Abstract

The characteristics of dark hollow beams passing through a two-Cassegrain-telescopes system in turbulent atmosphere in a slant path have been investigated. The distribution of the average intensity at the receiver telescope and the efficiency of power coupling with respect to propagation distance with different parameters are derived and numerically calculated. These studies illuminate that the power of the dark hollow beams is concentrated on a narrow annular aperture at the source plane and its power coupling with a transmitter Cassegrain telescope can remain quite high. For short distance between the two Cassegrain telescopes, the normalized average intensity distribution at receiver plane holds shape similar to that at the source plane, and the two Cassegrain telescopes keep high efficiency of the power coupling. But with the increment in the propagation distance, the power of the dark hollow beams gradually converges to the central and the spot spreads. The central obscuration of the receiver telescope blocks more of the power; meanwhile more of the power moves out beyond the edge of the receiving aperture. Therefore, the efficiency of the power coupling decreases with the increment in the propagation distance. In addition, the relations between the efficiency of power coupling and wavelength of laser beams are also numerically calculated and discussed.

© 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]

2007 (1)

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]

2006 (7)

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

H. T. Eyyuboðlu, 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]

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

Z. Mei, D. Zhao, and J. Gu, "Comparison of two approximate methods for hard-edged diffracted flat-topped light beams," Opt. Commun. 267, 58-64 (2006).
[CrossRef]

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. Eyyuboðlu, "Scintillation index of flat-topped Gaussian beams," Appl. Opt. 45, 3793-3797 (2006).
[CrossRef] [PubMed]

C. Arpali, C. Yazýcýoðlu, H. T. Eyyuboðlu, S. A. Arpali, and Y. Baykal, "Simulator for general-type beam propagation in turbulent atmosphere," Opt. Express 14, 8918-8928 (2006).
[CrossRef] [PubMed]

2005 (6)

2004 (1)

2003 (1)

2002 (1)

1988 (1)

J. J. Wen and M. A. Breazeale, "A diffraction beam field expressed as the superposition of Gaussian beams," J. Acoust. Soc. Am. 83,1752 (1988).
[CrossRef]

1979 (1)

Arpali, C.

Arpali, S. A.

Baykal, Y.

Breazeale, M. A.

J. J. Wen and M. A. Breazeale, "A diffraction beam field expressed as the superposition of Gaussian beams," J. Acoust. Soc. Am. 83,1752 (1988).
[CrossRef]

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]

Dogariu, A.

Eyyuboðlu, H. T.

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]

Gu, J.

Z. Mei, D. Zhao, and J. Gu, "Comparison of two approximate methods for hard-edged diffracted flat-topped light beams," Opt. Commun. 267, 58-64 (2006).
[CrossRef]

He, S.

Li, Y.

Mei, Z.

Z. Mei, D. Zhao, and J. Gu, "Comparison of two approximate methods for hard-edged diffracted flat-topped light beams," Opt. Commun. 267, 58-64 (2006).
[CrossRef]

Z. Mei and D. Zhao, "Controllable dark-hollow beams and their propagation characteristics," J. Opt. Soc. Am. A 22, 1898-1902 (2005).
[CrossRef]

Plonus, M. A.

Sermutlu, E.

H. T. Eyyuboðlu, 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]

Shirai, T.

Wang, S. C. H.

Wen, J. J.

J. J. Wen and M. A. Breazeale, "A diffraction beam field expressed as the superposition of Gaussian beams," J. Acoust. Soc. Am. 83,1752 (1988).
[CrossRef]

Wolf, E.

Yazýcýoðlu, C.

Zhang, Y.

Y. Zhang, "Nonparaxial propagation analysis of elliptical Gaussian beams diffracted by a circular aperture," Opt Commun. 248, 317-326 (2005).
[CrossRef]

Zhao, D.

Z. Mei, D. Zhao, and J. Gu, "Comparison of two approximate methods for hard-edged diffracted flat-topped light beams," Opt. Commun. 267, 58-64 (2006).
[CrossRef]

Z. Mei and D. Zhao, "Controllable dark-hollow beams and their propagation characteristics," J. Opt. Soc. Am. A 22, 1898-1902 (2005).
[CrossRef]

Appl. Opt. (2)

J. Acoust. Soc. Am. (1)

J. J. Wen and M. A. Breazeale, "A diffraction beam field expressed as the superposition of Gaussian beams," J. Acoust. Soc. Am. 83,1752 (1988).
[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 (4)

Opt Commun. (1)

Y. Zhang, "Nonparaxial propagation analysis of elliptical Gaussian beams diffracted by a circular aperture," Opt Commun. 248, 317-326 (2005).
[CrossRef]

Opt. Commun. (4)

Z. Mei, D. Zhao, and J. Gu, "Comparison of two approximate methods for hard-edged diffracted flat-topped light beams," Opt. Commun. 267, 58-64 (2006).
[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]

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

H. T. Eyyuboðlu, 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]

Opt. Express (3)

Opt. Express. (1)

H. T. Eyyuboðlu, 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)

Other (2)

X. Chu, Y. Ni, and G. Zhou, "Propagation analysis of flattened circular Gaussian beams with a circular aperture in turbulent atmosphere," Opt. Commun. (2007), doi:10.1016/ j.optcom.2007.02.035.
[CrossRef]

ITU-R Document 3J/31-E, "On propagation data and prediction methods required for the design of space-to-earth and earth to-space optical communication systems," Radio-communication Study Group Meeting, Budapest (2001), p. 7.

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Figures (7)

Fig. 1.
Fig. 1.

Transmitter and receiver configuration.

Fig. 2.
Fig. 2.

Variations of the peak value position with different parameters: (a) with parameter σ, (b) with waist width w 0, (c)with the order N.

Fig. 3.
Fig. 3.

Variations of the normalized power of the dark hollow beam before entering the transmitter telescope versus r.

Fig. 4.
Fig. 4.

Evolution of the normalized intensity distribution of the dark hollow beam in a slant path with λ=3.8μm and ζ=π/6: (a) before reaching the source plane, (b) with L=10km (Fw =1), (c) with L=15km (Fw = 0.7), and (d) with L=30km (Fw = 0.34).

Fig. 5.
Fig. 5.

Variation of the efficiency of the power coupling versus R with λ=3.8μm and ζ=π/6: (a) with L=10km (Fw = 1), (b) with L=15km (Fw = 0.7), (c) with L=30km (Fw = 0.34).

Fig. 6.
Fig. 6.

Relations between the efficiency of the power coupling and the altitude from the ground with the parameters λ=3.8μm, σ=0.7, w 0=0.2m, N =3, ζ=0, a=0.15m and b=0.4m.

Fig. 7.
Fig. 7.

Relations between efficiency of power coupling and wavelength with the parameters H=30 km, σ=0.7, w 0=0.2m, N =3, ζ=0, a=0.15m and b=0.4m.

Tables (1)

Tables Icon

Table 1. Efficiency of the power coupling with different parameters.

Equations (34)

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E x y 0 = t x y 0 E 0 x y 0 ,
t x y 0 = { 1 a 2 x 2 + y 2 b 2 0 others ,
E 0 x y 0 = n = 1 N ( 1 ) n 1 N ( N n ) [ exp ( nx 2 + ny 2 w 0 2 ) exp ( nx 2 + ny 2 σw 0 2 ) ] ,
< I p q L > = k 2 ( 2 πL ) 2 E x y 0 E * ξ η 0 × exp ( ik 2 L [ ( p x ) 2 + ( q y ) 2 ( p ξ ) 2 ( q η ) 2 ] ) × < exp [ ψ x y p q + ψ * ξ η p q ] > dxdyd ξdη
< exp [ ψ x y p q + ψ * ξ η p q ] > = exp [ 0.5 D ψ x ξ y η ]
= exp { 1 ρ 0 2 [ ( x ξ ) 2 + ( y η ) 2 ] } .
ρ 0 = ( 0.545 C ̄ n 2 k 2 L ) 3 5
C ̄ n 2 = 1 H 0 H C n 2 ( h ) dh .
C n 2 ( h ) = 8.148 × 10 56 V 2 h 10 exp ( h 1000 ) + 2.7 × 10 16 exp ( h 1500 ) + C 0 exp ( h 1000 )
t x y = j = 1 M B j { exp [ C j b 2 ( x 2 + y 2 ) ] exp [ C j a 2 ( x 2 + y 2 ) ] } ,
< I R L > = ρ 0 4 k 2 4 L 2 N 2 j = 1 M s = 1 M m = 1 N n = 1 N B j B s * N m N n { 1 β 1 β 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 β 2 ρ 0 4 1 ) ] + 1 β 1 β 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 β 2 ρ 0 4 1 ) ] 1 β 1 β 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 β 2 ρ 0 4 1 ) ] 1 β 1 β 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 β 2 ρ 0 4 1 ) ] 1 α 1 α 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 0 2 2 ) R 2 4 L 2 ( α 1 α 2 ρ 0 4 1 ) ] 1 α 1 α 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 0 2 2 ) R 2 4 L 2 ( α 1 α 2 ρ 0 4 1 ) ] + 1 α 1 α 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 0 2 2 ) R 2 4 L 2 ( α 1 α 2 ρ 0 4 1 ) ] + 1 α 1 α 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 0 2 2 ) R 2 4 L 2 ( α 1 α 2 ρ 0 4 1 ) ] }
β 1 = n w 0 2 + 1 ρ 0 2 + C s * b 2 ik 2 L ,
β 2 = m w 0 2 + 1 ρ 0 2 + C j b 2 + ik 2 L ,
β 1 = n σw 0 2 + 1 ρ 0 2 + C s * b 2 ik 2 L ,
β 2 ' = m σw 0 2 + 1 ρ 0 2 + C j b 2 + ik 2 L ,
α 1 = n w 0 2 + 1 ρ 0 2 + C s * a 2 ik 2 L ,
α 2 = m w 0 2 + 1 ρ 0 2 + C j a 2 + ik 2 L ,
α 1 = n σw 0 2 + 1 ρ 0 2 + C s * a 2 ik 2 L ,
α 2 ' = m σw 0 2 + 1 ρ 0 2 + C j a 2 + ik 2 L .
< I p q L > = ρ 0 4 k 2 4 L 2 N 2 j = 1 M s = 1 M m = 1 N n = 1 N ( N m ) ( N n ) B j B s * β 1 β 2 ρ 0 4 1 exp [ k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 β 2 ρ 0 4 1 ) ] .
P 0 = E 0 2 x y 0 dxdy = n = 1 N m = 1 N ( 1 ) n + m N 2 ( N n ) ( N m ) πmnw 0 2 ( 1 σ ) 2 ( 1 + σ ) ( m + n ) ( + n ) ( m + ) .
P R L = 2 π 0 R < I R L > RdR
= πρ 0 4 k 2 N 2 j = 1 M s = 1 M m = 1 N n = 1 N ( 1 ) m + n B j B s * ( N m ) ( N n ) [ ( T 1 + T 2 T 3 T 4 ) ( T 1 + T 2 T 3 T 4 ) ] ,
T 1 = 1 k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) { exp [ k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 β 2 ρ 0 4 1 ) ] 1 }
T 2 = 1 k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) { exp [ k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 β 2 ρ 0 4 1 ) ] 1 }
T 3 = 1 k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) { exp [ k 2 ρ 0 2 ( β 1 ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 β 2 ρ 0 4 1 ) ] 1 }
T 4 = 1 k 2 ρ 0 2 ( β 1 ' ρ 0 2 + β 2 ρ 0 2 2 ) { exp [ k 2 ρ 0 2 ( β 2 ' ρ 0 2 + β 2 ρ 0 2 2 ) R 2 4 L 2 ( β 1 ' β 2 ' ρ 0 4 1 ) ] 1 }
T 1 = 1 k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 0 2 2 ) { exp [ k 2 ρ 0 2 ( α 1 ρ 0 2 + α 0 ρ 0 2 2 ) R 2 4 L 2 ( α 1 α 2 ρ 0 4 1 ) ] 1 }
T 2 = 1 k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 0 2 2 ) { exp [ k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 1 2 2 ) R 2 4 L 2 ( α 1 α 2 ρ 0 4 1 ) ] 1 }
T 3 = 1 k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 0 2 2 ) { exp [ k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 1 2 2 ) R 2 4 L 2 ( α 1 α 2 ρ 0 4 1 ) ] 1 }
T 4 = 1 k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 0 2 2 ) { exp [ k 2 ρ 0 2 ( α 1 ρ 0 2 + α 2 ρ 1 2 2 ) R 2 4 L 2 ( α 1 α 2 ρ 0 4 1 ) ] 1 } .
S r 0 = 2 πrI r 0
I N ( x , y , 0 ) = E 2 ( x , y , 0 ) I Max ( x , y , 0 ) ,
I N ( x , y , 0 ) = I ( p , q , L ) I Max ( x , y , 0 ) .

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