a result of the study of hybrid vector vortex beams, it is shown that the longitudinal component of the Poynting vector exhibits a pronounced azimuthal asymmetry, indicating an asymmetric longitudinal energy flow in the focal region.

Keywords:
optical vortices, hybrid polarization, Richards–Wolf equations, tight focusing of light.

Acknowledgements:
The work was financially supported by the Russian Science Foundation under grant No. 25-29-01187.

Citation:
Zaitsev VD, Stafeev SS, Kozlova ES. Asymmetry of hybrid-polarized beams in the sharp focus. Computer Optics 2026; 50(5): 1977. doi: 10.18287/COJ1977.

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. Scientific Reports 2017; 7: 40195. DOI: 10.1038/srep40195.
  2. Kotlyar VV, Kovalev AA, Zaitsev VD. Inhomogeneously polarized light fields: Polarization singularity indices derived by analogy with the topological charge. Computer Optics 2022; 46(5): 671-681. DOI: 10.18287/2412-6179-CO-1126.
  3. 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 Research 2017; 5(6): 640-648. DOI: 10.1364/PRJ.5.000640.
  4. Kotlyar VV, Stafeev SS, Zaitsev VD, Telegin AM. Poincaré beams at the sharp focus: Inseparability, radial spin Hall effect, and reverse energy flow. Photonics 2022; 9(12): 969. DOI: 10.3390/photonics9120969.
  5. Chen J, Wan C, Zhan Q. Engineering photonic angular momentum with structured light: A review. Advanced Photonics 2021; 3(6): 064001. DOI: 10.1117/1.AP.3.6.064001.
  6. Qiu CW, Palima D, Novitsky A, Gao D. Engineering light-matter interaction for emerging optical manipulation applications. Nanophotonics 2014; 3(3): 181-201. DOI: 10.1515/nanoph-2013-0055.
  7. Kotlyar VV, Stafeev SS, Kovalev AA, Zaitsev VD. Focusing a cylindrical vector beam and the Hall effect. Computer Optics 2024; 48(1): 47-52. DOI: 10.18287/2412-6179-CO-1356.
  8. Kotlyar VV, Stafeev SS, Zaitsev VD. Sharp focusing of on-axis superposition of a high-order cylindrical vector beam and a beam with linear polarization. Computer Optics 2023; 47(1): 5-15. DOI: 10.18287/2412-6179-CO-1165.
  9. Lapin BP, Aliyeva SS, Yavorsky MA, Alexeyev CN. Optical vortices in add-drop filters. Computer Optics 2025; 49(3): 378-382. DOI: 10.18287/2412-6179-CO-1561.
  10. Lyu Y, Man Z, Zhao R, Meng P, Zhang W, Ge X, Fu S. Hybrid polarization induced transverse energy flow. Optics Communications 2021; 485: 126704. DOI: 10.1016/j.optcom.2020.126704.
  11. Wang XL, Li Y, Chen J, Guo CS, Ding J, Wang HT. A new type of vector fields with hybrid states of polarization. Optics Express 2010; 18(10): 10786-10795. DOI: 10.1364/OE.18.010786.
  12. Lerman GM, Stern L, Levy U. Generation and tight focusing of hybridly polarized vector beams. Optics Express 2010; 18(26): 27650-27657. DOI: 10.1364/OE.18.027650.
  13. Hu K, Chen Z, Pu J. Tight focusing properties of hybridly polarized vector beams. Journal of the Optical Society of America A 2012; 29(6): 1099-1104. DOI: 10.1364/JOSAA.29.001099.
  14. 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 Physics 2021; 31(4): 045001. DOI: 10.1088/1555-6611/abe7db.
  15. Khonina SN. Vortex beams with high-order cylindrical polarization: Features of focal distributions. Applied Physics B 2019; 125: 100. DOI: 10.1007/s00340-019-7212-1.
  16. 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.
  17. Chen S, Zhou X, Liu Y, Ling X, Luo H, Wen S. Generation of arbitrary cylindrical vector beams on the higher-order Poincaré sphere. Optics Letters 2014; 39(18): 5274-5276. DOI: 10.1364/OL.39.005274.
  18. Angelsky O, Mokhun I, Bekshaev A, Zenkova C, Zheng J. Polarization singularities: Topological and dynamical aspects. Frontiers in Physics 2023; 11: 1147788. DOI: 10.3389/fphy.2023.1147788.
  19. Dennis MR, O’Holleran K, Padgett MJ. Singular optics: Optical vortices and polarization singularities. Progress in Optics 2009; 53: 293-363. DOI: 10.1016/S0079-6638(08)00205-9.
  20. Panin DN, Osipov OV. Inhomogeneous chiral metamaterials: Optical wave reflection analysis with regard to the dispersion of material parameters. Computer Optics 2024; 48(6): 809-815. DOI: 10.18287/2412-6179-CO-1443.
  21. Babiker M, Yuan J, Koksal K, Lembessis VE. The super-chirality of vector twisted light. Optics Communications 2024; 554: 130185. DOI: 10.1016/j.optcom.2023.130185.
  22. Forbes KA. Comment on M. Babiker, J. Yuan, K. Koksal, and V. Lembessis, Optics Communications 554, 130185 (2024). Optics Communications 2024; 561: 130499. DOI: 10.1016/j.optcom.2024.130499.
  23. Stafeev SS, Zaitsev VD, Kotlyar VV. Helicity density of higher-order Poincaré beams in tight focus. Optics Communications 2025; 583: 131803. DOI: 10.1016/j.optcom.2025.131803.
  24. Holmes BM, Galvez EJ. Poincaré Bessel beams: Structure and propagation. Journal of Optics 2019; 21(10): 104001. DOI: 10.1088/2040-8986/ab3d7d.
  25. Richards B, Wolf E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system. Proceedings of the Royal Society A 1959; 253(1274): 358-379. DOI: 10.1098/rspa.1959.0200.
  26. 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.
  27. Abujetas DR, Sánchez-Gil JA. Spin angular momentum of guided light induced by transverse confinement and intrinsic helicity. ACS Photonics 2020; 7(2): 534-545. DOI: 10.1021/acsphotonics.9b01493.
  28. Kovalev A, Kotlyar V, Telegin A. Optical helicity of light in the tight focus. Photonics 2023; 10(7): 719. DOI: 10.3390/photonics10070719.
  29. Singh K, Tabebordbar N, Forbes A, Dudley A. Digital Stokes polarimetry and its application to structured light: Tutorial. Journal of the Optical Society of America A 2020; 37(11): C33-C44. DOI: 10.1364/JOSAA.397912.

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