Abstract

The behavior of scalar beams with nonuniform correlations in isotropic random media is investigated. An example illustrates the fact that the off-axis intensity maximum formed in the transverse cross section of a nonuniformly correlated beam on propagation in free space is suppressed when it passes at sufficiently large distances from its source through the isotropic turbulent atmosphere.

© 2012 Optical Society of America

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References

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  1. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  2. L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media (SPIE, 1998).
  3. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light By Particles (Cambridge University, 2006).
  4. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  5. O. Korotkova, Partially Coherent Beam Propagation in Turbulent Atmosphere with Applications (VDM, 2009).
  6. J. Schmidt, Numerical Simulation of Optical Wave Propagation With Examples in MATLAB, Vol. PM199 (SPIE, 2010).
  7. E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
    [CrossRef]
  8. D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
    [CrossRef]
  9. O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
    [CrossRef]
  10. T. Feng and Q. Lin, Acta Opt. Sin. 25, 293 (2005).
  11. O. Korotkova, J. Pu, and E. Wolf, J. Mod. Opt. 55, 1199 (2008).
    [CrossRef]
  12. O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
    [CrossRef]
  13. O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, Waves Random Complex Media 15, 353 (2005).
    [CrossRef]
  14. E. Shchepakina, N. Farwell, and O. Korotkova, Appl. Phys. B 105, 415 (2011).
    [CrossRef]
  15. O. Korotkova and N. Farwell, Opt. Commun. 284, 1740 (2011).
    [CrossRef]
  16. W. Gao and O. Korotkova, Opt. Commun. 270, 474 (2007).
    [CrossRef]
  17. M. S. Belenkii, A. I. Kon, and V. L. Mironov, Sov. J. Quantum Electron. 7, 287 (1977).
    [CrossRef]
  18. F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
    [CrossRef]
  19. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [CrossRef]
  20. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
    [CrossRef]
  21. A. Zilberman, E. Golbraikh, and N. S. Kopeika, Appl. Opt. 47, 6385 (2008).
    [CrossRef]
  22. O. Korotkova and E. Shchepakina, Opt. Lett. 35, 3772 (2010).
    [CrossRef]
  23. T. Shirai, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 20, 1094 (2003).
    [CrossRef]
  24. V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

2011 (3)

E. Shchepakina, N. Farwell, and O. Korotkova, Appl. Phys. B 105, 415 (2011).
[CrossRef]

O. Korotkova and N. Farwell, Opt. Commun. 284, 1740 (2011).
[CrossRef]

H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
[CrossRef]

2010 (1)

2008 (3)

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Appl. Opt. 47, 6385 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

O. Korotkova, J. Pu, and E. Wolf, J. Mod. Opt. 55, 1199 (2008).
[CrossRef]

2007 (2)

W. Gao and O. Korotkova, Opt. Commun. 270, 474 (2007).
[CrossRef]

F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
[CrossRef]

2005 (3)

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, Waves Random Complex Media 15, 353 (2005).
[CrossRef]

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

T. Feng and Q. Lin, Acta Opt. Sin. 25, 293 (2005).

2004 (1)

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

2003 (1)

2000 (1)

V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

1994 (1)

1986 (1)

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef]

1977 (1)

M. S. Belenkii, A. I. Kon, and V. L. Mironov, Sov. J. Quantum Electron. 7, 287 (1977).
[CrossRef]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media (SPIE, 1998).

Belenkii, M. S.

M. S. Belenkii, A. I. Kon, and V. L. Mironov, Sov. J. Quantum Electron. 7, 287 (1977).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Dogariu, A.

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, Waves Random Complex Media 15, 353 (2005).
[CrossRef]

T. Shirai, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 20, 1094 (2003).
[CrossRef]

Farwell, N.

E. Shchepakina, N. Farwell, and O. Korotkova, Appl. Phys. B 105, 415 (2011).
[CrossRef]

O. Korotkova and N. Farwell, Opt. Commun. 284, 1740 (2011).
[CrossRef]

Feng, T.

T. Feng and Q. Lin, Acta Opt. Sin. 25, 293 (2005).

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Gao, W.

W. Gao and O. Korotkova, Opt. Commun. 270, 474 (2007).
[CrossRef]

Golbraikh, E.

Gori, F.

James, D. F. V.

Kon, A. I.

M. S. Belenkii, A. I. Kon, and V. L. Mironov, Sov. J. Quantum Electron. 7, 287 (1977).
[CrossRef]

Kopeika, N. S.

Korotkova, O.

E. Shchepakina, N. Farwell, and O. Korotkova, Appl. Phys. B 105, 415 (2011).
[CrossRef]

O. Korotkova and N. Farwell, Opt. Commun. 284, 1740 (2011).
[CrossRef]

O. Korotkova and E. Shchepakina, Opt. Lett. 35, 3772 (2010).
[CrossRef]

O. Korotkova, J. Pu, and E. Wolf, J. Mod. Opt. 55, 1199 (2008).
[CrossRef]

W. Gao and O. Korotkova, Opt. Commun. 270, 474 (2007).
[CrossRef]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, Waves Random Complex Media 15, 353 (2005).
[CrossRef]

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

O. Korotkova, Partially Coherent Beam Propagation in Turbulent Atmosphere with Applications (VDM, 2009).

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light By Particles (Cambridge University, 2006).

Lajunen, H.

Lin, Q.

T. Feng and Q. Lin, Acta Opt. Sin. 25, 293 (2005).

Mironov, V. L.

M. S. Belenkii, A. I. Kon, and V. L. Mironov, Sov. J. Quantum Electron. 7, 287 (1977).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light By Particles (Cambridge University, 2006).

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

Nikishov, V. V.

V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

Philips, R. L.

L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media (SPIE, 1998).

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Pu, J.

O. Korotkova, J. Pu, and E. Wolf, J. Mod. Opt. 55, 1199 (2008).
[CrossRef]

Saastamoinen, T.

Salem, M.

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, Waves Random Complex Media 15, 353 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

Santarsiero, M.

Schmidt, J.

J. Schmidt, Numerical Simulation of Optical Wave Propagation With Examples in MATLAB, Vol. PM199 (SPIE, 2010).

Shchepakina, E.

E. Shchepakina, N. Farwell, and O. Korotkova, Appl. Phys. B 105, 415 (2011).
[CrossRef]

O. Korotkova and E. Shchepakina, Opt. Lett. 35, 3772 (2010).
[CrossRef]

Shirai, T.

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light By Particles (Cambridge University, 2006).

Wolf, E.

O. Korotkova, J. Pu, and E. Wolf, J. Mod. Opt. 55, 1199 (2008).
[CrossRef]

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, Waves Random Complex Media 15, 353 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

T. Shirai, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 20, 1094 (2003).
[CrossRef]

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Zilberman, A.

Acta Opt. Sin. (1)

T. Feng and Q. Lin, Acta Opt. Sin. 25, 293 (2005).

Appl. Opt. (1)

Appl. Phys. B (1)

E. Shchepakina, N. Farwell, and O. Korotkova, Appl. Phys. B 105, 415 (2011).
[CrossRef]

Int. J. Fluid Mech. Res. (1)

V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

J. Mod. Opt. (1)

O. Korotkova, J. Pu, and E. Wolf, J. Mod. Opt. 55, 1199 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (4)

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

O. Korotkova and N. Farwell, Opt. Commun. 284, 1740 (2011).
[CrossRef]

W. Gao and O. Korotkova, Opt. Commun. 270, 474 (2007).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

Opt. Eng. (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef]

Sov. J. Quantum Electron. (1)

M. S. Belenkii, A. I. Kon, and V. L. Mironov, Sov. J. Quantum Electron. 7, 287 (1977).
[CrossRef]

Waves Random Complex Media (1)

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, Waves Random Complex Media 15, 353 (2005).
[CrossRef]

Other (6)

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media (SPIE, 1998).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light By Particles (Cambridge University, 2006).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

O. Korotkova, Partially Coherent Beam Propagation in Turbulent Atmosphere with Applications (VDM, 2009).

J. Schmidt, Numerical Simulation of Optical Wave Propagation With Examples in MATLAB, Vol. PM199 (SPIE, 2010).

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Figures (2)

Fig. 1.
Fig. 1.

Transverse distribution of the beam’s spectral density, normalized by its initial on-axis value (unitless), at several distances from the source in (A) Tatarskii’s turbulence and (B) free space.

Fig. 2.
Fig. 2.

Position of the maximum value of the beams’ spectral density: (A) Tatarskii turbulence (solid curve) and free space (dashed curve) versus z, (B) non-Kolmogorov turbulence versus α at z=10km, with L0=10m.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

W0(ρ1,ρ2,ω)=exp[ρ12+ρ222σ02]×exp{[(ρ2ρ0)2(ρ1ρ0)2]2σc4},
W0(ρ1,ρ2,ω)=p(v)H0*(ρ1,v)H0(ρ2,v)dv,
p(v)=(πa2)1/2exp(v2/a2),
H0(ρ,v)=exp[ρ22σ02]exp[ik(ρ2ρ0)2v],
S(ρ,z,ω)=k24π2z2W0(ρ1,ρ2,ω)×exp[ik(ρρ1)2(ρρ2)22z]×exp[ψ*(ρ,ρ1,z)+ψ(ρ,ρ2,z)]Md2ρ1d2ρ2.
exp[ψ*(ρ,ρ1,z)+ψ(ρ,ρ2,z)]Mexp[π2k2z3(ρ1ρ2)20κ3Φ(κ)dκ],
S(ρ,z,ω)=p(v)Sv(ρ,z,ω)dv,
Sv(ρ,z,ω)=k24π2z2H0*(ρ1,v)H0(ρ2,v)×exp[ik(ρρ1)2(ρρ2)22z]×exp[π2k2z3(ρ1ρ2)20κ3Φ(κ)dκ]d2ρ1d2ρ2.
Sv(ρ,z,ω)=σ02w2(z,v)exp[(ρ2vzρ0)2w2(z,v)],
w2(z,v)=σ02(12vz)2+z2k2σ02+43π2z30κ3Φ(κ)dκ.
Φt(κ)=0.033Cn2κ11/3exp(κ2/κm2),
Φα(κ)=A(α)C˜n2exp(κ2/κm2)(κ2+κ02)α/2,3<α<5,

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