Abstract

We show that the far-field beam spreading and direction of partially coherent Gaussian–Schell model (GSM) beams are independent on the spatial coherence of the source through non-Kolmogorov atmospheric turbulence, which has potential applications in long-distance free-space optical communication. The effects of spatial coherence, exponent value α, and inner scale and outer scale of atmospheric turbulence on beam spreading are studied in details. The GSM beam has greater spreading for smaller inner scale or bigger outer scale through non-Kolmogorov turbulent atmosphere.

© 2010 Optical Society of America

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  1. D. Killinger, Opt. Photonics News 13(10), 36 (2002).
    [CrossRef]
  2. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005).
    [CrossRef]
  3. C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
    [CrossRef]
  4. A. Zilberman, E. Golbraikh, and N. S. Kopeika, Proc. SPIE 5987, 598702 (2005).
    [CrossRef]
  5. D. Dayton, B. Pierson, and B. Spielbusch, Opt. Lett. 17, 1737 (1992).
    [CrossRef] [PubMed]
  6. A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
    [CrossRef]
  7. A. Zilberman, E. Golbraikh, and N. S. Kopeika, Appl. Opt. 47, 6385 (2008).
    [CrossRef] [PubMed]
  8. I. Toselli, L. C. Andrews, R. L. Phillips, and Valter Ferreroa, Proc. SPIE 6457, 65510E-1 (2007).
  9. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
    [CrossRef]
  10. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
    [CrossRef]
  11. X. Ji and B. Lü, Opt. Commun. 251, 231 (2005).
    [CrossRef]
  12. J. C. Ricklin and F. M. Davidson, J. Opt. Soc. Am. A 20, 856 (2003).
    [CrossRef]
  13. Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
    [CrossRef]
  14. T. Shirai, A. Dogariu, and E. Wolf, Opt. Lett. 28, 610 (2003).
    [CrossRef] [PubMed]
  15. J. C. Leader, J. Opt. Soc. Am. 69, 73 (1979).
    [CrossRef]
  16. G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, Opt. Commun. 280, 264 (2007).
    [CrossRef]

2009

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

2008

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Appl. Opt. 47, 6385 (2008).
[CrossRef] [PubMed]

2007

G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, Opt. Commun. 280, 264 (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and Valter Ferreroa, Proc. SPIE 6457, 65510E-1 (2007).

2006

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

2005

X. Ji and B. Lü, Opt. Commun. 251, 231 (2005).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Proc. SPIE 5987, 598702 (2005).
[CrossRef]

2003

2002

D. Killinger, Opt. Photonics News 13(10), 36 (2002).
[CrossRef]

2000

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

1992

1979

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and Valter Ferreroa, Proc. SPIE 6457, 65510E-1 (2007).

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

Berman, G. P.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, Opt. Commun. 280, 264 (2007).
[CrossRef]

Bishop, A. R.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, Opt. Commun. 280, 264 (2007).
[CrossRef]

Cai, Y.

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Chernobrod, B. M.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, Opt. Commun. 280, 264 (2007).
[CrossRef]

Davidson, F. M.

Dayton, D.

Dogariu, A.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Ferreroa, Valter

I. Toselli, L. C. Andrews, R. L. Phillips, and Valter Ferreroa, Proc. SPIE 6457, 65510E-1 (2007).

Golbraikh, E.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Appl. Opt. 47, 6385 (2008).
[CrossRef] [PubMed]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Proc. SPIE 5987, 598702 (2005).
[CrossRef]

Gorshkov, V. N.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, Opt. Commun. 280, 264 (2007).
[CrossRef]

He, S.

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Ji, X.

X. Ji and B. Lü, Opt. Commun. 251, 231 (2005).
[CrossRef]

Jiang, W.

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

Killinger, D.

D. Killinger, Opt. Photonics News 13(10), 36 (2002).
[CrossRef]

Kopeika, N. S.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Appl. Opt. 47, 6385 (2008).
[CrossRef] [PubMed]

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Proc. SPIE 5987, 598702 (2005).
[CrossRef]

Kuperschmidt, I.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
[CrossRef]

Leader, J. C.

Ling, N.

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

Lü, B.

X. Ji and B. Lü, Opt. Commun. 251, 231 (2005).
[CrossRef]

Nguyen, D. C.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, Opt. Commun. 280, 264 (2007).
[CrossRef]

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and Valter Ferreroa, Proc. SPIE 6457, 65510E-1 (2007).

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

Pierson, B.

Rao, C.

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

Ricklin, J. C.

Shirai, T.

Shtemler, Y.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
[CrossRef]

Spielbusch, B.

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and Valter Ferreroa, Proc. SPIE 6457, 65510E-1 (2007).

Virtser, A.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
[CrossRef]

Wolf, E.

Zilberman, A.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Appl. Opt. 47, 6385 (2008).
[CrossRef] [PubMed]

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Proc. SPIE 5987, 598702 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Atmos. Res.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kuperschmidt, and Y. Shtemler, Atmos. Res. 88, 66 (2008).
[CrossRef]

IEEE Trans. Antennas Propag.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

J. Mod. Opt.

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, Opt. Commun. 280, 264 (2007).
[CrossRef]

X. Ji and B. Lü, Opt. Commun. 251, 231 (2005).
[CrossRef]

Opt. Eng.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Opt. Lett.

Opt. Photonics News

D. Killinger, Opt. Photonics News 13(10), 36 (2002).
[CrossRef]

Proc. SPIE

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Proc. SPIE 5987, 598702 (2005).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and Valter Ferreroa, Proc. SPIE 6457, 65510E-1 (2007).

Other

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

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Figures (4)

Fig. 1
Fig. 1

Normalized rms beam width w ( z ) of GSM through non-Kolmogorov turbulence as a function of propagation distance z for different global coherence parameter η = σ s σ μ .

Fig. 2
Fig. 2

Normalized rms beam width w ( z ) of GSM through non-Kolmogorov turbulence as a function of propagation distance z for different α.

Fig. 3
Fig. 3

Normalized rms beam width w ( z ) of GSM through non-Kolmogorov turbulence as a function of α for z = 5000 m .

Fig. 4
Fig. 4

Normalized rms beam width w ( z ) of GSM through non-Kolmogorov turbulence as a function of propagation distance z for different inner scale l 0 and different outer scale L 0 .

Equations (6)

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W ( 0 ) ( ρ 1 , ρ 2 , ω ) = exp [ ( | ρ 1 | 2 + | ρ 2 | 2 2 σ s 2 + | ρ 1 ρ 2 | 2 2 σ μ 2 ) ] ,
I ( ρ , z ) = W ( ρ , ρ , z ) = 1 ( λ z ) 2 d 2 ρ 1 d 2 ρ 2 × W ( 0 ) ( ρ 1 , ρ 2 , 0 ) exp [ i k ( ρ ρ 1 ) 2 ( ρ ρ 2 ) 2 2 z ] × exp [ ψ * ( ρ , ρ 1 , z ) + ψ ( ρ , ρ 2 ) , z ] ,
w ( z ) = { 2 σ s 2 + 2 z 2 k 2 σ 2 + 4 π 2 z 3 3 0 κ 3 Φ n ( κ ) d κ } 1 2 ,
Φ n ( κ , α ) = A ( α ) C ̃ n 2 exp [ ( κ 2 / κ m 2 ) ] ( κ 2 + κ 0 2 ) α 2 ,
0 κ < , 3 < α < 4 ,
w ( z ) = { 2 σ s 2 + 2 z 2 k 2 σ 2 + [ 2 π 2 A ( α ) C ̃ n 2 3 κ m 2 α β exp ( κ 0 2 κ m 2 ) Γ ( 2 α 2 , κ 0 2 κ m 2 ) 2 κ 0 4 α α 2 ] z 3 } 1 2 ,

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