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
M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. Opt. 42, 219–276 (2001).
A. E. Siegman, Lasers (Univ. Sci., MillValley, CA, 1986).
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).
D. M. Palacios, D. Rozas, and G. A. Swartzlander, Jr., “Observed Scattering into a Dark Optical Vortex Core,” Phys. Rev. Lett. 88, 103902 (2002).
S. A. Ponomarenko, “A Class of Partially Coherent Beams Carrying Optical Vortices,” J. Opt. Soc. Am. A 18, 150–156 (2001).
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).
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)].
S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Introduction to Statistical Radio Physics (Nauka, Moscow, 1978), Part 2 [in Russian].
V. P. Kandidov, “Monte Carlo Method in Nonlinear Statistical Optics,” Usp. Fiz. Nauk 166, 1309–1338 (1996) [Phys. Usp. 39, 1243 (1996)].
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 2000; Fizmatgiz, Moscow, 1962).
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, Cambridge, 1995; Fizmatlit, Moscow, 2000).
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).
D. Maleev and G. A. Swartzlander, Jr., “Propagation of Spatial Correlation Vortices,” J. Opt. Soc. Am. B 25(6), 915–922 (2008).
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).
E. G. Abramochkin and V. G. Volostnikov, “Two Dimensional Phase Problem: Differential Approach,” Opt. Commun. 74(3), 139–143 (1989).
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)].
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).
G. A. Swartzlander,Jr. and R. I. Hernandes-Aranda, “Optical Rankine Vortex and Anomalous Circulation of Light,” Phys. Rev. Lett. 99(16), 193901 (1939).
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).
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.
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].
G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers (Nauka, Moscow, 1974; McGraw-Hill, New York, 1961).
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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