Abstract

It is known that some partially coherent Gaussian Schell-model beams may generate, in free space, the same angular distribution of radiant intensity as a fully coherent laser beam. We show that this result also holds even if the beams propagate in atmospheric turbulence, irrespective of the particular model of turbulence used. The result is illustrated by an example.

© 2003 Optical Society of America

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References

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  1. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Press, Bellingham, Wash., 1998).
  2. E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
    [CrossRef]
  3. See, for example, P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
    [CrossRef]
  4. G. Gbur and E. Wolf, J. Opt. Soc. Am. A 19, 1592 (2002).
    [CrossRef]
  5. S. A. Ponomarenko, J.-J. Greffett, and E. Wolf, Opt. Commun. 208, 1 (2002).
    [CrossRef]
  6. A. Dogariu and S. Amarande, Opt. Lett. 28, 10 (2003).
    [CrossRef] [PubMed]
  7. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  8. Sec. 12.2 of Ref. 1.
  9. R. L. Fante, in Progress in Optics XXII, E. Wolf, ed. (Elsevier, Amsterdam, 1985), Chap. VI.
  10. Secs. 12.2.3 and 6.4.2 of Ref. 1.
  11. To evaluate Eq. (11), we first change the variables of integration by setting u=ρ0+ρ0′/2 and v=ρ0-ρ0′. Then, we use the relations ∫x2 exp-i2πxsdx=-2π-2δ″s and ∫fxδ″xdx=f″0, where δ″ is the second derivative of the Dirac delta function, f is an arbitrary function, and f″ is its second derivative.
  12. See Eqs. (29) and (30) of Ref. 4, corrected for any error. In formula (29) of Ref. 4 the multiplicative factor 2π2/3 should be replaced with 4π2/3; i.e., the formula should read F2=4π2/3∫0∞κ3Φnκdκ.

2003 (1)

2002 (2)

S. A. Ponomarenko, J.-J. Greffett, and E. Wolf, Opt. Commun. 208, 1 (2002).
[CrossRef]

G. Gbur and E. Wolf, J. Opt. Soc. Am. A 19, 1592 (2002).
[CrossRef]

1979 (1)

See, for example, P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

1978 (1)

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

Amarande, S.

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Press, Bellingham, Wash., 1998).

Collett, E.

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

De Santis, P.

See, for example, P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Dogariu, A.

Fante, R. L.

R. L. Fante, in Progress in Optics XXII, E. Wolf, ed. (Elsevier, Amsterdam, 1985), Chap. VI.

Gbur, G.

Gori, F.

See, for example, P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Greffett, J.-J.

S. A. Ponomarenko, J.-J. Greffett, and E. Wolf, Opt. Commun. 208, 1 (2002).
[CrossRef]

Guattari, G.

See, for example, P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Palma, C.

See, for example, P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Press, Bellingham, Wash., 1998).

Ponomarenko, S. A.

S. A. Ponomarenko, J.-J. Greffett, and E. Wolf, Opt. Commun. 208, 1 (2002).
[CrossRef]

Wolf, E.

S. A. Ponomarenko, J.-J. Greffett, and E. Wolf, Opt. Commun. 208, 1 (2002).
[CrossRef]

G. Gbur and E. Wolf, J. Opt. Soc. Am. A 19, 1592 (2002).
[CrossRef]

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

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

Opt. Commun. (3)

S. A. Ponomarenko, J.-J. Greffett, and E. Wolf, Opt. Commun. 208, 1 (2002).
[CrossRef]

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

See, for example, P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Opt. Lett. (1)

Other (7)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Press, Bellingham, Wash., 1998).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Sec. 12.2 of Ref. 1.

R. L. Fante, in Progress in Optics XXII, E. Wolf, ed. (Elsevier, Amsterdam, 1985), Chap. VI.

Secs. 12.2.3 and 6.4.2 of Ref. 1.

To evaluate Eq. (11), we first change the variables of integration by setting u=ρ0+ρ0′/2 and v=ρ0-ρ0′. Then, we use the relations ∫x2 exp-i2πxsdx=-2π-2δ″s and ∫fxδ″xdx=f″0, where δ″ is the second derivative of the Dirac delta function, f is an arbitrary function, and f″ is its second derivative.

See Eqs. (29) and (30) of Ref. 4, corrected for any error. In formula (29) of Ref. 4 the multiplicative factor 2π2/3 should be replaced with 4π2/3; i.e., the formula should read F2=4π2/3∫0∞κ3Φnκdκ.

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Figures (1)

Fig. 1
Fig. 1

Beam widths wz of equivalent GSM sources and of the corresponding laser as a function of the propagation distance, z. The parameters of the sources generating these beams are listed in Table 1.

Tables (1)

Tables Icon

Table 1 Parameters of Equivalent GSM Sources and of the Corresponding Laser

Equations (17)

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S0ρ,ω=A exp-ρ22σS2,
μ0ρ1-ρ2,ω=exp-ρ1-ρ222σμ2,
W0ρ1,ρ2,ω=A exp-ρ12+ρ224σS2×exp-ρ1-ρ222σμ2.
SL0ρ,ω=AL exp-ρ22σL2,
μL0ρ1-ρ2,ω1,
14σS2+1σμ2=14σL2,
AσS2=ALσL2.
Uρ,z=-ik expikz2πzU0ρ0expikρ-ρ022z×expψρ,ρ0,zd2ρ0,
Iρ,zU*ρ,zUρ,zm=k2πz2d2ρ0d2ρ0U0*ρ0U0ρ0×exp-ikρ-ρ02-ρ-ρ022z×expψ*ρ,ρ0,z+ψρ,ρ0,zm,
expψ*ρ,ρ0,z+ψρ,ρ0,zm=exp-4π2k2z010κΦnκ×1-J0κξρ0-ρ0dκdξ,
wzρ2Iρ,zd2ρIρ,zd2ρ1/2,
wz=2σS2+2k214σS2+1σμ2z2+43π20κ3Φnκdκz31/2,
wz=2σS2+12k2σL2z2+43π20κ3Φnκdκz31/2,
θspwzzz=12k2σL2+43π20κ3Φnκdκz1/2.
Φnκ=0.033Cn2κ-11/3 exp-κ2κm2,
wz=2σS2+2k214σS2+1σμ2z2+2.186Cn2l0-1/3z31/2,
θsp=2k214σS2+1σμ2+2.186Cn2l0-1/3z1/2.

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