## Two-frequency mutual coherence function of electromagnetic waves in random media: a path-integral variational solution

JOSA A, Vol. 19, Issue 10, pp. 2074-2084 (2002)

http://dx.doi.org/10.1364/JOSAA.19.002074

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### Abstract

By use of path-integral methods, a general expression is obtained for the two-frequency, two-position mutual coherence function of an electromagnetic pulse propagating through turbulent atmosphere. This expression is valid for arbitrary models of refractive-index fluctuations, wide band pulses, and turbulence of arbitrary strength. The approach presented in this paper was examined in the cases of plane-wave, spherical wave, and Gaussian beam propagation in power-law turbulence and compared with existing numerical and exact results. A number of new results were obtained for the Gaussian beam pulse. Expressions derived here should be applicable to a wide range of practical pulse propagation problems.

© 2002 Optical Society of America

**OCIS Codes**

(010.1290) Atmospheric and oceanic optics : Atmospheric optics

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(010.3310) Atmospheric and oceanic optics : Laser beam transmission

**History**

Original Manuscript: February 15, 2002

Revised Manuscript: May 13, 2002

Manuscript Accepted: May 15, 2002

Published: October 1, 2002

**Citation**

Alexandre V. Morozov, "Two-frequency mutual coherence function of electromagnetic waves in random media: a path-integral variational solution," J. Opt. Soc. Am. A **19**, 2074-2084 (2002)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-10-2074

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### References

- C. Y. Young, A. Ishimaru, L. C. Andrews, “Two-frequency mutual coherence function of a Gaussian beam pulse in weak optical turbulence: an analytic solution,” Appl. Opt. 35, 6522–6526 (1996). [CrossRef] [PubMed]
- C. Y. Young, L. C. Andrews, A. Ishimaru, “Time-of-arrival fluctuations of a space–time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. 37, 7655–7660 (1998). [CrossRef]
- I. Sreenivasiah, “Two-frequency mutual coherence function and pulse propagation in continuous random media: forward and backscattering solutions,” Ph.D. dissertation (University of Washington, Seattle, Wash.1976).
- I. Sreenivasiah, A. Ishimaru, “Beam-wave two-frequency mutual-coherence function and pulse propaga-tion in random media: an analytic solution,” Appl. Opt. 18, 1613–1618 (1979). [CrossRef] [PubMed]
- I. Sreenivasiah, A. Ishimaru, 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. 11, 775–778 (1976). [CrossRef]
- V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (U. S. Department of Commerce, Springfield, Va., 1971).
- C. H. Liu, “Pulse statistics in random media,” in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, V. U. Zavorotny, eds. (SPIE, Bellingham, Wash., 1993), pp. 291–304.
- R. P. Feynman, A. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
- L. S. Brown, Quantum Field Theory (Cambridge U. Press, Cambridge, UK, 1995).
- R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979). [CrossRef]
- C. M. Rose, I. M. Besieris, “Nth-order multifrequency coherence functions: a functional path integral approach,” J. Math. Phys. 20, 1530–1538 (1979). [CrossRef]
- C. M. Rose, I. M. Besieris, “Nth-order multifrequency coherence functions: a functional path integral approach. II,” J. Math. Phys. 21, 2114–2120 (1980). [CrossRef]
- J. Gozani, “Pulsed beam propagation through random media,” Opt. Lett. 21, 1712–1714 (1996). [CrossRef] [PubMed]
- S. Wandzura, “Meaning of quadratic structure functions,” J. Opt. Soc. Am. 70, 745–747 (1980). [CrossRef]
- C. H. Liu, K. C. Yeh, “Pulse spreading and wandering in random media,” Radio Sci. 14, 925–931 (1979). [CrossRef]
- L. C. Lee, J. R. Jokipii, “Strong scintillations in atsrophysics. II. A theory of temporal broadening of pulses,” Astrophys. J. 201, 532–543 (1975). [CrossRef]
- K. Furutsu, “An analytical theory of pulse wave propagation in turbulent media,” J. Math. Phys. 20, 617–628 (1979). [CrossRef]
- J. Oz, E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution:I,” Waves Random Media 7, 79–93 (1997). [CrossRef]
- J. Oz, E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution: II,” Waves Random Media 7, 95–106 (1997). [CrossRef]
- J. Oz, E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: point source,” Waves Random Media 7, 107–117 (1997). [CrossRef]
- J. Oz, E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: beam waves,” Waves Random Media 8, 159–174 (1998). [CrossRef]
- J. Oz, E. Heyman, “Modal solution to the plane wave two-frequency mutual coherence function in random media,” Radio Sci. 31, 1907–1917 (1996). [CrossRef]
- R. L. Fante, “Two-position, two-frequency mutual-coherence function in turbulence,” J. Opt. Soc. Am. 71, 1446–1451 (1981). [CrossRef]
- J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 45–106.
- V. I. Tatarskii, M. I. Charnotskii, J. Gozani, V. U. Zavorotny, “Path integral approach to wave propagation in random media, Part I: derivations and various formulations,” in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, V. U. Zavorotny, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 383–402.
- V. U. Zavorotny, M. I. Charnotskii, J. Gozani, V. I. Tatarskii, “Path integral approach to wave propagation in random media, Part II: exact formulations and heuristic approximations,” in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, V. U. Zavor-otny, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 403–421.
- J. Gozani, M. I. Charnotskii, V. I. Tatarskii, V. U. Zavorotny, “Path integral approach to wave propagation in random media, Part III: mixed representation; orthogonal expansion,” in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, V. U. Zavorotny, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 422–441.
- A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, New York, 1997).
- M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).
- R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978). [CrossRef]

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