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Vortex energy flow in the tight focus of a non-vortex field with circular polarization

V.V. Kotlyar 1,2, S.S. Stafeev 1,2, A.G. Nalimov 1,2

IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,

Molodogvardeyskaya 151, 443001, Samara, Russia,

Samara National Research University, Moskovskoye shosse, 34, 443086, Samara, Russia

 PDF, 647 kB

DOI: 10.18287/2412-6179-CO-582

Pages: 5-11.

Full text of article: Russian language.

Abstract:
Using Richards-Wolf formulas, we show that an axisymmetric circularly polarized vortex-free field can be focused into a sharp subwavelength focal spot, around which there is a  region where the light energy flow propagates along a spiral. This effect can be explained by the conversion of the spin angular momentum of the circularly polarized field into the orbital angular momentum near the focus, although the on-axis orbital angular momentum remains zero. It is also shown that a linearly polarized optical vortex with topological charge 2 forms near the focal plane an on-axis reverse energy flow (defined by the negative longitudinal component of the Poynting vector) whose amplitude is comparable with the direct energy flow.

Keywords:
Richards-Wolf formulae, relation between spin angular momentum and orbital angular momentum, reverse energy flow, linear polarization.

Citation:
Kotlyar VV, Stafeev SS, Nalimov AG. Vortex energy flow in the tight focus of a non-vortex field with circular polarization. Computer Optics 2020; 44(1): 5-11. DOI: 10.18287/2412-6179-CO-582.

Acknowledgements:
This work was supported by the Russian Science Foundation under project No. 17-19-01186 ("Theoretical background"), the RF Ministry of Science and Higher Education under the government project of FSRC «Crystallography and Photonics» RAS, ("Numerical simulation").

References:

  1. Irvine WTM. Bouwmeester D. Linked and knotted beams of light. Nat Phys 2008; 4(9): 716-720.
  2. Sugic D, Dennis MR. Singular knot bundle in light. J Opt Soc Am A 2018; 35(12): 1987-1999.
  3. Larocque H, Sugic D, Mortimer D, Taylor AJ, Fickler R, Boyd RW, Dennis MR, Karimi E. Reconstructing the topology of optical polarization knots. Nat Phys 2018; 14(11): 1079-1082.
  4. Berry MV. Wave dislocation reactions in non-paraxial Gaussian beams. J Mod Opt 1998; 45(9): 1845-1858.
  5. Volyar AV. Nonparaxial Gausian beams: 1. Vector fields. Tech Phys Lett 2000; 26(7): 573-575.
  6. Kotlyar VV, Stafeev SS, Kovalev AA. Reverse and toroidal flux of light fields with both phase and polarization higher-order singularities in the sharp focus area. Opt Express 2019; 27(12): 16689-16702. DOI: 10.1364/OE.27.016689.
  7. Kotlyar VV, Kovalev AA, Porfirev AP. Radial dependence of the angular momentum density of a paraxial optical vortex. Phys Rev A 2018; 97(5): 053833. DOI: 10.1103/PhysRevA.97.053833.
  8. Kotlyar VV, Kovalev AA, Nalimov AG. Energy density and energy flux in the focus of an optical vortex: reverse flux of light energy. Opt Lett 2018; 43(12): 2921-2924. DOI: 10.1364/OL.43.002921.
  9. Kotlyar VV, Stafeev SS, Nalimov AG. Energy backflow in the focus of a light beam with phase or polarization singularity. Phys Rev A 2019; 99(3): 033840. DOI: 10.1103/PhysRevA.99.033840.
  10. Aiello A, Banzer P, Neugebauer M, Leuchs G. From transverse angular momentum to photonic wheels. Nat Photon 2015; 9: 789-795. DOI: 10.1038/NPHOTON.2015.20.
  11. Bauer T, Neugebauer M, Leuchs G, Banzer P. Optical polarization Mobius strips and points of purely transverse spin density. Phys Rev Lett 2016; 117(1): 013601. DOI: 10.1103/PhysRevLett.117.013601.
  12. Eismann JS, Banzer P, Neugebauer M. Spin-orbit coupling and the evolution of transverse spin. Source: <https://arxiv.org/abs/1905.12539>.
  13. Hao X, Kuang C, Wang T, Liu X. Phase encoding for sharper focus of the azimuthally polarized beam. Opt Lett 2010; 35(23): 3928-3930. DOI: 10.1364/OL.35.003928.
  14. Qin F, Huang K, Wu J, Jiao J, Luo X, Qiu C, Hong M. Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light. Sci Rep 2015; 5: 09977. DOI: 10.1038/srep09977.
  15. Wang S, Li X, Zhou J, Gu M. Ultralong pure longitudinal magnetization needle induced by annular vortex binary optics. Opt Lett 2014; 39: 5022-5025.
  16. Yuan GH, Wei SB, Yuan XC. Nondiffracting transversally polarized beam. Opt Lett 2011; 36(17): 3479-3481. DOI: 10.1364/OL.36.003479.
  17. Suresh P, Mariyal C, Rajesh KB, Pillai TVS, Jaroszewicz Z. Generation of a strong uniform transversely polarized nondiffracting beam using a high-numerical-aperture lens axicon with a binary phase mask. Appl Opt 2013; 52(4): 849-853. DOI: 10.1364/AO.52.000849.
  18. Anita GT, Umamageswari N, Prabakaran K, Pillai TVS, Rajesh KB. Effect of coma on tightly focused cylindrically polarized vortex beams. Opt Laser Techn 2016; 76: 1-5. DOI: 10.1016/j.optlastec.2015.07.002.
  19. Yuan GH, Wei SB, Yuan XC. Generation of nondiffracting quasi-circular polarization beams using an amplitude modulated phase hologram. J Opt Soc Am A 2011; 28(8): 1716-1720. DOI: 10.1364/JOSAA.28.001716.
  20. Chen Z, Zhao D. 4Pi focusing of spatially modulated radially polarized vortex beams. Opt Lett 2012; 37(8): 1286-1288. DOI: 10.1364/OL.37.001286.
  21. Ndagano B, Sroor H, McLaren M, Rosales-Guzmán C, Forbes A. Beam quality measure for vector beams. Opt Lett 2016; 41(15): 3407-3410. DOI: 10.1364/OL.41.003407.
  22. Berry MV. Optical currents. J Opt A: Pure Appl Opt 2009; 11: 094001.
  23. Kotlyar VV, Nalimov AG. A vector optical vortex generated and focused using a metalens. Computer Оptics 2017; 41(5): 645-654. DOI: 10.18287/2412-6179-2017-41-5-645-654.
  24. Monteiro PB, Neto PAM, Nussenzveig HM. Angular momentum of focused beams: Beyond the paraxial approximation. Phys Rev A 2009; 79: 033830. DOI: 10.1103/PhysRevA.79.033830.
  25. Richards B, Wolf E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system. Proc Royal Soc A: Math, Phys Eng Sci 1959; 253(1274): 358-379. DOI: 10.1098/rspa.1959.0200.
  26. Youngworth KS, Brown TG. Focusing of high numerical aperture cylindrical-vector beams. Opt Express 2000; 7: 77-87.
  27. Bliokh KY, Bekshaev AY, Nori F. Extraordinary momentum and spin in evanescent waves. Nat Commun 2014; 5: 3300. DOI: 10.1038/ncomms4300.
  28. Bekshaev A, Bliokh KY, Soskin M. Internal flows and energy circulation in light beams. J Opt 2011; 13(5): 053001.

 


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