Vol. 28, issue 04, article # 3

Lukin I.P. Ring dislocation of the degree of coherence of a vortex Bessel beam in turbulent atmosphere. // Optika Atmosfery i Okeana. 2015. V. 28. No. 04. P. 298-308 [in Russian].
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The behavior of the degree of coherence of a coherent vortex Bessel optical beam propagating in a turbulent randomly inhomogeneous medium is theoretically considered. The influence of an optical vortex on the degree of coherence of the Bessel beam in a randomly inhomogeneous medium is studied. The analysis is based on the solution of the equation for the second-order mutual coherence function of optical beam field. On the basis of this solution, the behavior of the module of the second-order mutual coherence function (a degree of coherence), the vortex Bessel beam field is investigated. It is shown that at low levels of fluctuations in the turbulent atmosphere, in the central part of a two-dimensional field of the degree of coherence of vortex Bessel beams, the ring dislocation is formed; the number of rings is equal to value of a topological charge of an optical beam. The structure of a ring dislocation of the degree of coherence of vortex Bessel optical beams in turbulent atmosphere is studied in detail. For this purpose, two characteristics of the ring dislocation are introduced: the spatial coordinate and width of a ring. The influence of parameters of an optical beam (a cross-section wave number and a topological charge) and atmospheric turbulence (a coherence radius of a plane optical wave) on these characteristics of the ring dislocation of the degree of coherence of a vortex Bessel optical beam is considered.


Bessel beam, vortex beam, optical radiation, atmospheric turbulence, coherence, ring dislocation


  1. Andrews D.L. Structured light and its applications: An introduction to phase-structured beams and nanoscale optical forces. N.Y.: Academic Press, 2008. 341 p.

  2. Allen L., Barnett S.M., Padgett M.J. Optical angular momentum. Bristol: Institute of Physics, 2003. 300 p.

  3. Leach J., Padgett M.J., Barnett S.M., Franke-Arnold S., Courtial J. Measuring the orbital angular momentum of a single photon // Phys. Rev. Lett. 2002. V. 88, N 25. 257901.

  4. Gibson G., Courtial J., Padgett M.J., Vasnetsov M., Pas’ko V., Barnett S.M., Franke-Arnold S. Free-space information transfer using light beams carrying orbital angular momentum // Opt. Express. 2004. V. 12, N 22. P. 5448–5456.

  5. Paterson C. Atmospheric turbulence and orbital angular momentum of single photons for optical communication // Phys. Rev. Lett. 2005. V. 94, N 15. 153901.

  6. Gbur G. The evolution of vortex beams in atmospheric turbulence // Proc. SPIE. 2008. V. 6878. 687804.

  7. Gbur G., Tyson R.K. Vortex beam propagation through atmospheric turbulence and topological charge conservation // J. Opt. Soc. Amer. A. 2008. V. 25, N 1. P. 225–230.

  8. Yao A.M., Padgett M.J. Orbital angular momentum: Origins, behavior and applications // Adv. Opt. Photon. 2011. V. 3, N 2. P. 161–204.

  9. Aksjonov V.P., Poguca Ch.E. Vlijanie opticheskogo vihrja na sluchajnye smeshhenija Lagerra–Gaussova lazernogo puchka, rasprostranjajushhegosja v turbulentnoj atmosfere // Optika atmosf. i okeana. 2012. V. 25, N 7. P. 561–565.

  10. Aksenov V.P., Pogutsa Ch.E. Increase in laser beam resistance to random inhomogeneities of atmospheric permittivity with an optical vortex included in the beam structure // Appl. Opt. 2012. V. 51, N 30. P. 7262–7267.

  11. Abramochkin E.G., Volostnikov V.G. Spiral'nye puchki sveta // Uspehi fiz. nauk. 2004. V. 174, N 12. P. 1273–1300.

  12. Voljar A.V., Fadeeva T.A., Egorov Ju.A. Vektornye singuljarnosti gaussovyh puchkov v odnoosnyh kristallah: generacija opticheskih vihrej // Pis'ma v ZhTF. 2002. V. 28, Issue 22. P. 70–77.

  13. Wood R.W. Vortex rings // Nature (Gr. Brit.). 1901. V. 63, N 1635. P. 418–420.

  14. Gbur G., Visser T.D. Coherence vortices in partially coherent beams // Opt. Commun. 2003. V. 222, N 1–6. P. 117–125.

  15. Gbur G., Visser T.D., Wolf E. “Hidden” singularities in partially coherent wavefields // J. Opt. A: Pure Appl. Opt. 2004. V. 6, N 5. P. S239–S242.

  16. Bogatyryova G.V., Fel’de Ch.V., Polyanskii P.V., Ponomarenko S.A., Soskin M.S., Wolf E. Partially coherent vortex beams with a separable phase // Opt. Lett. 2003. V. 28, N 11. P. 878–880.

  17. Maleev I.D., Palacios D.M., Marathay A.S., Swartzlander G.A. Spatial correlation vortices in partially coherent light: Theory // J. Opt. Soc. Amer. B. 2004. V. 21, N 11. P. 1895–1900.

  18. Ding Ch., Pan L., Lu B. Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel–Gauss pulsed beams // J. Opt. Soc. Amer. A. 2009. V. 26, N 12. P. 2654–2661.

  19. Lukin I.P. Formation of a ring dislocation of a coherence of a vortex optical beam in turbulent atmosphere // Proc. SPIE. 2013. V. 9066. 90660Q.

  20. Borghi R., Santarsiero M., Gori F. Axial intensity of apertured Bessel beams // J. Opt. Soc. Amer. A. 1997. V. 14, N 1. P. 23–26.

  21. Chen B., Chen Z., Pu J. Propagation of partially coherent Bessel–Gaussian beams in turbulent atmosphere // Opt. Laser Technol. 2008. V. 40, N 6. P. 820–827.

  22. Zhu K., Zhou G., Li X., Zheng X., Tang H. Propagation of Bessel–Gaussian beams with optical vortices in turbulent atmosphere // Opt. Express. 2008. V. 16, N 26. P. 21315–21320.

  23. Lukin I.P. Ustojchivost' kogerentnyh vihrevyh besselevyh puchkov pri rasprostranenii v turbulentnoj atmosfere // Optika atmosf. i okeana. 2014. V. 27, N 5. P. 367–374.

  24. Lukin I.P. Mean intensity of the vortex Bessel beams propagating in turbulent atmosphere // Appl. Opt. 2014. V. 53, N 15. P. 3287–3293.

  25. Durnin J. Exact solutions for nondiffracting beams. I. The scalar theory // J. Opt. Soc. Amer. A. 1987. V. 4, N 4. P. 651–654.

  26. Jiang Zh., Lu Q., Liu Z. Propagation of apertured Bessel beams // Appl. Opt. 1995. V. 34, N 31. P. 7183–7185.

  27. Rytov S.M., Kravcov Ju.A., Tatarskij V.I. Vvedenie v statisticheskuju radiofiziku. Part 2. Sluchajnye polja. M.: Nauka, 1978. 464 p.

  28. Eyyuboğlu H.T. Propagation of higher order Bessel–Gaussian beams in turbulence // Appl. Phys. B. 2007. V. 88, N 2. P. 259–265.

  29. Lukin I.P. Kogerentnost' besseleva puchka v turbulentnoj atmosfere // Optika atmosf. i okeana. 2012. V. 25, N 5. P. 393–402.

  30. Eyyuboğlu H.T., Baykal Y., Cai Y. Complex degree of coherence for partially coherent general beams in atmospheric turbulence // J. Opt. Soc. Amer. A. 2007. V. 24, N 9. P. 2891–2901.

  31. Eyyuboğlu H.T. Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence // Opt. Laser Technol. 2008. V. 40, N 1. P. 156–166.

  32. Martinez-Herrero R., Manjavacas A. Overall second-order parametric characterization of light beams propagating through spiral phase elements // Opt. Commun. 2009. V. 282, N 4. P. 473–477.