Abstract

Results obtained on the intensity fluctuations of flat-topped Gaussian beams in weakly turbulent non-Kolmogorov horizontal atmospheric optics links are represented. Effects on the scintillation index of the power law α that describes the non-Kolmogorov spectrum are examined. Our results correctly reduce to the existing intensity fluctuations of flat-topped beams in Kolmogorov turbulence. Variation of the scintillation index against non-Kolmogorov power law α exhibits a peak at the worst power law αw, which happens to be smaller than the Kolmogorov power law of 11/3. If the power law is smaller (larger) than αw, increase in α will increase (decrease) the intensity fluctuations. Evaluation of the scintillation index at the worst power law results in smaller fluctuations for a Gaussian beam at short propagation distances; however, at long propagation distances flatter beams happen to possess smaller fluctuations. The scintillation change versus the source size follows a similar trend regardless whether the flat-topped beam propagates in a Kolmogorov or non-Kolmogorov medium.

© 2012 Optical Society of America

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References

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  2. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010

2009

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antennas Propag. 57, 1783–1788 (2009).
[CrossRef]

2008

Y. Cai, “Scintillation properties of non-circular flat-topped beams,” J. Opt. A 10, 075003 (2008).
[CrossRef]

2007

X. Ji, X. Chen, S. Chen, X. Li, and B. Lu, “Influence of atmospheric turbulence on the spatial correlation properties of partially coherent flat-topped beams,” J. Opt. Soc. Am. A 24, 3554–3563 (2007).
[CrossRef]

A. Tunick, “Analysis of free-space laser signal intensity over a 2.33 km optical path,” Proc. SPIE 6708, 670802 (2007).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferreroa, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E(2007).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

2006

D. C. Cowan, J. Recolons, L. C. Andrews, and C. Y. Young, “Propagation of flattened Gaussian beams in the atmosphere: a comparison of theory with a computer simulation model,” Proc. SPIE 6215, 62150B (2006).
[CrossRef]

Y. Baykal, “Formulation of correlations for general-type beams in atmospheric turbulence,” J. Opt. Soc. Am. A 23, 889–893 (2006).
[CrossRef]

Y. Baykal and H. T. Eyyuboğlu, “Scintillation index of flat-topped-Gaussian beams,” Appl. Opt. 45, 3793–3797 (2006).
[CrossRef]

2005

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosol and non Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

2002

2000

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

1996

1995

T. W. Nicholls, G. D. Boreman, and C. Dainty, “Use of a Shack–Hartmann wavefront sensor to measure deviations from a Kolmogorov phase spectrum,” Opt. Lett. 20, 2460–2462 (1995).
[CrossRef]

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

1994

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antennas Propag. 57, 1783–1788 (2009).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferreroa, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E(2007).
[CrossRef]

D. C. Cowan, J. Recolons, L. C. Andrews, and C. Y. Young, “Propagation of flattened Gaussian beams in the atmosphere: a comparison of theory with a computer simulation model,” Proc. SPIE 6215, 62150B (2006).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

Baykal, Y.

Bishop, K. P.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Boreman, D.

Boreman, G. D.

Cai, Y.

Y. Cai, “Scintillation properties of non-circular flat-topped beams,” J. Opt. A 10, 075003 (2008).
[CrossRef]

Chen, S.

Chen, X.

Cowan, D. C.

D. C. Cowan, J. Recolons, L. C. Andrews, and C. Y. Young, “Propagation of flattened Gaussian beams in the atmosphere: a comparison of theory with a computer simulation model,” Proc. SPIE 6215, 62150B (2006).
[CrossRef]

Dainty, C.

Du, W.

Eyyuboglu, H. T.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antennas Propag. 57, 1783–1788 (2009).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

Ferreroa, V.

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferreroa, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E(2007).
[CrossRef]

Gerçekcioglu, H.

H. Gerçekcioğlu and Y. Baykal, “Annular beam scintillations in non-Kolmogorov weak turbulence,” Appl. Phys. B, submitted.

Golbraikh, E.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283, 1229–1235 (2010).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosol and non Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

Guo, H.

Han, Q.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

Ji, X.

Jiang, W.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

Keating, D. D. B.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Kopeika, N. S.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283, 1229–1235 (2010).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosol and non Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

Korotkova, O.

Kyrazis, D. T.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Li, X.

Li, Y.

Ling, N.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

Lu, B.

Luo, B.

Ma, J.

Nicholls, T. W.

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antennas Propag. 57, 1783–1788 (2009).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferreroa, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E(2007).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

Preble, A. J.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Rao, C.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

Recolons, J.

D. C. Cowan, J. Recolons, L. C. Andrews, and C. Y. Young, “Propagation of flattened Gaussian beams in the atmosphere: a comparison of theory with a computer simulation model,” Proc. SPIE 6215, 62150B (2006).
[CrossRef]

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Shchepakina, E.

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Tan, L.

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antennas Propag. 57, 1783–1788 (2009).
[CrossRef]

Tosellia, I.

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferreroa, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E(2007).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

Tunick, A.

A. Tunick, “Analysis of free-space laser signal intensity over a 2.33 km optical path,” Proc. SPIE 6708, 670802 (2007).
[CrossRef]

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Wissler, J.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Wu, G.

Young, C. Y.

D. C. Cowan, J. Recolons, L. C. Andrews, and C. Y. Young, “Propagation of flattened Gaussian beams in the atmosphere: a comparison of theory with a computer simulation model,” Proc. SPIE 6215, 62150B (2006).
[CrossRef]

Yu, S.

Zilberman, A.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283, 1229–1235 (2010).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosol and non Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

Appl. Opt.

IEEE Trans. Antennas Propag.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antennas Propag. 57, 1783–1788 (2009).
[CrossRef]

J. Mod. Opt.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

J. Opt. A

Y. Cai, “Scintillation properties of non-circular flat-topped beams,” J. Opt. A 10, 075003 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283, 1229–1235 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferreroa, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E(2007).
[CrossRef]

I. Tosellia, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

D. C. Cowan, J. Recolons, L. C. Andrews, and C. Y. Young, “Propagation of flattened Gaussian beams in the atmosphere: a comparison of theory with a computer simulation model,” Proc. SPIE 6215, 62150B (2006).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosol and non Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

A. Tunick, “Analysis of free-space laser signal intensity over a 2.33 km optical path,” Proc. SPIE 6708, 670802 (2007).
[CrossRef]

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

H. Gerçekcioğlu and Y. Baykal, “Annular beam scintillations in non-Kolmogorov weak turbulence,” Appl. Phys. B, submitted.

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Figures (9)

Fig. 1.
Fig. 1.

(a) Normalized field distributions of flat-topped Gaussian beams at the source plane for various N; (b) normalized intensity distributions of the same flat-topped Gaussian beams as in (a).

Fig. 2.
Fig. 2.

m2 versus L for various N at Wo=1cm, Wo=2cm, and α=3.50.

Fig. 3.
Fig. 3.

m2 versus N for various Wo and α.

Fig. 4.
Fig. 4.

m2 versus L for various α at Wo=2cm and N=5.

Fig. 5.
Fig. 5.

m2 versus L for various α at Wo=2cm and N=10.

Fig. 6.
Fig. 6.

m2 versus α for various N at Wo=1cm, Wo=2cm, and L=2km.

Fig. 7.
Fig. 7.

m2 versus L for various N at Wo=2cm showing αw that makes the scintillation index maximum.

Fig. 8.
Fig. 8.

m2 versus L for various α to emphasize the turning point m2 against α.

Fig. 9.
Fig. 9.

(a) m2 versus Wo for various α and N at L=1km; (b) m2 versus Weff for various α and N at L=1km.

Equations (5)

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

m2=4πRe{0Ldη0κdκ02πdθ[ZFT1(η,κ)+ZFT2(η,κ)]Φn(κ,α)},
ZFT1(η,κ)=(2πλ|T|)2n1=1Nn2=1N(Nn1)(Nn2)(1)n1+n2{[1+iλLn1/(2πWo2)][1+iλLn2/(2πWo2)]}1×exp(iλ(Lη)4π{[1+iληn1/(2πWo2)][1+iλLn1/(2πWo2)]+[1+iληn2/(2πWo2)][1+iλLn2/(2πWo2)]}κ2),
ZFT2(η,κ)=(2πλ|T|)2n1=1Nn2=1N(Nn1)(Nn2)(1)n1+n2{[1+iλLn1/(2πWo2)][1iλLn2/(2πWo2)]}1×exp(iλ(Lη)4π{[1+iληn1/(2πWo2)][1+iλLn1/(kWo2)][1iληn2/(2πWo2)][1iλLn2/(kWo2)]}κ2),
T=n=1N(1)n1(Nn)[1+iλLn/(2πWo2)]1,
m2=(2π)4A(α)C˜n2Γ(1α/2)λ2Re{1|T|2n1=1Nn2=1N(1)n1+n2(Nn1)(Nn2){[1+iλLn1/(2πWo2)][1+iλLn2/(2πWo2)]}1×0Ldη(iλ(Lη)4π{[1+iληn1/(2πWo2)][1+iλLn1/(2πWo2)][1iληn2/(2πWo2)][1iλLn2/(2πWo2)]})1+α/21T2[n1=1Nn2=1N(1)n1+n2(Nn1)(Nn2){[1+iλLn1/(2πWo2)][1+iλLn2/(2πWo2)]}1×0Ldη(iλ(Lη)4π{[1+iληn1/(2πWo2)][1+iλLn1/(2πWo2)]+[1+iληn2/(2πWo2)][1+iλLn2/(2πWo2)]})1+α/2]}.

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