Abstract

The propagation of a cosh-Gaussian beam through an arbitrary ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity at any receiver plane are obtained. As an elementary example, the average intensity and its radius at the image plane of a cosh-Gaussian beam through a thin lens are studied. To show the effects of a lens on the average intensity and the intensity radius of the laser beam in turbulent atmosphere, the properties of a collimated cosh-Gaussian beam and a focused cosh-Gaussian beam for direct propagation in turbulent atmosphere are studied and numerically calculated. The average intensity profiles of a cosh-Gaussian beam through a lens can have a shape similar to that of the initial beam for a longer propagation distance than that of a collimated cosh-Gaussian beam for direct propagation. With the increment in the propagation distance, the average intensity radius at the image plane of a cosh-Gaussian beam through a thin lens will be smaller than that at the focal plane of a focused cosh-Gaussian beam for direct propagation. Meanwhile, the intensity distributions at the image plane of a cosh-Gaussian beam through a lens with different w 0 and Ω0 are also studied.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. H. T. Eyyubo?lu, C. Arpali, and Y. Baykal, "Flat topped beams and their characteristics in turbulent media," Opt. Express. 14, 4196-4207 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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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]
  15. X. Chu and G. Zhou, "Power coupling of a two-Cassegrain-telescopes system in turbulent atmosphere in a slant path," Opt. Express 15, 7697-7707 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2007 (5)

Y. Cai and D. Ge. "Analytical formula for a decentered elliptical Gaussian beam propagating in a turbulent atmosphere," Opt. Commun. 271, 509-516 (2007).
[CrossRef]

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B. 87, 547-552 (2007).
[CrossRef]

H. T. Eyyubo?lu and Y. Baykal, "Generalized beams in ABCDGH systems," Opt. Commun. 272, 22-31 (2007).
[CrossRef]

Y. Zhang, Y. Song, Z. Chen, J. Ji, and Z. Shi "Virtual sources for a cosh-Gaussian beam" Opt. Lett. 32, 292-294 (2007).
[CrossRef] [PubMed]

X. Chu and G. Zhou, "Power coupling of a two-Cassegrain-telescopes system in turbulent atmosphere in a slant path," Opt. Express 15, 7697-7707 (2007).
[CrossRef] [PubMed]

2006 (7)

Y. Cai and S. He, "Propagation of various dark hollow beams in turbulent atmosphere," Opt. Express 14,1353-1367 (2006).
[CrossRef] [PubMed]

Y. Baykal and H. T. Eyyubo?lu, "Scintillation index of flat-topped Gaussian beams," Appl. Opt. 45, 3793-3797 (2006).
[CrossRef] [PubMed]

H. T. Eyyubo?lu, Y. Baykal, and E. Sermutlu, "Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere," Opt. Commun. 265, 399-405 (2006).
[CrossRef]

X. Ji, T. Huang, and B. Lu "Spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere," Acta Physica Sinica 55, 978-982 (2006).

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects, Opt. Eng. 45, 076001-12 (2006).
[CrossRef]

H. T. Eyyubo?lu, C. Arpali, and Y. Baykal, "Flat topped beams and their characteristics in turbulent media," Opt. Express. 14, 4196-4207 (2006).
[CrossRef] [PubMed]

Y. Cai, "Propagation of various flat-topped beams in a turbulent atmosphere," J. Opt. A: Pure Appl. Opt. 8, 537-545 (2006).
[CrossRef]

2005 (6)

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Beam wander effects on the scintillation index of a focused beam," Proc. SPIE 5793, 28-37 (2005).
[CrossRef]

H. T. Eyyubo?lu, "Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere," Opt. Commun. 245, 37-47 (2005).
[CrossRef]

K. Duan and B. Lu, "Propagation of Hermite-Laguerre-Gaussian beams through a paraxial optical ABCD system with rectangular hard-edged aperture," Opt. Commun. 250, 1-9 (2005).
[CrossRef]

H. T. Eyyubo?lu and Y. Baykal, "Average intensity and spreading of cosh-Gaussian beams in the turbulent atmosphere," Appl. Opt. 44, 976-983 (2005).
[CrossRef] [PubMed]

Y. Baykal, "Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium," J. Opt. Soc. Am. A 22, 672-679 (2005).
[CrossRef]

H. T. Eyyubo?lu, "Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere," J. Opt. Soc. Am. A 22, 1527-1535 (2005).
[CrossRef]

2004 (1)

2003 (2)

T. Shirai, A. Dogariu, and E. Wolf, "Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 20, 1094-1102 (2003).
[CrossRef]

D. Zhao, H. Mao, W. Zhang, and S. Wang, "Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system," Opt. Commun. 224, 5-12 (2003).
[CrossRef]

1998 (1)

1987 (1)

1979 (1)

Andrews, L. C.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects, Opt. Eng. 45, 076001-12 (2006).
[CrossRef]

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Beam wander effects on the scintillation index of a focused beam," Proc. SPIE 5793, 28-37 (2005).
[CrossRef]

Arpali, C.

H. T. Eyyubo?lu, C. Arpali, and Y. Baykal, "Flat topped beams and their characteristics in turbulent media," Opt. Express. 14, 4196-4207 (2006).
[CrossRef] [PubMed]

Baykal, Y.

Cai, Y.

Y. Cai and D. Ge. "Analytical formula for a decentered elliptical Gaussian beam propagating in a turbulent atmosphere," Opt. Commun. 271, 509-516 (2007).
[CrossRef]

Y. Cai and S. He, "Propagation of various dark hollow beams in turbulent atmosphere," Opt. Express 14,1353-1367 (2006).
[CrossRef] [PubMed]

Y. Cai, "Propagation of various flat-topped beams in a turbulent atmosphere," J. Opt. A: Pure Appl. Opt. 8, 537-545 (2006).
[CrossRef]

Casperson, L. W.

Chen, Z.

Chu, X.

X. Chu and G. Zhou, "Power coupling of a two-Cassegrain-telescopes system in turbulent atmosphere in a slant path," Opt. Express 15, 7697-7707 (2007).
[CrossRef] [PubMed]

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B. 87, 547-552 (2007).
[CrossRef]

Dogariu, A.

Duan, K.

K. Duan and B. Lu, "Propagation of Hermite-Laguerre-Gaussian beams through a paraxial optical ABCD system with rectangular hard-edged aperture," Opt. Commun. 250, 1-9 (2005).
[CrossRef]

Eyyuboglu, H. T.

H. T. Eyyubo?lu and Y. Baykal, "Generalized beams in ABCDGH systems," Opt. Commun. 272, 22-31 (2007).
[CrossRef]

Y. Baykal and H. T. Eyyubo?lu, "Scintillation index of flat-topped Gaussian beams," Appl. Opt. 45, 3793-3797 (2006).
[CrossRef] [PubMed]

H. T. Eyyubo?lu, Y. Baykal, and E. Sermutlu, "Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere," Opt. Commun. 265, 399-405 (2006).
[CrossRef]

H. T. Eyyubo?lu, C. Arpali, and Y. Baykal, "Flat topped beams and their characteristics in turbulent media," Opt. Express. 14, 4196-4207 (2006).
[CrossRef] [PubMed]

H. T. Eyyubo?lu, "Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere," Opt. Commun. 245, 37-47 (2005).
[CrossRef]

H. T. Eyyubo?lu and Y. Baykal, "Average intensity and spreading of cosh-Gaussian beams in the turbulent atmosphere," Appl. Opt. 44, 976-983 (2005).
[CrossRef] [PubMed]

H. T. Eyyubo?lu, "Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere," J. Opt. Soc. Am. A 22, 1527-1535 (2005).
[CrossRef]

H. T. Eyyubo?lu and Y. Baykal, "Reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere," Opt. Express 12, 4659-4674 (2004).
[CrossRef] [PubMed]

Ge, D.

Y. Cai and D. Ge. "Analytical formula for a decentered elliptical Gaussian beam propagating in a turbulent atmosphere," Opt. Commun. 271, 509-516 (2007).
[CrossRef]

Hanson, S. G.

He, S.

Huang, T.

X. Ji, T. Huang, and B. Lu "Spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere," Acta Physica Sinica 55, 978-982 (2006).

Ji, J.

Ji, X.

X. Ji, T. Huang, and B. Lu "Spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere," Acta Physica Sinica 55, 978-982 (2006).

Lu, B.

X. Ji, T. Huang, and B. Lu "Spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere," Acta Physica Sinica 55, 978-982 (2006).

K. Duan and B. Lu, "Propagation of Hermite-Laguerre-Gaussian beams through a paraxial optical ABCD system with rectangular hard-edged aperture," Opt. Commun. 250, 1-9 (2005).
[CrossRef]

Mao, H.

D. Zhao, H. Mao, W. Zhang, and S. Wang, "Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system," Opt. Commun. 224, 5-12 (2003).
[CrossRef]

Ni, Y.

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B. 87, 547-552 (2007).
[CrossRef]

Parenti, R. R.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects, Opt. Eng. 45, 076001-12 (2006).
[CrossRef]

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Beam wander effects on the scintillation index of a focused beam," Proc. SPIE 5793, 28-37 (2005).
[CrossRef]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects, Opt. Eng. 45, 076001-12 (2006).
[CrossRef]

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Beam wander effects on the scintillation index of a focused beam," Proc. SPIE 5793, 28-37 (2005).
[CrossRef]

Plonus, M. A.

Sasiela, R. J.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects, Opt. Eng. 45, 076001-12 (2006).
[CrossRef]

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Beam wander effects on the scintillation index of a focused beam," Proc. SPIE 5793, 28-37 (2005).
[CrossRef]

Sermutlu, E.

H. T. Eyyubo?lu, Y. Baykal, and E. Sermutlu, "Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere," Opt. Commun. 265, 399-405 (2006).
[CrossRef]

Shi, Z.

Shirai, T.

Song, Y.

Tovar, A. A.

Wang, S.

D. Zhao, H. Mao, W. Zhang, and S. Wang, "Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system," Opt. Commun. 224, 5-12 (2003).
[CrossRef]

Wang, S. C. H.

Wolf, E.

Yura, H. T.

Zhang, W.

D. Zhao, H. Mao, W. Zhang, and S. Wang, "Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system," Opt. Commun. 224, 5-12 (2003).
[CrossRef]

Zhang, Y.

Zhao, D.

D. Zhao, H. Mao, W. Zhang, and S. Wang, "Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system," Opt. Commun. 224, 5-12 (2003).
[CrossRef]

Zhou, G.

X. Chu and G. Zhou, "Power coupling of a two-Cassegrain-telescopes system in turbulent atmosphere in a slant path," Opt. Express 15, 7697-7707 (2007).
[CrossRef] [PubMed]

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B. 87, 547-552 (2007).
[CrossRef]

Acta Physica Sinica (1)

X. Ji, T. Huang, and B. Lu "Spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere," Acta Physica Sinica 55, 978-982 (2006).

Appl. Opt. (2)

Appl. Phys. B. (1)

X. Chu, Y. Ni, and G. Zhou, "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere," Appl. Phys. B. 87, 547-552 (2007).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

Y. Cai, "Propagation of various flat-topped beams in a turbulent atmosphere," J. Opt. A: Pure Appl. Opt. 8, 537-545 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (6)

H. T. Eyyubo?lu, "Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere," Opt. Commun. 245, 37-47 (2005).
[CrossRef]

Y. Cai and D. Ge. "Analytical formula for a decentered elliptical Gaussian beam propagating in a turbulent atmosphere," Opt. Commun. 271, 509-516 (2007).
[CrossRef]

D. Zhao, H. Mao, W. Zhang, and S. Wang, "Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system," Opt. Commun. 224, 5-12 (2003).
[CrossRef]

K. Duan and B. Lu, "Propagation of Hermite-Laguerre-Gaussian beams through a paraxial optical ABCD system with rectangular hard-edged aperture," Opt. Commun. 250, 1-9 (2005).
[CrossRef]

H. T. Eyyubo?lu, Y. Baykal, and E. Sermutlu, "Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere," Opt. Commun. 265, 399-405 (2006).
[CrossRef]

H. T. Eyyubo?lu and Y. Baykal, "Generalized beams in ABCDGH systems," Opt. Commun. 272, 22-31 (2007).
[CrossRef]

Opt. Eng. (1)

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects, Opt. Eng. 45, 076001-12 (2006).
[CrossRef]

Opt. Express (3)

Opt. Express. (1)

H. T. Eyyubo?lu, C. Arpali, and Y. Baykal, "Flat topped beams and their characteristics in turbulent media," Opt. Express. 14, 4196-4207 (2006).
[CrossRef] [PubMed]

Opt. Lett. (1)

Proc. SPIE (1)

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, "Beam wander effects on the scintillation index of a focused beam," Proc. SPIE 5793, 28-37 (2005).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Propagation geometry of image system in turbulent atmosphere.

Fig. 2.
Fig. 2.

The normalized average intensity profiles of a cosh-Gaussian beam in turbulent atmosphere. (a) At image plane of a lens with w 0=0.2m and Ω0=30m -1; (b) At receiver plane for direct propagation with F→∞, w 0=0.2m and Ω0=30m -1; (c) At focal plane (L=F) for direct propagation with w 0=0.2m and Ω0=30m -1; (d) At image plane of a lens with L=20km.

Equations (22)

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E 0 ( x 0 , y 0 , 0 ) = exp [ x 0 2 + y 0 2 w 0 2 i k ( x 0 2 + y 0 2 ) 2 F ] cosh ( Ω 0 x 0 ) cosh ( Ω 0 y 0 ) ,
E ( x , y , L ) = 1 i λ B exp ( i k L ) E 0 ( x 0 , y 0 , 0 )
× exp { i k 2 B [ A ( x 0 2 + y 0 2 ) + D ( x 2 + y 2 ) 2 ( x x 0 + y y 0 ) ] + ψ ( x 0 , y 0 , x , y ) } d x 0 d y 0 ,
I ( x , y , L ) = 1 λ 2 B 2 E 0 ( x 01 , y 01 , 0 ) E 0 * ( x 02 , y 02 , 0 )
× exp { i k 2 B [ A ( x 01 2 x 02 2 + y 01 2 y 02 2 ) 2 ( x x 01 x x 02 + y y 01 y y 02 ) ] }
× exp [ ψ ( x 01 , y 01 , x , y ) + ψ ( x 02 , y 02 , x , y ) ] d x 01 d y 01 d x 02 d y 02 ,
exp [ ψ ( x 01 , y 01 , x , y ) + ψ ( x 02 , y 02 , x , y ) ] = exp [ D w ( r 01 r 02 ) 2 ] ,
D w ( r 01 r 02 ) 2 = [ ( x 01 x 02 ) 2 + ( y 01 y 02 ) 2 ] ρ 0 2 ,
ρ 0 = B σ 0 = B [ 1.46 k 2 C n 2 0 L d z b 5 3 ( z ) ] 3 5 ,
I ( x , y , L ) = w 0 2 4 w 2 exp [ 2 ( x 2 + y 2 ) w 2 + 4 B 2 Ω 0 2 k 2 w 2 ] { cos ( 4 B Ω 0 k w 2 x ) + exp ( 4 Ω 0 2 w 0 2 k 2 σ 0 2 w 2 ) cosh [ 2 ( B A F ) Ω 0 w 0 2 x F w 2 ] }
× { cos ( 4 B Ω 0 k w 2 y ) + exp ( 4 Ω 0 2 w 0 2 k 2 σ 0 2 w 2 ) cosh [ 2 ( B A F ) Ω 0 w 0 2 y F w 2 ] } ,
w 2 = 4 B 2 ( k 2 w 0 2 ) + w 0 2 ( A B F ) 2 + 8 ( k 2 σ 0 2 ) .
I ( x , y , L ) = w 0 2 4 w 2 exp [ 2 ( x 2 + y 2 ) w 2 ] [ 1 + exp ( 4 Ω 0 2 w 0 2 k 2 σ 0 2 w 2 ) cosh ( 2 m Ω 0 w 0 2 x w 2 ) ] [ 1 + exp ( 4 Ω 0 2 w 0 2 k 2 σ 0 2 w 2 ) cosh ( 2 m Ω 0 w 0 2 y w 2 ) ] ,
w 2 = m 2 w 0 2 + 8 ( k 2 σ 0 2 ) ,
b ( z ) = { z 2 z z 1 0 < z z 1 L z z 1 < z L .
σ 0 = z 2 1 ( 0.5475 k 2 C n 2 L ) 3 5 .
I ( x , L ) = w 0 2 w exp ( 2 x 2 w 2 + 2 L 2 Ω 0 2 k 2 w 2 ) [ cos ( 4 L Ω 0 k w 2 x ) + exp ( 4 Ω 0 2 w 0 2 k 2 σ 0 2 w 2 ) cosh ( 2 Ω 0 w 0 2 x w 2 ) ] ,
w 2 = w 0 2 + 4 L 2 ( k 2 w 0 2 ) + 8 L 2 ( k 2 ρ 0 2 ) .
I ( x , L ) = w 0 2 w exp ( 2 x 2 w 2 + 2 L 2 Ω 0 2 k 2 w 2 ) [ cos ( 4 L Ω 0 k w 2 x ) + exp ( 4 Ω 0 2 w 0 2 k 2 σ 0 2 w 2 ) ] ,
w 2 = 4 L 2 ( k 2 w 0 2 ) + 8 L 2 ( k 2 ρ 0 2 ) .
I ( x , L ) = w 0 2 w exp ( 2 x 2 w 2 ) [ 1 + exp ( 4 Ω 0 2 w 0 2 k 2 σ 0 2 w 2 ) cosh ( 2 m Ω 0 w 0 2 x w 2 ) ] .
I N ( x , L ) = I ( x , L ) Max [ I ( x 0 , 0 ) ] ,

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