Abstract

In J. Opt. Soc. Am. A 29, 169 (2012), Gerçekcioğlu and Baykal presented an investigation of the dependence of the scintillation index of flat-topped Gaussian beams on the exponent α of the power-law-type spectra of non-Kolmogorov turbulence. In particular, they found that the scintillation index reaches a maximum at α3.2. We show that this conclusion is an artifact of their specific calculation, and depends on the choice of the length unit. Gerçekcioğlu and Baykal’s calculations are made for the 3<α<5 range of the spectral exponent. We show that for the homogeneous and isotropic turbulence the correct range is 3<α<4, when Markov approximation is used.

© 2012 Optical Society of America

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References

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  1. H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence,” J. Opt. Soc. Am. A 29, 169–173 (2012).
    [CrossRef]
  2. M. I. Charnotskii, “Asymptotic analysis of finite-beam scintillation in a turbulent medium,” Waves Random Media 4, 243–273 (1994).
    [CrossRef]
  3. V. I. Tatarskii, Wave Propagation in Random Media (McGraw-Hill, 1961).
  4. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics. 4. Wave Propagation through Random Media (Springer, 1988).

2012 (1)

1994 (1)

M. I. Charnotskii, “Asymptotic analysis of finite-beam scintillation in a turbulent medium,” Waves Random Media 4, 243–273 (1994).
[CrossRef]

Baykal, Y.

Charnotskii, M. I.

M. I. Charnotskii, “Asymptotic analysis of finite-beam scintillation in a turbulent medium,” Waves Random Media 4, 243–273 (1994).
[CrossRef]

Gerçekcioglu, H.

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics. 4. Wave Propagation through Random Media (Springer, 1988).

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics. 4. Wave Propagation through Random Media (Springer, 1988).

Tatarskii, V. I.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics. 4. Wave Propagation through Random Media (Springer, 1988).

V. I. Tatarskii, Wave Propagation in Random Media (McGraw-Hill, 1961).

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

Waves Random Media (1)

M. I. Charnotskii, “Asymptotic analysis of finite-beam scintillation in a turbulent medium,” Waves Random Media 4, 243–273 (1994).
[CrossRef]

Other (2)

V. I. Tatarskii, Wave Propagation in Random Media (McGraw-Hill, 1961).

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics. 4. Wave Propagation through Random Media (Springer, 1988).

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Figures (2)

Fig. 1.
Fig. 1.

Dependence of scintillation index on α. Dashed curves, C˜n2=1015m3α. Solid curves, C˜n2=4.64·1017cm3α.

Fig. 2.
Fig. 2.

Dependence of scintillation index on α for W0=2cm. Heavy solid: fixed coherent radius; long-dashed: fixed spherical wave scintillation index; short-dashed: fixed plane wave scintillation index; and thin solid: fixed Dn(L/k).

Equations (9)

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Dn(ρ⃗)=[n(R⃗+ρ⃗)n(R⃗)]2=Cn2ρα3.
rC=(A(α)π2Γ(2α2)23αΓ(α2)(α2)C˜n2k2L)12α,
mPW2=A(α)π2Γ(1α2)sinπα42αC˜n2k3α2Lα2,mSW2=A(α)π2Γ(1α2)sinπα4B(α2,α2)C˜n2k3α2Lα2.
C˜n2(Lk)α32=const,
Dn(r⃗)=C˜n2r3α=2A(α)C˜n2d3KKα[1cos(r⃗·K⃗)]=8πA(α)C˜n20dKK2α[1sin(rK)rK],
Φn(K⃗)=Φn(Kx,Ky,Kz)Φn(Kx,Ky,0)
D(r⃗)=4πk20Ldzd2κΦn(κ⃗,0)[1cos[κ⃗·r⃗(1xL)]]=8π2A(α)(α1)[0dpp1α(1J0(p))]C˜n2k2Lrα2=8π2A(α)(α1)22αΓ(4α2)(α2)Γ(α2)C˜n2k2Lrα2,
m2=4πk20Ldzd2κΦn(κ⃗,0){1cos[κ2zk(1zL)]}=8π2A(α)B(α2,α2)[0dpp1α(1cosp2)]C˜n2k3α/2Lα/2.
m2=8π2k20Ldz0κdκΦn(κ)exp[κ2a21+Ω2(1zL)2][1cos(LΩ2+zL+LΩ2κ2(Lz)k)],

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