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The “cumulant” method for solution of problems of wave propagation in random media

Abstract

The “cumulant” method for solving problems of radiation propagation in randomly inhomogeneous media is described. Integral expressions for statistical moments of the wave complex amplitude in general form with the Feynman representation of Green’s function of the quasioptics parabolic equation have been obtained in the framework of the “cumulant” method. It was shown that taking into account some approximation of the processes of radiation multiple scattering in the “cumulant” method allows us to obtain expressions for statistical moments of intensity to an accuracy sufficient to restore the lognormal distribution function.

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References

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

    Google Scholar 

  2. V. E. Zuev, V. A. Banakh, and V. V. Pokasov, Modern Problems of Atmospheric Optics, Vol. 5: Optics of Turbulent Atmosphere (Gidrometeoizdat, Leningrad, 1988) [in Russian].

    Google Scholar 

  3. R. Kh. Almaev and A. A. Suvorov, “Phase Fluctuations in Waves Reflected from a Phase-Conjugate Mirror in a Randomly Inhomogeneous Medium,” Kvant. Elektron. 20, 874–878 (1993) [Quantum Electron. 23, 758 (1993)].

    Google Scholar 

  4. R. Kh. Almaev and A. A. Suvorov, “Statistics of Strong Irradiance Fluctuations in an Absorbing Turbulent Atmosphere,” Izv. RAN, Fiz. Atmos. Okeana 37, 781–788 (2001).

    Google Scholar 

  5. R. Kh. Almaev and A. A. Suvorov, “Saturation of Irradiance Fluctuations in a Weakly Absorbing Turbulent Atmosphere,” Izv. RAN, Fiz. Atmos. Okeana 44, 360–370 (2008).

    Google Scholar 

  6. S. M. Rytov, “Diffraction of Light by Ultrasonic Waves,” Izv. AN SSSR, Ser. Fiz., No. 2, 223–259 (1937).

  7. V. L. Mironov, Laser Beam Propagation in a Turbulent Atmosphere (Nauka, Novosibirsk, 1981) [in Russian].

    Google Scholar 

  8. R. Feynmann and A. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965; Mir, Moscow, 1968).

    Google Scholar 

  9. A. N. Malakhov, Cumulative Analysis of Random Non-Gaussian Processes and Their Transformations (Radio Svyaz’, Moscow, 1978) [in Russian].

    Google Scholar 

  10. Yu. A. Kravtsov and Z. I. Feizulin, “Some Consequences of the Huygens-Kirchhoff Principle for a Smoothly Nonuniform Medium,” Izv. Vyssh. Uchebn. Zaved., Ser. Radiofiz. 10, 886–893 (1967).

    Google Scholar 

  11. Yu. A. Kravtsov, Z. I. Feizulin, and A. G. Vinogradov, Radio Propagation through the Earth’s Atmosphere (Radio Svyaz’, Moscow, 1983) [in Russian].

    Google Scholar 

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Original Russian Text © R.Kh. Almaev, A.A. Suvorov, 2011, published in Optica Atmosfery i Okeana.

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Almaev, R.K., Suvorov, A.A. The “cumulant” method for solution of problems of wave propagation in random media. Atmos Ocean Opt 24, 1–5 (2011). https://doi.org/10.1134/S1024856011010040

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  • DOI: https://doi.org/10.1134/S1024856011010040

Keywords

  • Statistical Moment
  • Inhomogeneous Medium
  • Complex Phase
  • Turbulent Atmosphere
  • Laser Beam Propagation