Vectorial vortex Hankel beams with circular polarization
V.V. Kotlyar
, A.A. Kovalev, M.A. Volynov


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

Full text of article: Russian language.


We have considered circularly polarized vectorial Hankel beams. These beams are a generalization of the spherical wave with embedded optical vortex. Explicit analytical expressions have been derived for all six components of the electric and magnetic vectors of the electromagnetic field. These expressions are an exact solution of Maxwell's equations. We have shown the difference in free space propagation for Hankel beams with left and right circular polarization. For the far field, we also obtained expressions for the components of the Umov-Poynting vector and angular momentum.

optical vortex, Hankel beam, circular polarization, Maxwell equations, orbital angular momentum.

Kotlyar VV, Kovalev AA, Volynov MA. Vectorial vortex Hankel beams with circular polarization. Computer Optics 2016; 40(6): 765-771. DOI: 10.18287/2412-6179-2016-40-6-765-771.


  1. Mishra SR. A vector wave analysis of a Bessel beam. Opt Commun 1991; 85(2-3): 159-161. DOI: 10.1016/0030-4018(91)90386-R.
  2. Bouchal Z, Olivík M. Non-diffractive vector Bessel beams. J Mod Opt 1995; 42(8): 1555-1566. DOI: 10.1080/09500349514551361.
  3. Horak R, Bouchal Z, Bajer J. Nondiffracting stationary electromagnetic fields. Opt Commun 1997; 133(1-6): 315-327. DOI: 10.1016/S0030-4018(96)00490-7.
  4. Jauequi R, Hacyan S. Quantum-mechanical properties Bessel beams. Phys Rev A 2005; 71(3): 033411. DOI: 10.1103/PhysRevA.71.033411.
  5. Yu YZ, Dou WB. Vector analyses of nondiffracting Bessel beams. Prog in Electr Res Lett 2008; 5: 57-71.
  6. Wang Y, Dou W, Meng H. Vector analyses of linearly and circularly polarized Bessel beams using Herz vector potentials. Opt Express 2014; 22(7): 7821-7830. DOI: 10.1364/OE.22.007821.
  7. Kotlyar VV, Kovalev AA, Soifer VA. Nonparaxial Hankel vortex beams of the first and second types. Computer Optics 2015; 39(3): 299-304.
  8. Kotlyar VV, Kovalev AA. Vectorial Hankel laser beams carrying orbital angular momentum. Computer Optics 2015; 39(4): 449-452. DOI: 10.18287/0134-2452-2015-39-4-449-452.
  9. Kotlyar VV, Kovalev AA, Soifer VA. Vectorial rotating vortex Hankel laser beams. J Opt 2016; 18(9): 095602. DOI: 10.1088/2040-8978/18/9/095602.
  10. Cerjan A, Cerjan C. Orbital angular momentum of Laguerre-Gaussian beams beyond the paraxial approximation. J Opt Soc Am A 2011; 28(11): 2253-2260. DOI: 10.1364/JOSAA.28.002253.
  11. Youngworth KS, Brown TG. Focusing of high numerical aperture cylindrical-vector beams. Opt Express 2000; 7(2): 77-87. DOI: 10.1364/OE.7.000077.
  12. Zhan Q, Leger JR. Focus shaping using cylindrical vector beams. Opt Express 2002; 10(7): 324-331. DOI: 10.1364/OE.10.000324.
  13. Allen L, Beijersergen 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.
  14. Volke-Sepulveda K, Garcés-Chávez V, Chávez-Cedra S, Arlt J, Dholakia K. Orbital angular momentum of a high-order Bessel light beam. J Opt B: Quantum Semiclass Opt 2002; 4(2): S82-S89.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail:; Phones: +7 (846) 332-56-22, Fax: +7 (846) 332-56-20