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Atmospheric and Oceanic Optics

, Volume 29, Issue 5, pp 431–440 | Cite as

Spatial scales of coherence of diffraction-free beams in a turbulent atmosphere

  • I. P. LukinEmail author
Optics of Stochastically-Heterogeneous Media

Abstract

Coherent properties of diffraction-free optical beams propagating in a turbulent atmosphere are studied. The analysis is based on the solution of the equation for the second-order mutual coherence function of an optical radiation field. The behavior of the degree of coherence of the diffraction-free (cosine and fundamental Bessel) optical beams depending on the beam parameters and characteristics of the turbulent atmosphere is investigated. It turns out that the oscillating character of the degree of coherence of these beams is a fundamental property of diffraction-free beams, which is shown under weak fluctuations in a turbulent atmosphere. At high levels of fluctuations in a turbulent atmosphere, the degree of coherence of a diffraction-free cosine beam becomes closer to that of a plane wave, and of a diffraction-free fundamental Bessel beam, to a spherical wave. The analysis of two spatial scales of the degree of coherence of optical beams has shown that the integral scale of the degree of coherence for diffraction-free beams is a more representative characteristic than the coherence length; the former definitely correlates with optical radiation propagation conditions in a turbulent atmosphere.

Keywords

Bessel beam optical radiation atmospheric turbulence second-order mutual coherence function coherence 

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References

  1. 1.
    L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, Bristol, 2003).CrossRefGoogle Scholar
  2. 2.
    D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic press, New York, 2008).Google Scholar
  3. 3.
    M. A. Mahmoud, M. Y. Shalaby, and D. Khalil, “Propagation of Bessel beams generated using finitewidth Durnin ring,” Appl. Opt. 52 2, 256–253 (2013).ADSCrossRefGoogle Scholar
  4. 4.
    M. Ornigotti and A. Aiello, “Generalized Bessel beams with two indices,” Opt. Lett. 39 19, 5618–5621 (2014).ADSCrossRefGoogle Scholar
  5. 5.
    V. A. Banakh and A. V. Falits, “Numerical simulation of propagation of laser beams formed by multielement apertures in a turbulent atmosphere under thermal blooming,” Atmos. Oceanic Opt. 26 6, 455–465 (2013).CrossRefGoogle Scholar
  6. 6.
    V. A. Banakh and A. V. Falits, “Efficiency of combined beam focusing under thermal blooming,” Atmos. Oceanic Opt. 27 3, 211–217 (2014).CrossRefGoogle Scholar
  7. 7.
    V. A. Banakh and A. V. Falits, “Turbulent broadening of Laguerre-Gaussian beam in the atmosphere,” Opt. Spectrosc. 117 6, 949–955 (2014).ADSCrossRefGoogle Scholar
  8. 8.
    F. O. Fahrbach, V. Gurchenkov, K. Alessandri, P. Nassoy, and A. Rohrbach, “Self-reconstructing sectioned bessel beams offer submicron optical sectioning for large fields of view in light-sheet microscopy,” Opt. Express 21 9, 11425–11440 (2013).ADSCrossRefGoogle Scholar
  9. 9.
    L. Gong, Y. Ren, G. Xue, Q. Wang, J. Zhou, M. Zhong, Z. Wang, and Y. Li, “Generation of nondiffracting Bessel beam using digital micromirror device,” Appl. Opt. 52 19, 4566–4575 (2013).ADSCrossRefGoogle Scholar
  10. 10.
    Z. Xie, V. Armbruster, and T. Grosjean, “Axicon on a Gradient Index Lens (AXIGRIN): Integrated optical bench for Bessel beam generation from a point-like source,” Appl. Opt. 53 26, 6103–6107 (2014).ADSCrossRefGoogle Scholar
  11. 11.
    C. Alyingoz, B. Yalizay, and S. Akturk, “Propagation characteristics of Bessel beams generated by continuous, incoherent light sources,” J. Opt. Soc. Amer., A 32 8, 1567–1575 (2015).ADSCrossRefGoogle Scholar
  12. 12.
    P. Birch, I. Ituen, R. Young, and Ch. Chatwin, “Longdistance Bessel beam propagation through Kolmogorov turbulence,” J. Opt. Soc. Amer., A 32 11, 2066–2073 (2015).ADSCrossRefGoogle Scholar
  13. 13.
    X. Wei, Ch. Liu, L. Niu, Z. Zhang, K. Wang, Z. Yang, and J. Liu, “Generation of arbitrary order Bessel beams via 3D printed axicons at the terahertz frequency range,” Appl. Opt. 54 36, 10641–10649 (2015).ADSCrossRefGoogle Scholar
  14. 14.
    A. P. Kiselev, “Localized light waves: Paraxial and exact solutions of the wave equation (a review),” Opt. Spectrosc. 102 4, 603–622 (2007).ADSCrossRefGoogle Scholar
  15. 15.
    H. T. Eyyuboglu, Y. Baykal, and Y. Cai, “Complex degree of coherence for partially coherent general beams in atmospheric turbulence,” J. Opt. Soc. Amer., A 24 9, 2891–2901 (2007).ADSCrossRefGoogle Scholar
  16. 16.
    M. S. Belen’kii, V. P. Lukin, V. L. Mironov, and V. V. Pokasov, Coherence of Laser Radiation in the Atmosphere (Nauka, Novosibirsk, 1985) [in Russian].Google Scholar
  17. 17.
    I. P. Lukin, “Coherence of Bessel beam in a turbulent atmosphere,” Atmos. Ocean. Opt. 25 5, 328–337 (2012).CrossRefGoogle Scholar
  18. 18.
    I. P. Lukin, “Bessel-Gaussian beam phase fluctuations in randomly inhomogeneous media,” Atmos. Oceanic Opt. 23 3, 236–240 (2010).CrossRefGoogle Scholar
  19. 19.
    S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Introduction to Statistical Radiophysics. Random Fields (Nauka, Moscow, 1978) [in Russian].zbMATHGoogle Scholar
  20. 20.
    I. P. Lukin, “Ring dislocation of the coherence degree of a vortex Bessel beam in a turbulent atmosphere,” Atmos. Oceanic Opt. 28 5, 415–425 (2015).CrossRefGoogle Scholar
  21. 21.
    I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Nauka, Moscow, 1108) [in Russian].Google Scholar
  22. 22.
    M. V. Fedoryuk, Saddle-point Method (Nauka, Moscow, 1977) [in Russian].zbMATHGoogle Scholar
  23. 23.
    S. A. Akhmanov, Yu. E. D’yakov, and A. S. Chirkin, Introduction into Statistical Radiophysics and Optics (Nauka, Moscow, 1981) [in Russian].Google Scholar
  24. 24.
    A. V. Shchegrov and E. Wolf, “Partially coherent conical beams,” Opt. Lett. 25 3, 141–143 (2000).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.V.E. Zuev Institute of Atmospheric Optics, Siberian BranchRussian Academy of SciencesTomskRussia

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