Abstract

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. For computations of the statistical measures it is therefore desirable to have a solution for the high-frequency field propagating along an isolated ray trajectory. A new reference wave is applied to obtain an analytic solution of the parabolic wave equation that describes propagation along the ray trajectory of the deterministic-background medium. The methodology is based on defining a paired-field measure as a product of an unknown field propagating in a disturbed medium and the complex-conjugate component propagating in a medium without random fluctuations. When a solution of the equation for the paired-field measure is obtained, the solution of the deterministic component can be extracted from the paired solution to determine the solution of the unknown field in an explicit form.

© 2003 Optical Society of America

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  1. R. Mazar and L. B. Felsen, J. Acoust. Soc. Am. 86, 2292 (1989).
    [Crossref]
  2. R. Mazar and L. B. Felsen, Opt. Lett. 12, 301 (1987).
    [Crossref] [PubMed]
  3. V. U. Zavorotny, V. I. Klyatskin, and V. I. Tatarskii, Sov. Phys. JETP 46, 252 (1978).
  4. R. Dashen, J. Math. Phys. 20, 894 (1979).
    [Crossref]
  5. S. M. Flatte, D. R. Bernstein, and R. Dashen, Phys. Fluids 26, 1701 (1983).
    [Crossref]
  6. R. Dashen, S. M. Flatte, and S. A. Reynolds, J. Acoust. Soc. Am. 77, 1716 (1985).
    [Crossref]
  7. J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, J. Math. Phys. 27, 171 (1986).
    [Crossref]
  8. S. M. Flatte, S. A. Reynolds, and R. Dashen, J. Acoust. Soc. Am. 82, 967 (1987).
    [Crossref]
  9. R. Mazar, J. Acoust. Soc. Am. 111, 809 (2002).
    [Crossref] [PubMed]
  10. R. Mazar and A. Bronshtein, Opt. Lett. 27, 52 (2002).
    [Crossref]
  11. R. Mazar and A. Bronshtein, Phys. Rev. E 65, 66617 (2002).
    [Crossref]
  12. A. Bronshtein and R. Mazar, Waves Random Media 12, 267 (2002).
    [Crossref]
  13. S. Frankenthal, M. J. Beran, and A. M. Whitman, J. Acoust. Soc. Am. 71, 348 (1982).
    [Crossref]
  14. M. J. Beran, A. M. Whitman, and S. Frankenthal, J. Acoust. Soc. Am. 71, 1124 (1982).
    [Crossref]
  15. R. Mazar, J. Opt. Soc. Am. A 7, 34 (1990).
    [Crossref]
  16. R. Mazar and A. Bronshtein, J. Acoust. Soc. Am. 91, 802 (1992).
    [Crossref]
  17. V. I. Klyatskin, Stochastic Equations and Waves in Randomly Inhomogeneous Media (Nauka, Moscow, 1980).
  18. R. Mazar, L. Kodner, and G. Samelsohn, J. Opt. Soc. Am. A 14, 2809 (1997).
    [Crossref]

2002 (4)

R. Mazar, J. Acoust. Soc. Am. 111, 809 (2002).
[Crossref] [PubMed]

R. Mazar and A. Bronshtein, Opt. Lett. 27, 52 (2002).
[Crossref]

R. Mazar and A. Bronshtein, Phys. Rev. E 65, 66617 (2002).
[Crossref]

A. Bronshtein and R. Mazar, Waves Random Media 12, 267 (2002).
[Crossref]

1997 (1)

R. Mazar, L. Kodner, and G. Samelsohn, J. Opt. Soc. Am. A 14, 2809 (1997).
[Crossref]

1992 (1)

R. Mazar and A. Bronshtein, J. Acoust. Soc. Am. 91, 802 (1992).
[Crossref]

1990 (1)

1989 (1)

R. Mazar and L. B. Felsen, J. Acoust. Soc. Am. 86, 2292 (1989).
[Crossref]

1987 (2)

R. Mazar and L. B. Felsen, Opt. Lett. 12, 301 (1987).
[Crossref] [PubMed]

S. M. Flatte, S. A. Reynolds, and R. Dashen, J. Acoust. Soc. Am. 82, 967 (1987).
[Crossref]

1986 (1)

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, J. Math. Phys. 27, 171 (1986).
[Crossref]

1985 (1)

R. Dashen, S. M. Flatte, and S. A. Reynolds, J. Acoust. Soc. Am. 77, 1716 (1985).
[Crossref]

1983 (1)

S. M. Flatte, D. R. Bernstein, and R. Dashen, Phys. Fluids 26, 1701 (1983).
[Crossref]

1982 (2)

S. Frankenthal, M. J. Beran, and A. M. Whitman, J. Acoust. Soc. Am. 71, 348 (1982).
[Crossref]

M. J. Beran, A. M. Whitman, and S. Frankenthal, J. Acoust. Soc. Am. 71, 1124 (1982).
[Crossref]

1979 (1)

R. Dashen, J. Math. Phys. 20, 894 (1979).
[Crossref]

1978 (1)

V. U. Zavorotny, V. I. Klyatskin, and V. I. Tatarskii, Sov. Phys. JETP 46, 252 (1978).

Beran, M. J.

S. Frankenthal, M. J. Beran, and A. M. Whitman, J. Acoust. Soc. Am. 71, 348 (1982).
[Crossref]

M. J. Beran, A. M. Whitman, and S. Frankenthal, J. Acoust. Soc. Am. 71, 1124 (1982).
[Crossref]

Bernstein, D. R.

S. M. Flatte, D. R. Bernstein, and R. Dashen, Phys. Fluids 26, 1701 (1983).
[Crossref]

Bronshtein, A.

R. Mazar and A. Bronshtein, Phys. Rev. E 65, 66617 (2002).
[Crossref]

A. Bronshtein and R. Mazar, Waves Random Media 12, 267 (2002).
[Crossref]

R. Mazar and A. Bronshtein, Opt. Lett. 27, 52 (2002).
[Crossref]

R. Mazar and A. Bronshtein, J. Acoust. Soc. Am. 91, 802 (1992).
[Crossref]

Codona, J. L.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, J. Math. Phys. 27, 171 (1986).
[Crossref]

Creamer, D. B.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, J. Math. Phys. 27, 171 (1986).
[Crossref]

Dashen, R.

S. M. Flatte, S. A. Reynolds, and R. Dashen, J. Acoust. Soc. Am. 82, 967 (1987).
[Crossref]

R. Dashen, S. M. Flatte, and S. A. Reynolds, J. Acoust. Soc. Am. 77, 1716 (1985).
[Crossref]

S. M. Flatte, D. R. Bernstein, and R. Dashen, Phys. Fluids 26, 1701 (1983).
[Crossref]

R. Dashen, J. Math. Phys. 20, 894 (1979).
[Crossref]

Felsen, L. B.

R. Mazar and L. B. Felsen, J. Acoust. Soc. Am. 86, 2292 (1989).
[Crossref]

R. Mazar and L. B. Felsen, Opt. Lett. 12, 301 (1987).
[Crossref] [PubMed]

Flatte, S. M.

S. M. Flatte, S. A. Reynolds, and R. Dashen, J. Acoust. Soc. Am. 82, 967 (1987).
[Crossref]

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, J. Math. Phys. 27, 171 (1986).
[Crossref]

R. Dashen, S. M. Flatte, and S. A. Reynolds, J. Acoust. Soc. Am. 77, 1716 (1985).
[Crossref]

S. M. Flatte, D. R. Bernstein, and R. Dashen, Phys. Fluids 26, 1701 (1983).
[Crossref]

Frankenthal, S.

M. J. Beran, A. M. Whitman, and S. Frankenthal, J. Acoust. Soc. Am. 71, 1124 (1982).
[Crossref]

S. Frankenthal, M. J. Beran, and A. M. Whitman, J. Acoust. Soc. Am. 71, 348 (1982).
[Crossref]

Frehlich, R. G.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, J. Math. Phys. 27, 171 (1986).
[Crossref]

Henyey, F. S.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, J. Math. Phys. 27, 171 (1986).
[Crossref]

Klyatskin, V. I.

V. U. Zavorotny, V. I. Klyatskin, and V. I. Tatarskii, Sov. Phys. JETP 46, 252 (1978).

V. I. Klyatskin, Stochastic Equations and Waves in Randomly Inhomogeneous Media (Nauka, Moscow, 1980).

Kodner, L.

R. Mazar, L. Kodner, and G. Samelsohn, J. Opt. Soc. Am. A 14, 2809 (1997).
[Crossref]

Mazar, R.

A. Bronshtein and R. Mazar, Waves Random Media 12, 267 (2002).
[Crossref]

R. Mazar, J. Acoust. Soc. Am. 111, 809 (2002).
[Crossref] [PubMed]

R. Mazar and A. Bronshtein, Phys. Rev. E 65, 66617 (2002).
[Crossref]

R. Mazar and A. Bronshtein, Opt. Lett. 27, 52 (2002).
[Crossref]

R. Mazar, L. Kodner, and G. Samelsohn, J. Opt. Soc. Am. A 14, 2809 (1997).
[Crossref]

R. Mazar and A. Bronshtein, J. Acoust. Soc. Am. 91, 802 (1992).
[Crossref]

R. Mazar, J. Opt. Soc. Am. A 7, 34 (1990).
[Crossref]

R. Mazar and L. B. Felsen, J. Acoust. Soc. Am. 86, 2292 (1989).
[Crossref]

R. Mazar and L. B. Felsen, Opt. Lett. 12, 301 (1987).
[Crossref] [PubMed]

Reynolds, S. A.

S. M. Flatte, S. A. Reynolds, and R. Dashen, J. Acoust. Soc. Am. 82, 967 (1987).
[Crossref]

R. Dashen, S. M. Flatte, and S. A. Reynolds, J. Acoust. Soc. Am. 77, 1716 (1985).
[Crossref]

Samelsohn, G.

R. Mazar, L. Kodner, and G. Samelsohn, J. Opt. Soc. Am. A 14, 2809 (1997).
[Crossref]

Tatarskii, V. I.

V. U. Zavorotny, V. I. Klyatskin, and V. I. Tatarskii, Sov. Phys. JETP 46, 252 (1978).

Whitman, A. M.

M. J. Beran, A. M. Whitman, and S. Frankenthal, J. Acoust. Soc. Am. 71, 1124 (1982).
[Crossref]

S. Frankenthal, M. J. Beran, and A. M. Whitman, J. Acoust. Soc. Am. 71, 348 (1982).
[Crossref]

Zavorotny, V. U.

V. U. Zavorotny, V. I. Klyatskin, and V. I. Tatarskii, Sov. Phys. JETP 46, 252 (1978).

J. Acoust. Soc. Am. (1)

R. Dashen, S. M. Flatte, and S. A. Reynolds, J. Acoust. Soc. Am. 77, 1716 (1985).
[Crossref]

J. Acoust. Soc. Am. (6)

S. Frankenthal, M. J. Beran, and A. M. Whitman, J. Acoust. Soc. Am. 71, 348 (1982).
[Crossref]

M. J. Beran, A. M. Whitman, and S. Frankenthal, J. Acoust. Soc. Am. 71, 1124 (1982).
[Crossref]

R. Mazar and A. Bronshtein, J. Acoust. Soc. Am. 91, 802 (1992).
[Crossref]

R. Mazar and L. B. Felsen, J. Acoust. Soc. Am. 86, 2292 (1989).
[Crossref]

S. M. Flatte, S. A. Reynolds, and R. Dashen, J. Acoust. Soc. Am. 82, 967 (1987).
[Crossref]

R. Mazar, J. Acoust. Soc. Am. 111, 809 (2002).
[Crossref] [PubMed]

J. Math. Phys. (2)

R. Dashen, J. Math. Phys. 20, 894 (1979).
[Crossref]

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, J. Math. Phys. 27, 171 (1986).
[Crossref]

J. Opt. Soc. Am. A (1)

R. Mazar, L. Kodner, and G. Samelsohn, J. Opt. Soc. Am. A 14, 2809 (1997).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Lett. (2)

Phys. Fluids (1)

S. M. Flatte, D. R. Bernstein, and R. Dashen, Phys. Fluids 26, 1701 (1983).
[Crossref]

Phys. Rev. E (1)

R. Mazar and A. Bronshtein, Phys. Rev. E 65, 66617 (2002).
[Crossref]

Sov. Phys. JETP (1)

V. U. Zavorotny, V. I. Klyatskin, and V. I. Tatarskii, Sov. Phys. JETP 46, 252 (1978).

Waves Random Media (1)

A. Bronshtein and R. Mazar, Waves Random Media 12, 267 (2002).
[Crossref]

Other (1)

V. I. Klyatskin, Stochastic Equations and Waves in Randomly Inhomogeneous Media (Nauka, Moscow, 1980).

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Equations (9)

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gσ-ik2n0σr12g-ik2n0σbσ·r1g=ikμr1,σg+1n0σn0σσg.
Πσ-ikn0σv·qΠ-i2kn0σq2Π+ikn0σbσ·vΠ-i2kn0σbσ·qΠ=ikμv+q,σΠ+2n0σn0σσΠ,
Π¯(v,ρ,σ|v0,ρ0,σ0)=k2π2-dqdq0Π(v,q,σ|v0,q0,σ0)×exp-ikρ·q-ρ0·q0.
Π¯σ+ρn0σ·vμv,σ·ρΠ¯=ikμv,σΠ¯+12kn0bσ·ρΠ¯+ikp22n0σΠ¯+2n0σn0σσΠ¯.
dvdζ=ρn0ζ, vζ=σ=v,
dρdζ=vμv,ζ, ρζ=σ=ρ,
dΠ¯dζ=ikμv,ζΠ¯+1kn0ζb(ζ)·ρΠ¯+ikρ22n0ζΠ¯+2n0σn0σσΠ¯.
Π¯(v,ρ,σ|v0,ρ0,σ0)=n0σn0σ02Π¯[vfσ0,ρfσ0,σ0|v0,ρ0,σ0]×expik2σ0σdζn0ζρf2ζexp1kσ0σdζbζ·ρζn0ζ×expikσ0σdζμv-ζσρfξn0ξdξ,ζ,
g(r,σ|r0,σ0)=1Jn0σn0σ0-dpΛikr-σ0σdζρfζn0ζ-r0×expik2σ0σdζρf2ζn0ζ×expikσ0σdξbξ·ρfξn0ξ×expikσ0σdζμr-σ0σρfξn0ξdξ,ζ,

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