Longitudinal component of the Poynting vector of a tightly focused optical vortex with circular polarization
Stafeev S.S., Nalimov A.G.

Image Processing Systems Institute f RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Samara, Russia,
Samara National Research University, Samara, Russia

We numerically investigated the focusing of optical vortices with the wavelength λ = 532 nm and right-hand circular polarization by using a diffractive lens with the numerical aperture NA = 0.95. The simulation was carried out using the Richards-Wolf formulae and the FDTD-method. The focusing of optical vortices with topological charges equal to ±1 and ±2 was investigated. It was shown that the focusing of optical vortices with circular polarization by a wide-aperture diffractive lens can produce an intensity distribution with the negative value of the longitudinal component of the Poynting vector.

Richards-Wolf formulae, FDTD-method, optical vortex, tractor beam.

Stafeev SS, Nalimov AG. Longitudinal component of the Poynting vector of a tightly focused optical vortex with circular polarization. Computer Optics 2018; 42(2): 190-196. DOI: 10.18287/2412-6179-2018-42-2-190-196.


  1. 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.
  2. 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.
  3. Wang S, Li X, Zhou J, Gu M. Ultralong pure longitudinal magnetization needle induced by annular vortex binary optics. Opt Lett 2014; 39(17): 5022-5025. DOI: 10.1364/OL.39.005022.
  4. Yuan GH, Wei SB, Yuan X-C. Nondiffracting transversally polarized beam. Opt Lett 2011; 36(17): 3479-3481. DOI: 10.1364/OL.36.003479.
  5. 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.
  6. Anita GT, Umamageswari N, Prabakaran K, Pillai TVS, Rajesh KB. Effect of coma on tightly focused cylindrically polarized vortex beams. Opt Laser Technol 2016; 76: 1-5. DOI: 10.1016/j.optlastec.2015.07.002.
  7. Yuan GH, Wei SB, Yuan X-C. Generation of nondiffracting quasi-circular polarization beams using an amplitude modulated phase hologram. JOSA A 2011; 28(8): 1716-1720. DOI: 10.1364/JOSAA.28.001716.
  8. 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.
  9. 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.
  10. Sukhov S, Dogariu A. On the concept of “tractor beams”. Opt Lett 2010; 35(22): 3847-3849. DOI: 10.1364/OL.35.003847.
  11. Kotlyar VV, Nalimov AG. A vector optical vortex generated and focused using a metalens. Computer ptics 2017; 41(5): 645-654. DOI: 10.18287/2412-6179-2017-41-5-645-654.
  12. Monteiro PB, Neto PAM, Nussenzveig HM. Angular momentum of focused beams: Beyond the paraxial approximation Phys Rev A 2009; 79(3): 033830. DOI: 10.1103/PhysRevA.79.033830.
  13. Born M, Wolf E, Principles of Optics. 6-th ed. – Pergamon, 1986.
  14. 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: Mathematical, Physical and Engineering Sciences 1959; 253(1274): 358-379. DOI: 10.1098/rspa.1959.0200.
  15. 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.

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