Abstract

An analytical formula for the average intensity of an elliptical Gaussian beam (EGB) propagating in a turbulent atmosphere is derived. The spreading properties of an EGB in a turbulent atmosphere are studied. It is found that an EGB will eventually become a circular Gaussian beam in a turbulent atmosphere. This interesting phenomenon is quite different from the propagation of an EGB in free space. The evolution properties are closely related to the parameters of the beam and the turbulent atmosphere.

© 2006 Optical Society of America

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  1. J. A. Arnaud and H. Kogelnik, Appl. Opt. 8, 1687 (1969).
    [CrossRef] [PubMed]
  2. W. H. Carter, J. Opt. Soc. Am. 62, 1195 (1972).
    [CrossRef]
  3. C. R. Giuliano, J. H. Marburger, and A. Yariv, Appl. Phys. Lett. 21, 57 (1972).
    [CrossRef]
  4. F. Cornolti, M. Lucchesi, and B. Zambon, Opt. Commun. 75, 129 (1990).
    [CrossRef]
  5. J. Alda, S. Wang, and E. Bernabeu, Opt. Commun. 80, 350 (1991).
    [CrossRef]
  6. Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Optik (Stuttgart) 85, 67 (1990).
  7. S. Medhekar, S. Konar, and M. S. Sodha, Opt. Lett. 20, 2192 (1995).
    [CrossRef] [PubMed]
  8. T. Freegarde, J. Coutts, J. Walz, D. Leibfried, and T. W. Hänsch, J. Opt. Soc. Am. B 14, 2010 (1997).
    [CrossRef]
  9. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
    [CrossRef]
  10. S. M. Mian, B. Taheri, and J. P. Wicksted, J. Opt. Soc. Am. B 13, 856 (1996).
    [CrossRef]
  11. W. Zhang, J. Tian, Z. Liu, W. Zhou, C. Zhang, and G. Zhang, Appl. Opt. 42, 2219 (2003).
    [CrossRef] [PubMed]
  12. S. R. Seshadri, J. Opt. Soc. Am. A 20, 1818 (2003).
    [CrossRef]
  13. Y. Cai and Q. Lin, Appl. Opt. 41, 4336 (2002).
    [CrossRef] [PubMed]
  14. C. C. Davis, I. I. Smolyaninov, and S. D. Milner, IEEE Commun. Mag. 41, 51 (2003).
    [CrossRef]
  15. H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, and B. K. Ryu, IEEE Wireless Commun. 10, 45 (2003).
    [CrossRef]
  16. Z. I. Feizulin and Y. A. Kravtsov, Radiophys. Quantum Electron. 10, 33 (1967).
    [CrossRef]
  17. S. C. H. Wang and M. A. Plonus, J. Opt. Soc. Am. 69, 1297 (1979).
    [CrossRef]
  18. C. Y. Young, Y. V. Gilchrest, and B. R. Macon, Opt. Eng. 41, 1097 (2002).
    [CrossRef]
  19. T. Shirai, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 20, 1094 (2003).
    [CrossRef]
  20. H. T. Eyyuboglu and Y. Baykal, Opt. Express 12, 4659 (2004).
    [CrossRef] [PubMed]
  21. Y. Baykal, J. Opt. Soc. Am. A 21, 1290 (2004).
    [CrossRef]
  22. H. T. Eyyuboglu and Y. Baykal, Appl. Opt. 44, 976 (2005).
    [CrossRef] [PubMed]

2005 (1)

2004 (2)

2003 (5)

C. C. Davis, I. I. Smolyaninov, and S. D. Milner, IEEE Commun. Mag. 41, 51 (2003).
[CrossRef]

H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, and B. K. Ryu, IEEE Wireless Commun. 10, 45 (2003).
[CrossRef]

W. Zhang, J. Tian, Z. Liu, W. Zhou, C. Zhang, and G. Zhang, Appl. Opt. 42, 2219 (2003).
[CrossRef] [PubMed]

T. Shirai, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 20, 1094 (2003).
[CrossRef]

S. R. Seshadri, J. Opt. Soc. Am. A 20, 1818 (2003).
[CrossRef]

2002 (2)

C. Y. Young, Y. V. Gilchrest, and B. R. Macon, Opt. Eng. 41, 1097 (2002).
[CrossRef]

Y. Cai and Q. Lin, Appl. Opt. 41, 4336 (2002).
[CrossRef] [PubMed]

1997 (2)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

T. Freegarde, J. Coutts, J. Walz, D. Leibfried, and T. W. Hänsch, J. Opt. Soc. Am. B 14, 2010 (1997).
[CrossRef]

1996 (1)

1995 (1)

1991 (1)

J. Alda, S. Wang, and E. Bernabeu, Opt. Commun. 80, 350 (1991).
[CrossRef]

1990 (2)

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Optik (Stuttgart) 85, 67 (1990).

F. Cornolti, M. Lucchesi, and B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

1979 (1)

1972 (2)

W. H. Carter, J. Opt. Soc. Am. 62, 1195 (1972).
[CrossRef]

C. R. Giuliano, J. H. Marburger, and A. Yariv, Appl. Phys. Lett. 21, 57 (1972).
[CrossRef]

1969 (1)

1967 (1)

Z. I. Feizulin and Y. A. Kravtsov, Radiophys. Quantum Electron. 10, 33 (1967).
[CrossRef]

Alda, J.

J. Alda, S. Wang, and E. Bernabeu, Opt. Commun. 80, 350 (1991).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Optik (Stuttgart) 85, 67 (1990).

Allen, L.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Arnaud, J. A.

Baykal, Y.

Bernabeu, E.

J. Alda, S. Wang, and E. Bernabeu, Opt. Commun. 80, 350 (1991).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Optik (Stuttgart) 85, 67 (1990).

Cai, Y.

Carter, W. H.

Cornolti, F.

F. Cornolti, M. Lucchesi, and B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Coutts, J.

Davis, C. C.

C. C. Davis, I. I. Smolyaninov, and S. D. Milner, IEEE Commun. Mag. 41, 51 (2003).
[CrossRef]

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Dogariu, A.

Dolezal, F.

H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, and B. K. Ryu, IEEE Wireless Commun. 10, 45 (2003).
[CrossRef]

Elbatt, T.

H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, and B. K. Ryu, IEEE Wireless Commun. 10, 45 (2003).
[CrossRef]

Eyyuboglu, H. T.

Feizulin, Z. I.

Z. I. Feizulin and Y. A. Kravtsov, Radiophys. Quantum Electron. 10, 33 (1967).
[CrossRef]

Freegarde, T.

Gilchrest, Y. V.

C. Y. Young, Y. V. Gilchrest, and B. R. Macon, Opt. Eng. 41, 1097 (2002).
[CrossRef]

Giuliano, C. R.

C. R. Giuliano, J. H. Marburger, and A. Yariv, Appl. Phys. Lett. 21, 57 (1972).
[CrossRef]

Hänsch, T. W.

Izadpanah, H.

H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, and B. K. Ryu, IEEE Wireless Commun. 10, 45 (2003).
[CrossRef]

Kogelnik, H.

Konar, S.

Kravtsov, Y. A.

Z. I. Feizulin and Y. A. Kravtsov, Radiophys. Quantum Electron. 10, 33 (1967).
[CrossRef]

Kukshya, V.

H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, and B. K. Ryu, IEEE Wireless Commun. 10, 45 (2003).
[CrossRef]

Leibfried, D.

Lin, Q.

Y. Cai and Q. Lin, Appl. Opt. 41, 4336 (2002).
[CrossRef] [PubMed]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Optik (Stuttgart) 85, 67 (1990).

Liu, Z.

Lucchesi, M.

F. Cornolti, M. Lucchesi, and B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

Macon, B. R.

C. Y. Young, Y. V. Gilchrest, and B. R. Macon, Opt. Eng. 41, 1097 (2002).
[CrossRef]

Marburger, J. H.

C. R. Giuliano, J. H. Marburger, and A. Yariv, Appl. Phys. Lett. 21, 57 (1972).
[CrossRef]

Medhekar, S.

Mian, S. M.

Milner, S. D.

C. C. Davis, I. I. Smolyaninov, and S. D. Milner, IEEE Commun. Mag. 41, 51 (2003).
[CrossRef]

Padgett, M. J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

Plonus, M. A.

Ryu, B. K.

H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, and B. K. Ryu, IEEE Wireless Commun. 10, 45 (2003).
[CrossRef]

Seshadri, S. R.

Shirai, T.

Smolyaninov, I. I.

C. C. Davis, I. I. Smolyaninov, and S. D. Milner, IEEE Commun. Mag. 41, 51 (2003).
[CrossRef]

Sodha, M. S.

Taheri, B.

Tian, J.

Walz, J.

Wang, S.

J. Alda, S. Wang, and E. Bernabeu, Opt. Commun. 80, 350 (1991).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Optik (Stuttgart) 85, 67 (1990).

Wang, S. C.

Wicksted, J. P.

Wolf, E.

Yariv, A.

C. R. Giuliano, J. H. Marburger, and A. Yariv, Appl. Phys. Lett. 21, 57 (1972).
[CrossRef]

Young, C. Y.

C. Y. Young, Y. V. Gilchrest, and B. R. Macon, Opt. Eng. 41, 1097 (2002).
[CrossRef]

Zambon, B.

F. Cornolti, M. Lucchesi, and B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

Zhang, C.

Zhang, G.

Zhang, W.

Zhou, W.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

C. R. Giuliano, J. H. Marburger, and A. Yariv, Appl. Phys. Lett. 21, 57 (1972).
[CrossRef]

IEEE Commun. Mag. (1)

C. C. Davis, I. I. Smolyaninov, and S. D. Milner, IEEE Commun. Mag. 41, 51 (2003).
[CrossRef]

IEEE Wireless Commun. (1)

H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, and B. K. Ryu, IEEE Wireless Commun. 10, 45 (2003).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (2)

Opt. Commun. (3)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).
[CrossRef]

F. Cornolti, M. Lucchesi, and B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

J. Alda, S. Wang, and E. Bernabeu, Opt. Commun. 80, 350 (1991).
[CrossRef]

Opt. Eng. (1)

C. Y. Young, Y. V. Gilchrest, and B. R. Macon, Opt. Eng. 41, 1097 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (Stuttgart) (1)

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Optik (Stuttgart) 85, 67 (1990).

Radiophys. Quantum Electron. (1)

Z. I. Feizulin and Y. A. Kravtsov, Radiophys. Quantum Electron. 10, 33 (1967).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Evolution of the normalized average intensity (contour graph) of an EGB at several propagation distances z in a turbulent atmosphere: (a) z = 0 , (b) z = 0.8 km , (c) z = 2 km , (d) z = 4 km .

Equations (11)

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E ( ρ , z , t ) = i k 2 π z exp ( i k z ) E ( r 1 , 0 ) exp [ i k 2 ( r 1 , ρ ) + Ψ ( r 1 , ρ ) i 2 π f t ] d r 1 ,
I ( ρ , z ) = k 2 4 π 2 z 2 E ( r 1 , 0 ) E * ( r 2 , 0 ) exp [ i k 2 z ( r 1 , ρ ) 2 + i k 2 z ( r 2 ρ ) 2 ] exp [ Ψ ( r 1 , ρ ) + Ψ * ( r 2 , ρ ) ] d r 1 d r 2 .
exp [ Ψ ( r 1 , ρ ) + Ψ * ( r 2 , ρ ) ] = exp [ 0.5 D Ψ ( r 1 r 2 ) ] = exp [ 1 ρ 0 2 ( r 1 r 2 ) 2 ] ,
I ( ρ , z ) = k 2 4 π 2 [ det ( B ̃ ) ] 1 2 E ( r 1 , 0 ) E * ( r 2 , 0 ) exp [ i k 2 ( r ̃ T B ̃ 1 r ̃ 2 r ̃ B ̃ 1 ρ ̃ + ρ ̃ T B ̃ 1 ρ ̃ ) ] exp ( i k 2 r ̃ T P ̃ r ̃ ) d r ̃ ,
B ̃ = [ z I 0 0 z I ] , P ̃ = 2 i k ρ 0 2 [ I I I I ] ,
E ( r 1 , 0 ) = E 0 exp ( i k 2 r 1 T Q 1 1 r 1 ) ,
Q 1 1 = [ q 0 x 1 q 0 x y 1 q 0 x y 1 q 0 y 1 ]
E ( r 1 , 0 ) E * ( r 2 , 0 ) = E 0 2 exp ( i k 2 r 1 T Q 1 1 r 1 ) exp [ i k 2 r 2 T ( Q 1 1 ) * r 2 ] = E 0 2 exp [ i k 2 r ̃ T Q ̃ 1 1 r ̃ ] ,
Q ̃ 1 1 = [ Q 1 1 0 0 ( Q 1 1 ) * ] .
I ( ρ , z ) = E 0 2 { det [ I ̃ + B ̃ ( Q ̃ 1 1 + P ̃ ) ] } 1 2 exp { i k 2 ρ ̃ T [ ( Q ̃ 1 1 + P ̃ ) 1 + B ̃ ] 1 ρ ̃ } ,
I ( ρ , z ) = E 0 2 det ( I + BQ 1 1 ) 1 2 { det [ ( I + BQ 1 1 ) * ] } 1 2 exp [ i k 2 ρ T ( Q 1 + B ) 1 ρ + i k 2 ρ T ( Q 1 + B ) 1 * ρ ] ,

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