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Method of Spherical Phase Screens for Modeling the Propagation of Diverging Beams in Inhomogeneous Media

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Abstract

The phase-screen (split-step) method is widely used for modeling wave propagation in inhomogeneous media. The method of plane phase screens is best known. However, for modeling a 2D problem of radio occultation sounding of the Earth’s atmosphere, the method of cylindrical phase screen was developed many years ago. In this paper, we propose a further generalization of this method for the 3D problem on the basis of spherical phase screens. In the paraxial approximation, we derive the formula for the vacuum screen-to-screen propagator. We also infer the expression for the phase thickness of a thin layer of aisotropic random media. We describe a numerical implementation of this method and give numerical examples of its application for modeling a diverging laser beam propagating on a 25-km-long atmospheric path.

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REFERENCES

  1. V. L. Mironov and S. I. Tuzova, “The Huygens-Kirchhoff method in the problems of optic radiation propagation in a medium with large-scale discrete inhomogeneities,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 27 (4), 535–537 (1984).

    Google Scholar 

  2. J. M. Martin and S. M. Flatté, “Simulation of point-source scintillation through three-dimensional random media,” J. Opt. Soc. Am., A, 7, 838–847 (1990).

    Article  Google Scholar 

  3. J. Martin, “Simulation of wave propagation in random media: theory and applications,” in Wave Propagation in Random Media (Scintillation), Ed. by V. I. Tatarski, A. Ishimaru, and V. U. Zavorotny (SPIE, Bellingham, and IOP, Bristol, 1992).

    Google Scholar 

  4. V. P. Kandidov, “The Monte Carlo method in nonlinear statistical optics,” Phys.-Usp. 39, 1243–1272 (1996).

    Article  Google Scholar 

  5. I. P. Lukin, D. S. Rychkov, A. V. Falits, K. S. Lai, and M. R. Liu, “A phase screen model for the numerical simulation of laser beam propagation in rain,” Quantum Electron. 39 (9) 863–868 (2009).

    Article  Google Scholar 

  6. M. E. Gorbunov and A. S. Gurvich, “Microlab-1 experiment: multipath effects in the lower troposphere,” J. Geophys. Res.: Atmos. 103 (D12), 826 (1998). https://doi.org/10.1029/98JD00806

    Article  Google Scholar 

  7. Y. Cao, S. L. Dvorak, X. Ye, and B. Herman, “A new cylindrical phase screen method for modeling electromagnetic wave propagation through an inhomogeneous 2-D atmosphere,” Radio Sci. 42, RS4027 (2007). https://doi.org/10.1029/2006rs003550

    Article  Google Scholar 

  8. M. E. Gorbunov, V. V. Vorob’ev, and K. B. Lauritsen, “Fluctuations of refractivity as a systematic error source in radio occultations,” Radio Sci. 50 (7), 656–669 (2015). https://doi.org/10.1002/2014RS005639

    Article  Google Scholar 

  9. M. I. Charnotskii, J. Gozani, V. I. Tatarskii, and V. U. Zavorotny, “IV Wave propagation theories in random media based on the path-integral approach,” Progress in Optics, 32, 203–266 (1993).

    Article  Google Scholar 

  10. V. A. Zverev, Radiooptics: Signal Transformation in Radio and Optics (Sovetskoe radio, Moscow, 1975) [in Russian].

  11. DELICAT. http://www.delicat.inoe.ro/.

  12. P. Vrancken, DELICAT – Demonstration of Lidar-Based CAT (Clear Air Turbulence) detection, Aviation Turbulence Workshop, August 2013, NCAR, Boulder, CO, USA (NCAR, Boulder, CO, 2013).

  13. V. I. Talanov, “Focusing of light in cubic media,” Zh. Eksp. Teor. Fiz., Pis’ma Red. 11 (6), 303–305 (1970).

    Google Scholar 

  14. N. N. Rozanov, Special Chapters of Mathematical Physics. Part I. Electromagnetic Waves in Vacuum (SPb GUITMO, St. Petersburg, 2005) [in Russian].

  15. S. N. Gurbatov, O. V. Rudenko, and A. I. Saichev, Waves and Structures in Nonlinear Nondispersive Media (Fizmatlit, Moscow, 2008; Springer, Berlin 2011).

  16. C. L. Rino, The Theory of Scintillation with Applications in Remote Sensing (Wiley-IEEE Press, Hoboken, 2011).

    Book  Google Scholar 

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Funding

This work was financially supported by the Russian Foundation for Basic Research (grant no. 18-35-00368).

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Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017, Moscow, Russia

    M. E. Gorbunov, O. A. Koval & A. E. Mamontov

  2. Hydrometeorological Research Centre of Russian Federation, 123242, Moscow, Russia

    M. E. Gorbunov

Authors
  1. M. E. Gorbunov
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  2. O. A. Koval
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  3. A. E. Mamontov
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Correspondence to M. E. Gorbunov.

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Translated by V. Selikhanovich

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Gorbunov, M.E., Koval, O.A. & Mamontov, A.E. Method of Spherical Phase Screens for Modeling the Propagation of Diverging Beams in Inhomogeneous Media. Izv. Atmos. Ocean. Phys. 56, 52–60 (2020). https://doi.org/10.1134/S0001433820010041

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  • DOI: https://doi.org/10.1134/S0001433820010041

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