Abstract

Numerical experiments are carried out for a plane wave propagating in the atmospheric turbulence for a weak to strong fluctuation condition, i.e., the Rytov index being in a large range of 2×103 to 20. Mainly two categories of propagation events are explored for the same range of Rytov index. In one category the propagation distance and also the Fresnel length are kept fixed with the turbulence strength changing. In the other the turbulence strength is kept fixed with the distance changing. The statistical characteristics of the scintillation index, the maximum and minimum of the intensity, the fractal dimension of the intensity image, and the number density of the phase singularity are analyzed. The behaviors of the fractal dimension and the density of the phase singularity present obvious differences for the two categories of propagation. The fractal dimension depends both on the Rytov index and the Fresnel length. In both weak and strong fluctuation conditions the dimension generally increases with the Rytov index, but is at minimum at the onset region. The phase singularity density is coincident with the theoretical results under a weak fluctuation condition, and has a slowly increasing manner with the Rytov index in the strong fluctuation condition. The dependence on the Fresnel size is confident and there is no saturation for the phase singularity.

© 2008 Optical Society of America

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References

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2005 (2)

R. Rao, "Optical properties of atmospheric turbulence and their effects on light propagation," Proc. SPIE 5832, 1-11 (2005).
[CrossRef]

F. S. Vetelino, C. Young, L. Andrews, K. Grant, K. Corbett, and B. Clare, "Scintillation vs. experiment," Proc. SPIE 5793, 166-177 (2005).
[CrossRef]

2003 (1)

C. Young, A. J. Masino, and F. Thomas, "Phase fluctuations in moderate and strong turbulence," Proc. SPIE 4976, 141-148 (2003).
[CrossRef]

2002 (1)

R. Rao, "Collimated laser beam in a turbulent atmosphere: fractal structure and phase branch points," High Power Laser and Particle Beams 14, 501-504 (2002).

2000 (2)

1999 (1)

1998 (1)

1995 (2)

1993 (1)

1992 (1)

1990 (1)

1989 (1)

1988 (2)

Acta Photon. Sin. (1)

K. Yuan and R. Rao, "Density of Phase branch points for a light wave propagation in atmospheric turbulence," Acta Photon. Sin. (to be published).

Appl. Opt. (7)

High Power Laser and Particle Beams (1)

R. Rao, "Collimated laser beam in a turbulent atmosphere: fractal structure and phase branch points," High Power Laser and Particle Beams 14, 501-504 (2002).

J. Opt. Soc. Am. A (5)

Proc. SPIE (3)

R. Rao, "Optical properties of atmospheric turbulence and their effects on light propagation," Proc. SPIE 5832, 1-11 (2005).
[CrossRef]

F. S. Vetelino, C. Young, L. Andrews, K. Grant, K. Corbett, and B. Clare, "Scintillation vs. experiment," Proc. SPIE 5793, 166-177 (2005).
[CrossRef]

C. Young, A. J. Masino, and F. Thomas, "Phase fluctuations in moderate and strong turbulence," Proc. SPIE 4976, 141-148 (2003).
[CrossRef]

Other (10)

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (Ketterl, 1971).

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press and Oxford Univ. Press, 1997).

J. W. Strohbehn, Laser Beam Propagation in the Atmosphere (Springer-Verlag, 1978).

A. D. Wheelon, Electromagnetic Scintillation I. Geometrical Optics (Cambridge Univ. Press, 2001).

A. D. Wheelon, Electromagnetic Scintillation II. Weak Scattering (Cambridge Univ. Press, 2005).

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

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, 1994).
[CrossRef]

R. Rao, Light Propagation in the Turbulent Atmosphere (Anhui Science and Technology Press, 2005).

V. I. Tatarskii, A. Ishimaru, and V. U. Zavorotny, Wave Propagation in Random Media (Scintillation) (SPIE Press, 1992).

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Figures (7)

Fig. 1
Fig. 1

Maximum and minimum intensity as functions of the Rytov index for two categories of propagation events, one with a fixed distance 6000   m , and the other with a fixed turbulence strength C n 2 = 10 16 m 2 / 3 .

Fig. 2
Fig. 2

Scintillation index and the ratio of the maximum and minimum intensity as functions of the Rytov index for two categories of propagation events, one with a fixed distance 6000 m, and the other with a fixed turbulence strength C n 2 = 10 16 m 2 / 3 .

Fig. 3
Fig. 3

Ratio of the maximum and minimum intensity as a function of scintillation index for two categories of propagation events, one with a fixed distance 6000   m , and the other with a fixed turbulence strength C n 2 = 10 16 m 2 / 3 .

Fig. 4
Fig. 4

Fractal dimension at eight scales as functions of the Rytov index, respectively, for the constant distance case (upper) and the constant C n 2 case (lower).

Fig. 5
Fig. 5

Fractal dimension at eight scales as functions of the Rytov index, respectively, for two constant distance cases and two constant C n 2 cases.

Fig. 6
Fig. 6

Density of the pairs of branch points as functions of Rytov index for two categories of propagation events, one with a fixed distance 6000   m , and the other with a fixed turbulence strength C n 2 = 10 16 m 2 / 3 .

Fig. 7
Fig. 7

Number of pairs of branch points per square Fresnel length as functions of Rytov index for two categories of propagation events, one with a fixed distance 6000   m , and the other with a fixed turbulence strength C n 2 = 10 16 m 2 / 3 .

Tables (4)

Tables Icon

Table 1 Numerical Simulation Parameters for the Category of Propagation Events with a Fixed Distance 6000 m. N Fr = 21.85, Δ x = 1 mm

Tables Icon

Table 2 Numerical Simulation Parameters for the Category of Propagation Events with a Fixed Turbulence Strength C n 2 = 10−16 m−2∕3, Δ x = 1 mm

Tables Icon

Table 3 Numerical Simulation Results for the Category of Propagation Events with a Fixed Distance 6000 m

Tables Icon

Table 4 Numerical Simulation Results for the Category of Propagation Events with a Fixed Turbulence Strength C n 2 = 10−16 m−2∕3

Equations (13)

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β 0 2 ( L ) = 1.23 C n 2 k 7 / 6 L 11 / 6 ,
l Fr ( L ) = λ L .
Δ x > l Fr ( L ) / N Z N G .
ρ 0 = [ 1.4572 k 2 0 L C n 2 ( z ) d z ] 3 / 5 .
log ( I max / I min ) = 0.4374 8.169 × [ 1 + exp ( log β I 2 + 0.4956 0.1899 ) ] 1 .
V ( k ) = C k 3 D f ,
U ( i , j , k + 1 ) = max { U ( i , j , k ) + 1 , max l , m S [ U ( l , m , k ) ] } ,
L ( i , j , k + 1 ) = min { L ( i , j , k ) 1 , min l , m S [ L ( l , m , k ) ] } ,
w h e r e S = { ( k , m ) | distance [ ( k , m ) , ( i , j ) ] < 1 } .
U ( i , j , 0 ) = L ( i , j , 0 ) = 1024 [ log I ( i , j ) log I min ] / 10 .
Φ n ( κ , z ) = 0.033 C n 2 ( z ) κ 11 / 3 exp ( κ 2 / κ m 2 ) ,
σ χ ρ 2 = β 0 2 / l Fr 2 [ 6.8178 l Fr 1 / 3 κ m 1 / 3 11.1131 × sin ( 0.833 arctan ( 0.1592 l Fr 2 κ m 2 ) ) ] .
n b p = 0.059 ( l Fr κ m ) 1 / 6 σ χ ρ 2   erfc ( 1 .6891 l Fr 5 / 6 κ m 1 / 6 / σ χ ρ 2 ) .

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