Skip to main content
Log in

Singular Atmospheric Optics: From Wavefront Dislocations to Synthesis of Vortex Laser Beams

  • Published:
Atmospheric and Oceanic Optics Aims and scope Submit manuscript

Abstract

Studies on the singular optics of scalar wave fields carried out in the world and at V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences (IAO SB RAS) are reviewed. The study results of the processes of origination and annihilation of phase singularities are generalized. The methods for singular phase reconstruction and their applicability to the problems of adaptive focusing of radiation in randomly inhomogeneous media are examined. The energy, statistical, and topological properties of vortex optical beams propagating through a turbulent atmosphere are analyzed. The results of the synthesis of vortex beams with quickly controllable orbital angular momentum by the matrix approach developed at IAO SB RAS are described.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. M. V. Berry, “Making waves in physics. Three wave singularities from the miraculous 1830s,” Nature 403, 21 (2000).

    Article  ADS  Google Scholar 

  2. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. Roy. Soc. Lond. A 336, 165–190 (1974).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73 (5), 403–408 (1989).

    Article  ADS  Google Scholar 

  4. N. N. Rozanov, “About generation of radiation with wavefront dislocations,” Opt. Spektrosk. 75 (4), 861–867 (1993).

    Google Scholar 

  5. P. V. Korolenko and V. N. Tikhomirov, “Structure of the wavefront coupled mode systems,” Quantum Electron. 21 (9), 1034–1035 (1991).

    ADS  Google Scholar 

  6. M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt 42, 219–276 (2001).

    Article  ADS  Google Scholar 

  7. Optical Vortices.Horizons in World Physics, Ed. by K. Vasnetsov and K. Staliunas (Nova Science, New York, 1999), vol. 228.

    Google Scholar 

  8. O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).

    Article  ADS  Google Scholar 

  9. C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Vortex-preserving weakly guiding anisotropic twisted fibres,” J. Opt. A: Pure Appl. Opt. 46, 162–S165 (2004).

    Article  Google Scholar 

  10. E. G. Abramochkin and V. G. Volostnikov, “Relationship between two-dimensional intensity and phase in fresnel diffraction zone,” Opt. Commun. 74 (3-4), 144–148 (1989).

    Article  ADS  Google Scholar 

  11. A. Ya. Bekshaev and A. I. Karamoch, “Astigmatic telescopic transformation of a high-order optical vortex,” Opt. Commun. 281 (23), 5687–5696 (2008).

    Article  ADS  Google Scholar 

  12. M. J. Padgett and L. Allen, “The Poynting vector in Laguerre–Gaussian laser modes,” Opt. Commun. 121 (1-3), 36–40 (1995).

    Article  ADS  Google Scholar 

  13. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24 (9), S951–S962 (1992).

    Article  Google Scholar 

  14. L. Torner, J. P. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13, 873–881 (2005).

    Article  ADS  Google Scholar 

  15. A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, “Azimuthons: Spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).

    Article  ADS  Google Scholar 

  16. V. P. Lukin and B. V. Fortes, “The influence of wave-front dislocations on the phase conjugation instability at compensation for thermal blooming,” Atmos. Ocean. Opt. 8 (3), 435–447 (1995).

    Google Scholar 

  17. V. A. Tartakovskii and N. N. Maier, “Phase dislocations and focal spots,” Atmos. Ocean. Opt. 9 (11), 926–929 (1996).

    Google Scholar 

  18. T. I. Arsen’yan, S. I. Kaul’, P. V. Korolenko, S. A. Ubogov, and N. N. Fedotov, “Wavefront disclocations in a turbulent medium,” Radiotekh. Elektron. 37 (10), 1773–1777 (1992).

    Google Scholar 

  19. I. Freund, N. Svartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101 (3-4), 247–264 (1993).

    Article  ADS  Google Scholar 

  20. I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander, Jr., “Spatial correlation vortices in partially coherent light: Theory,” J. Opt. Soc. Am. B 21, 1895–1900 (2004).

    Article  ADS  Google Scholar 

  21. N. B. Baranova and B. Ya. Zel’dovich, “Dislocations of the wave-front surface and zeros of the amplitude,” JETP 53 (5). S. 925–929 (1981).

    Google Scholar 

  22. V. A. Zhuravlev, I. K. Kobozev, and Yu. A. Kravtsov, “Detecting dislocations by measuring the energy flux of an acoustic field,” JETP 77 (5), 808–814 (1993).

    ADS  MathSciNet  Google Scholar 

  23. L. Allen, M. W. Beijersbergen, R. Spreeuw, J.C., and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A: 45, 8185–8189 (1992).

    Article  ADS  Google Scholar 

  24. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, M. Barnett Stephen, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).

    Article  ADS  Google Scholar 

  25. A. M. Yao and M. J. Padgett, “Orbital angular momentum: Origins, behavior and applications,” Adv. Opt. Photon 3, 161–204 (2011).

    Article  Google Scholar 

  26. Twisted photons: Applications of Light with Orbital Angular Momentum, Ed. by J.P. Torres and L. Torner (Wiley-VCH, Weinheim, 2011).

    Google Scholar 

  27. A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

  28. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams advances,” Opt. Photon 7, 66–106 (2015).

    Article  Google Scholar 

  29. V. P. Aksenov, V. V. Kolosov, V. A. Tartakovskii, and B. V. Fortes, “Optical vortices in inhomogeneous media,” Atmos. Ocean. Opt. 12 (10), 912–918 (1999).

    Google Scholar 

  30. V. P. Aksenov, I. V. Izmailov, B. N. Poizner, and O. V. Tikhomirova, “Wave and ray spatial dynamics of the light field in the generation, evolution, and annihilation of phase dislocations,” Opt. Spectrosc. 92 (3), 409–418 (2002).

    Article  ADS  Google Scholar 

  31. V. P. Aksenov and A. V. Ustinov, “Vortex backwash during spatial evolution of "vortex” laser beams,” A-tmos. Ocean. Opt. 16 (8), 626–632 (2003).

    Google Scholar 

  32. V. V. Kolosov, “Energy streamlines in the vicinity of dislocations of a three-dimensional wave field,” Atmos. Ocean. Opt. 9 (12), 1037–1042 (1996).

    Google Scholar 

  33. V. P. Aksenov, V. A. Banakh, and O. V. Tikhomirova, “Vizualization of wavefront dislocations of optical speckle-fields,” Atmos. Ocean. Opt. 10 (12), 998–1000 (1997).

    Google Scholar 

  34. V. P. Aksenov, V. A. Banakh, and O. V. Tikhomirova, “Visualization of the phase singularities in wave-front sensors,” Proc. SPIE—Int. Soc. Opt. Eng. 3487, 117–122 (1997).

  35. V. P. Aksenov, V. A. Banakh, and O. V. Tikhomirova, “Potential and vortex features of optical speckle field and visualization of wave-front singularities,” Appl. Opt. 37 (21), 4536–4540 (1998).

    Article  ADS  Google Scholar 

  36. V. P. Aksenov, F. Yu. Kanev, and Ch. E. Pogutsa, “Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre–Gaussian beam passing through a random phase screen,” Atmos. Ocean. Opt. 23 (5), 344–352 (2010).

    Article  Google Scholar 

  37. V. P. Aksenov and Ch. E. Pogutsa, “Optical scully vortex and its spatial evolution,” Appl. Opt. 51 (10), C140–C143 (2012).

    Article  Google Scholar 

  38. D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31 (15), 2865–2882 (1992).

    Article  ADS  Google Scholar 

  39. H. Takajo and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5 (3), 416–425 (1988).

    Article  ADS  Google Scholar 

  40. H. Takajo and T. Takahashi, “Noniterative method for obtainning the exact solution for the normal equation in least-square phase estimation from the phase difference,” J. Opt. Soc. Am. A 5 (11), 1818–1827 (1988).

    Article  ADS  Google Scholar 

  41. V. P. Aksenov and O. V. Tikhomirova, “Theory of singular-phase reconstruction for optical speckle field in the turbulent atmosphere,” J. Opt. Soc. Am. A 19 (2), 345–355 (2002).

    Article  ADS  Google Scholar 

  42. F. A. Starikov, V. P. Aksenov, F. Yu. Kanev, I. V. Izmailov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, and S. A. Sukharev, “Wavefront reconstruction of an optical vortex by a Hartmann–Shack Sensor,” Opt. Lett. 32 (16), 2291–2294 (2007).

    Article  ADS  Google Scholar 

  43. F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Correction of vortex laser beam in a closed-loop adaptive system with bimorph mirror,” Opt. Lett. 34 (15), 2264–2267 (2009).

    Article  ADS  Google Scholar 

  44. V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, and F. A. Starikov, “Algorithms for the reconstruction of the singular wave front of laser radiation: Analysis and improvement of accuracy,” Quantum Electron. 38 (7), 673–677 (2008).

    Article  ADS  Google Scholar 

  45. V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, and D. S. Kuksenok, “Registration of vortex beam parameters in a turbulent atmosphere,” J. Opt. 15, 044008 (2013).

    Article  ADS  Google Scholar 

  46. V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, and B. N. Poizner, “Detection of the topological charge of an optical vortex from measurements of the intensity at the interferometer output: Principles and simulation,” Atmos. Ocean. Opt. 24 (3), 306–312 (2011).

    Article  Google Scholar 

  47. V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, and B. N. Poizner, “Optical vortex detector as a basis for a data transfer system: Operational principle, model, and simulation of the influence of turbulence and noise,” Opt. Commun. 285 (2012).

  48. V. P. Aksenov and Ch. E. Pogutsa, “Increase in laser beam resistance to random inhomogeneities of atmospheric permittivity with an optical vortex included in the beam structure,” Appl. Opt. 51 (30), 7262–7267 (2012).

    Article  ADS  Google Scholar 

  49. V. P. Aksenov and Ch. E. Pogutsa, “The effect of optical vortex on random Laguerre–Gauss shifts of a laser beam propagating in a turbulent atmosphere,” Atmos. Ocean. Opt. 26 (1), 13–17 (2013).

    Article  Google Scholar 

  50. V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15, 044007 (2013).

    Article  ADS  Google Scholar 

  51. V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence,” Appl. Opt. 53 (17), 3607–3614 (2014).

    Article  ADS  Google Scholar 

  52. V. P. Aksenov and V. V. Kolosov, “Scintillations of optical vortex in randomly inhomogeneous medium,” Photon. Res. 3 (2), 44–47 (2015).

    Article  Google Scholar 

  53. V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Probability distribution of strong intensity fluctuations of vortex laser beams in the turbulent atmosphere,” Opt. Atmos. Okeana 31 (5), 349–354 (2018).

    Google Scholar 

  54. V. P. Aksenov and V. V. Kolosov, “Probability density of field and intensity fluctuations of structured light in a turbulent atmosphere,” J. Opt. 21 (3), 035605 (2019).

    Article  ADS  Google Scholar 

  55. V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Properties of vortex beams formed by an array of fibre lasers and their propagation in a turbulent atmosphere,” Quantum Electron. 46 (8), 726–732 (2016).

    Article  ADS  Google Scholar 

  56. V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, http://arxiv.org/abs/1802.03172. Cited May 17, 2019.

  57. V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Statistical characteristics of common and synthesized vortex beams in a turbulent atmosphere,” Proc. SPIE—Int. Soc. Opt. Eng. 10035, 100352 (2016).

  58. V. P. Aksenov, V. V. Dudorov, V. V. Kolosov, and V. Yu. Venedictov, “Probability distribution of intensity fluctuations of arbitrary-type laser beams in the turbulent atmosphere,” Opt. Express 27 (77), 24705–24716 (2019).

    Article  ADS  Google Scholar 

  59. M. Berry, “Paraxial beams of spinning light,” Proc. SPIE—Int. Soc. Opt. Eng. 3487, 6–11 (1998).

  60. V. P. Aksenov and Ch. E. Pogutsa, “Fluctuations of the orbital angular momentum of a laser beam, carrying an optical vortex, in the turbulent atmosphere,” Quantum Electron. 38 (4), 343–348 (2008).

    Article  ADS  Google Scholar 

  61. V. P. Aksenov and Ch. E. Pogutsa, “Statistical characteristics of orbital angular momentum of a laser beam in a turbulent atmosphere: Two ways of description,” in Proc. XVII International Symposium “Atmospheric and Ocean Optics. Atmospheric Physics” (Publishing House of IAO SB RAS, Tomsk, 2011), p. B200–B202 [in Russian].

  62. V. P. Aksenov and Ch. E. Pogutsa, “Variance of weak fluctuations of orbital angular momentum of Gaussian laser beam induced by atmospheric turbulence,” Imag. Syst. Appl., Paper# JTu4A, 30 (2014).

  63. V. P. Aksenov, V. V. Kolosov, G. A. Filimonov, and C. E. Pogutsa, “Orbital angular momentum of a laser beam in a turbulent medium: Preservation of the average value and variance of fluctuations,” J. Opt. 18, 054013 (2016).

    Article  ADS  Google Scholar 

  64. M. Charnotskii, “Transverse linear and orbital angular momenta of beam waves and propagation in random media,” J. Opt. 20, 025602 (2018).

    Article  ADS  Google Scholar 

  65. V. P. Aksenov, V. V. Dudorov, G. A. Filimonov, V. V. Kolosov, and V. Yu. Venediktov, “Vortex beams with zero orbital angular momentum and non-zero topological charge,” Opt. Laser Technol. 104, 159–163 (2018).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to V. P. Aksenov, V. V. Dudorov or V. V. Kolosov.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by O. Ponomareva

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aksenov, V.P., Dudorov, V.V. & Kolosov, V.V. Singular Atmospheric Optics: From Wavefront Dislocations to Synthesis of Vortex Laser Beams. Atmos Ocean Opt 33, 109–115 (2020). https://doi.org/10.1134/S1024856020010029

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1024856020010029

Keywords:

Navigation