Solution for the fourth moment equation of waves in random continuum under strong fluctuations: General theory and plane wave solution

IEEE Transactions on Antennas and Propagation

Volumn 55, Issue 6 I, 2007, Pages 1613-1621

  Xu, Zheng Wen ^a,b   Wu, Jian ^a   Wu, Zhen Sen ^b   Li, Qiang ^a,c  

^a CHINA RESEARCH INSTITUTE OF RADIOWAVE PROPAGATION   (China)

^b XIDIAN UNIVERSITY   (China)

^c LEIBNIZ INSTITUTE OF ATMOSPHERIC PHYSICS   (Germany)

Author keywords

Electromagnetic propagation in random media; Electromagnetic scattering by random media; Ionospheric electromagnetic propagation; Ionospheric scintillation

Indexed keywords

APPROXIMATION THEORY; ELECTROMAGNETIC WAVE PROPAGATION; GREEN'S FUNCTION; IONOSPHERE; METHOD OF MOMENTS; SCINTILLATION;

FOURTH MOMENT EQUATION; INTENSITY CORRELATION FUNCTION; PLANE WAVE; RANDOM MEDIA; RYTOV APPROXIMATION;

ELECTROMAGNETIC WAVE SCATTERING;

EID: 34249301581     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2007.897301     Document Type: Article

References (44)

1. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation. Springfield, VA.: U.S. Dept. Commerce, 1971.
2. A. Ishimaru, Wave Propagation and Scattering in Random Media. New York: Academic Press, 1978.
3. K. C. Yeh and C. H. Liu, "Radio wave scintillations in the ionosphere," Proc. IEEE, vol. 70, no. 4, pp. 324-360, Apr. 1982.
4. D. L. Knepp and W. A. Brown, "Average received signal power after two-way propagation through ionized turbulence," Radio Sci., vol. 32, no. 4, pp. 1575-1596, 1997.
5. V. I. Shishov, "Theory of wave propagation in random media," Izvestia VUZ. Radiofizika, vol. 11, no. 6, pp. 866-875, 1968.
6. H. G. Booker, "The use of radio stars to study irregular refraction of radio waves in the ionosphere," Proc. IRE, vol. 46, pp. 298-314, Jan. 1958.
7. W. P. Brown, "Moment equations for waves propagated in random media," J. Opt. Soc. Am., vol. 62, pp. 45-54, Jan. 1972.
8. R. L. Fante, "Two-position, two-frequency mutual-coherence function in turbulence," J. Opt. Soc. Am., vol. 71, no. 12, pp. 1446-1451, 1981.
9. L. C. Lee, "Wave propagation in a random medium: A complete set of the moment equations with different wave numbers," J. Math. Phys., vol. 15, no. 9, pp. 1431-1435, 1974.
10. C. H. Liu, A. W. Wernik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Antennas Propag., vol. 22, pp. 152-155, Jul. 1974.
11. C. L. Rino, "On the application of phase screen models to the interpretation of ionospheric scintillation data," Radio Sci., vol. 17, pp. 855-867, 1982.
12. D. L. Knepp, "Multiple phase-screen calculation of the temporal behavior of stochastic waves," Proc. IEEE, vol. 71, no. 6, pp. 722-737, 1983.
13. B. J. Uscinski, "Analytical solution of the fourth-moment equation and interpretation as a set of phase screens," J. Opt. Soc. Am. A, vol. 2, no. 12, pp. 2077-2091, 1985.
14. R. Dashen, "Path integrals for waves in random media," J. Math. Phys., vol. 20, no. 5, pp. 894-920, 1979.
15. S. Y. Lee, C. H. Liu, and K. C. Yeh, "Waves in random continuum described by path integrals," in Research Topics in Electromagnetic Wave Theory, J.A. Kong, Ed. New York: Wiley, 1981, ch. 2, pp. 1-32.
16. S. M. Flatté, "Wave propagation through random media: Contribution from ocean acoustics," Proc. IEEE, vol. 71, no. 11, pp. 1267-1294, 1983.
17. J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, and F. S. Henyey, "Solution for the fourth moment of waves propagating in random media," Radio Sci., vol. 21, no. 6, pp. 929-948, 1986.
18. M. Tur, "Numerical solutions for the fourth moment of a finite beam propagating in a random medium," J. Opt. Soc. Am. A, vol. 2, no. 12, pp. 2161-2170, 1985.
19. J. M. Martin and S. M. Flatté, "Intensity images and statistics from numerical simulation of wave propagation in three-dimensional random media," Appl. Opt., vol. 27, pp. 2111-2126, 1988.
20. V. S. Filinov, "Monte Carlo simulation in the theory of wave propagation in random media: II. Scintillation index, second and fourth moments," Waves Random Media, vol. 5, no. 3, pp. 277-287, 1995.
21. C. Macaskill, "An improved solution to the fourth moment equation for intensity fluctuations," Proc. R. Soc. Lond. A, vol. 386, pp. 461-474, 1983.
22. R. Mazar, J. Gozani, and M. Tur, "Two-scale solution for the intensity fluctuations of two-frequency wave propagation in a random medium," J. Opt. Soc. Am. A, vol. 2, no. 12, pp. 2152-2160, 1985.
23. M. Spivack and B. J. Uscinski, "The split step solution in random wave propagation," J. Comput. Appl. Math., vol. 27, no. 3, pp. 349-361, 1989.
24. J. Wu, "Analytic solutions of the two-frequency and two-position mutual coherence function for wave propagating through random media," Chin. J. Electron., vol. 8, no. 3, pp. 313-316, 1999.
25. J. Wu and R. Y. Liu, "The solution of the forward multiple scattering moment equation and its applications to ionospheric scintillations," Sciencia Sinica (Series A), vol. 19, no. 12, pp. 1322-1332, 1989.
26. Z.-W. Xu, J.Wu, and Z.-S. Wu, "Second-order statistics of radio wave propagation through the structured ionosphere," J. Atmos. Solar-Terr. Phys., vol. 66, no. 11, pp. 971-980, 2004.
27. Z.-S. Wang, "Wave propagation in a random medium: The solution of the m-nth moment equation with different wavenumbers," Lett. Math. Phys. vol. 13, no. 4, pp. 261-271, 1987.
28. V. E. Gherm, N. N. Zernov, S. M. Radicella, and H. J. Strangeways, "Propagation model for signal fluctuations on transionospheric radio links," Radio Sci., vol. 35, no. 5, pp. 1221-1232, 2000.
29. R. Mazar and A. Bronshtein, "Reference-wave solution for the two-frequency field in random media," Phys. Rev. E, vol. 65, no. 6, 2002, paper no. 066617.
30. G. Samelsohn and V. Freilikher, "Two-frequency mutual coherence function and pulse propagation in random media," Phys. Rev. E, vol. 65, no. 4, 2002, paper no. 046617.
31. A. S. Gurvich, V. Kan, V. I. Tatarskii, and V. U. Zavorotnyi, "Four-point field coherence function in a turbulent medium," Opt. Acta, vol. 26, no. 5, pp. 543-553, 1979.
32. R. L. Fante, "Electromagnetic beam propagation in turbulent media: An update," Proc. IEEE., vol. 68, no. 11, pp. 1424-1443, 1980.
33. G. Z. Li, J. Wu, J. Y. Huang, and S. Q. Peng, "An analytical solution for the two-frequency and two-position mutual coherence function of wave propagation through random ionospheric media," Chinese J. Radio Sci. vol. 18, no. 2, pp. 157-160, 2003.
34. V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, and K. K. Sabel'feld, "Space structure of strong intensity fluctuations of light in a turbulent medium," Opt. Acta, vol. 26, no. 5, pp. 531-542, 1979.
35. K. C. Yeh and C. H. Liu, "An investigation of temporal moments of stochastic waves," Radio Sci., vol. 12, no. 5, pp. 671-680, 1977.
36. V. H. Rumsey, "Scintillations due to a concentrated layer with a power-law turbulence spectrum," Radio Sci., vol. 10, no. 1, pp. 107-114, 1975.
37. R. G. Rastogi, P. V. Koparkar, H. Chandra, and M. R. Deshpande, "Multifrequency studies of equatorial ionospheric scintillations at Ootacamund," J. Atmos. Terr. Phys., vol. 52, no. 1, pp. 69-76, 1990.
38. I. P. Shkarofsky, "Generalized turbulence space-correlation and wave-number spectrum-function pairs," Can. J. Phys., vol. 46, pp. 2133-2153, 1968.
39. K. C. Yeh, C. H. Liu, and Y. Youakim, "A theoretical study of the ionospheric scintillation behavior caused by multiple scattering," Radio Sci., vol. 10, no. 1, pp. 97-106, 1975.
40. I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case," Radio Sci., vol. 11, no. 10, pp. 775-778, 1976.
41. D. L. Knepp, "Analytic solution for the two-frequency mutual coherence function for spherical wave propagation," Radio Sci., vol. 18, no. 4, pp. 535-549, 1983.
42. J. Oz and E. Heyman, "Modal solution to the two-frequency mutual coherence function in random media," Radio Sci., vol. 31, no. 6, pp. 1907-1918, 1996.
43. J. Oz and E. Heyman, "Modal theory for the two-frequency mutual coherence function in random media: General theory and plane wave solution: I," Waves Random Media, vol. 7, no. 1, pp. 79-93, 1997.
44. J. Oz and E. Heyman, "Modal theory for the two-frequency mutual coherence function in random media: General theory and plane wave solution: II," Waves Random Media, vol. 7, no. 1, pp. 95-106, 1997.