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Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre-Gaussian beam passing through a random phase screen

Abstract

The spatial evolution of the energy distribution and local wave-propagation vector of a fluctuating laser vortex beam is studied. The beam’s fluctuations are induced by its propagation through a thin (in comparison with the total propagation path) layer of a turbulent medium (phase screen). It is shown that the vortex energy flow typical for a coherent beam is also manifested in the mean parameters of a partially coherent beam. In particular, the mean wave tilt is representable as a sum of the vortex and potential components. The rotor of the vector field of mean wave tilts plays the determining part in the circular energy motion. The vortex component for a screen with a quadratic structure function of phase fluctuations corresponds to one of the models of rotational fluid motion called the Scully vortex. The potential component of the mean energy direction field can result in beam focusing with an increase in the distance from the screen. The direction of the mean energy flow lines (mean diffraction rays) allows for an analogy between the evolution of an optical vortex carried by a Laguerre-Gaussian beam and the breakdown of the rotational fluid flow.

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References

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

    Google Scholar 

  2. A. E. Siegman, Lasers (Univ. Sci., MillValley, CA, 1986).

    Google Scholar 

  3. C. Y. Young, Y. V. Gilchrest, and B. R. Macon, “Turbulence Induced Beam Spreading of Higher Order Mode Optical Waves,” Opt. Eng. 41, 1097–1103 (2002).

    Article  ADS  Google Scholar 

  4. D. M. Palacios, D. Rozas, and G. A. Swartzlander, Jr., “Observed Scattering into a Dark Optical Vortex Core,” Phys. Rev. Lett. 88, 103902 (2002).

    Article  ADS  Google Scholar 

  5. S. A. Ponomarenko, “A Class of Partially Coherent Beams Carrying Optical Vortices,” J. Opt. Soc. Am. A 18, 150–156 (2001).

    Article  ADS  Google Scholar 

  6. L. Allen, M. W. Beijersbergen, R. Spreeuw, 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 

  7. 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,” Kvantov. Elektron. 38(4), 343–348 (2008) [Quantum Electron. 38, 343–348 (2008)].

    Article  Google Scholar 

  8. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Introduction to Statistical Radio Physics (Nauka, Moscow, 1978), Part 2 [in Russian].

    Google Scholar 

  9. V. P. Kandidov, “Monte Carlo Method in Nonlinear Statistical Optics,” Usp. Fiz. Nauk 166, 1309–1338 (1996) [Phys. Usp. 39, 1243 (1996)].

    Article  Google Scholar 

  10. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 2000; Fizmatgiz, Moscow, 1962).

    Google Scholar 

  11. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, Cambridge, 1995; Fizmatlit, Moscow, 2000).

    Google Scholar 

  12. 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(11), 1895–1900 (2004).

    ADS  Google Scholar 

  13. D. Maleev and G. A. Swartzlander, Jr., “Propagation of Spatial Correlation Vortices,” J. Opt. Soc. Am. B 25(6), 915–922 (2008).

    Article  ADS  Google Scholar 

  14. G. Gbur and G. A. Swartzlander, Jr., “Complete Transverse Representation of a Correlation Singularity of a Partially Coherent Field,” J. Opt. Soc. Am. B 25(9), 1422–1429 (2008).

    Article  ADS  Google Scholar 

  15. E. G. Abramochkin and V. G. Volostnikov, “Two Dimensional Phase Problem: Differential Approach,” Opt. Commun. 74(3), 139–143 (1989).

    Article  ADS  Google Scholar 

  16. 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. Spektrosk. 92(3), 468–474 (2002) [Opt. Spectrosc. 92, 425 (2002)].

    Article  Google Scholar 

  17. M. Vorontsov and V. Kolosov, “Target-in-the-Loop Beam Control: Basic Considerations for Analysis and Wave-Front Sensing,” J. Opt. Soc. Am. A 22(1), 126–141 (2005).

    Article  ADS  Google Scholar 

  18. G. A. Swartzlander,Jr. and R. I. Hernandes-Aranda, “Optical Rankine Vortex and Anomalous Circulation of Light,” Phys. Rev. Lett. 99(16), 193901 (1939).

    Google Scholar 

  19. S. V. Alekseenko, P. A. Kuibin, and V. L. Okulov, Theory of Concentrated Vortices. An Introduction (Inst. Teplofiz. SO RAN, Novosibirsk, 2003; Springer, New York, 2007).

    Google Scholar 

  20. V. P. Aksenov and Ch. E. Pogutsa, “Spatial Evolution of Optical Vortex Behind Random Phase Screen,” in Proc. of the 16th Intern. Symp. on Optics of Atmosphere and Ocean. Atmosphere Physics (IOA SO RAN, Tomsk, 2009), pp. 159–162.

    Google Scholar 

  21. V. P. Lukin and B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 1999) [in Russian].

    Google Scholar 

  22. G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers (Nauka, Moscow, 1974; McGraw-Hill, New York, 1961).

    Google Scholar 

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Original Russian Text © V.P. Aksenov, F.Yu. Kanev, Ch.E. Pogutsa, 2010, published in Optica Atmosfery i Okeana.

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Aksenov, V.P., Kanev, F.Y. & Pogutsa, C.E. 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, 344–352 (2010). https://doi.org/10.1134/S1024856010050027

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  • DOI: https://doi.org/10.1134/S1024856010050027

Keywords

  • Vortex
  • Oceanic Optic
  • Poynting Vector
  • Phase Screen
  • Coherent Beam