Abstract

The problem of coherence length optimization in a spatially partially coherent beam for free space optical communication is investigated. The weak turbulence regime is considered. An expression for the scintillation index in a series form is derived and conditions for obtaining improvement in outage probability through optimization in the coherence length of the beam are described. A numerical test for confirming performance improvement due to coherence length optimization is proposed. The effects of different parameters, including the phase front radius of curvature, transmission distance, wavelength and beamwidth are studied. The results show that, for smaller distances and larger beamwidths, improvements in outage probability of several orders of magnitude can be achieved by using partially coherent beams.

© 2010 Optical Society of America

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References

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  1. O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43(2), 330-341 (2004).
    [CrossRef]
  2. J. C. Ricklin, and F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication," J. Opt. Soc. Am. A 19(9), 1794-1802 (2002).
    [CrossRef]
  3. V. A. Banakh, V. M. Buldakov, and V. L. Mironov, "Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere," Opt. Spektrosk 54, 1054-1059 (1983).
  4. T. J. Schulz, "Optimal beam for propagation through random media," Opt. Lett. 30(10), 1093-1095 (2005).
    [CrossRef] [PubMed]
  5. D. G. Voelz, and X. Xiao, "Metric for optimizing spatially partially coherent beams for propagation through turbulence," Opt. Eng. 48(3), (2009).
    [CrossRef]
  6. H. T. Eyyuboglu, Y. Baykal, E. Sermtlu, O. Korotkova, and Y. Cai, "Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media," J. Opt. Soc. Am. A 26(2), 387-394 (2009).
    [CrossRef]
  7. H. T. Eyyuboglu, Y. Baykal and X. Ji, "Scintillations of Laguerre Gaussian beams," Applied Physics B - Laser and Optics 98(4), 857-863 (2010).
    [CrossRef]
  8. Y. Baykal, H. T. Eyyuboglu, and Y. Cai, "Scintillations of partially coherent multiple Gaussian beams in turbulence," Appl. Opt. 48(10), 1943-1954 (2009).
    [CrossRef] [PubMed]
  9. S. Zhu, Y. Cai, and O. Korotkova, "Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam," Opt. Express 18(12), 12587-12598 (2010).
    [CrossRef] [PubMed]
  10. E. Tervonen, A. T. Friberg, and J. Turunen, "Gaussian Schell-model beams generated with synthetic acousto-optic holograms," J. Opt. Soc. Am. A 9(5), 796-803 (1992).
    [CrossRef]
  11. S. R. Seshadri, "Partially coherent Gaussian Schell-model electromagnetic beams," J. Opt. Soc. Am. A 16(6), 1373-1380 (1999).
    [CrossRef]
  12. L. C. Andrews, and R. L. Phillips, Laser beam propagation through random media, 2nd Ed., The Society of Photo-Optical Instrumentation Engineers, 2005.
    [CrossRef]

2010 (2)

H. T. Eyyuboglu, Y. Baykal and X. Ji, "Scintillations of Laguerre Gaussian beams," Applied Physics B - Laser and Optics 98(4), 857-863 (2010).
[CrossRef]

S. Zhu, Y. Cai, and O. Korotkova, "Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam," Opt. Express 18(12), 12587-12598 (2010).
[CrossRef] [PubMed]

2009 (3)

2005 (1)

2004 (1)

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43(2), 330-341 (2004).
[CrossRef]

2002 (1)

1999 (1)

1992 (1)

1983 (1)

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, "Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere," Opt. Spektrosk 54, 1054-1059 (1983).

Andrews, L. C.

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43(2), 330-341 (2004).
[CrossRef]

Banakh, V. A.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, "Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere," Opt. Spektrosk 54, 1054-1059 (1983).

Baykal, Y.

Buldakov, V. M.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, "Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere," Opt. Spektrosk 54, 1054-1059 (1983).

Cai, Y.

Davidson, F. M.

Eyyuboglu, H. T.

Friberg, A. T.

Ji, X.

H. T. Eyyuboglu, Y. Baykal and X. Ji, "Scintillations of Laguerre Gaussian beams," Applied Physics B - Laser and Optics 98(4), 857-863 (2010).
[CrossRef]

Korotkova, O.

Mironov, V. L.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, "Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere," Opt. Spektrosk 54, 1054-1059 (1983).

Phillips, R. L.

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43(2), 330-341 (2004).
[CrossRef]

Ricklin, J. C.

Schulz, T. J.

Sermtlu, E.

Seshadri, S. R.

Tervonen, E.

Turunen, J.

Voelz, D. G.

D. G. Voelz, and X. Xiao, "Metric for optimizing spatially partially coherent beams for propagation through turbulence," Opt. Eng. 48(3), (2009).
[CrossRef]

Xiao, X.

D. G. Voelz, and X. Xiao, "Metric for optimizing spatially partially coherent beams for propagation through turbulence," Opt. Eng. 48(3), (2009).
[CrossRef]

Zhu, S.

Appl. Opt. (1)

Applied Physics B - Laser and Optics (1)

H. T. Eyyuboglu, Y. Baykal and X. Ji, "Scintillations of Laguerre Gaussian beams," Applied Physics B - Laser and Optics 98(4), 857-863 (2010).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Eng. (2)

D. G. Voelz, and X. Xiao, "Metric for optimizing spatially partially coherent beams for propagation through turbulence," Opt. Eng. 48(3), (2009).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43(2), 330-341 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Spektrosk (1)

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, "Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere," Opt. Spektrosk 54, 1054-1059 (1983).

Other (1)

L. C. Andrews, and R. L. Phillips, Laser beam propagation through random media, 2nd Ed., The Society of Photo-Optical Instrumentation Engineers, 2005.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Outage probability for C n 2 = 10 14 m 2 / 3 , W 0 = 0.05 m, F 0 = ∞, and λ = 1.55μm at distances of 1000, 1500 and 2000 meters.

Fig. 2
Fig. 2

The derivative of the scintillation index and target values for the same parameters given in Fig. 1

Fig. 3
Fig. 3

Outage probability versus F 0 for C n 2 = 10 14 m 2 / 3 , W 0 = 0.05 m and λ = 1μm.

Fig. 4
Fig. 4

The SI derivative with respect to lc and target values for the parameters given in Fig. 3

Fig. 5
Fig. 5

Outage probability versus beamwidths for C n 2 = 10 14 m 2 / 3 , collimated beam, and lc = ∞. Cases 1, 2, 3 and 4 refer to (z, λ) pairs of (1500 m, 1 μm), (1500 m, 1.55 μm), (2000 m, 1 μm), and (2000 m, 1.55 μm) respectively.

Fig. 6
Fig. 6

SI derivatives and target values with respect to beamwidths for z = 1500 m, λ = 1μm, F 0 = ∞, Ith = 0.025. The optimal value for W 0 is found to be 0.019 m.

Fig. 7
Fig. 7

SI derivatives with respect to lc and target values to determine benefits of PCBs at various beamwidths for the parameters λ = 1μm and F 0 = ∞.

Equations (42)

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I ¯ ( ρ ) = K n W 0 2 W 2 exp ( 2 ρ 2 W 2 )
W = W 0 [ r 0 2 + ( ξ s + 2 W 0 2 ρ 0 2 ) z 0 2 ] 1 / 2 ,
σ I 2 = 4.42 σ R 2 z e 5 / 6 σ pe 2 W 0 2 ( r 0 2 + ξ s z 0 2 ) + 3.86 σ R 2 { 0.4 [ ( 1 + 2 r e ) 2 + 4 z e 2 ] 5 / 12 cos [ 5 6 tan 1 ( 1 + 2 r e 2 z e ) ] 11 16 z e 5 / 6 }
r e = r 0 r 0 2 + ξ s z 0 2 , z e = ξ s z 0 r 0 2 + ξ s z 0 2
σ pe 2 = ζ 1 ( λ z 2 W 0 ) 2 ( 2 W 0 F p ) 5 / 3 [ 1 ζ 2 ( F p 2 C r 2 W 0 2 + ζ 3 ) 1 / 6 ]
P out = 0 I th p ( I ) dI
P out = 0 I th 1 I 2 π σ lnI 2 exp { [ ln ( I / I ¯ ) + 0.5 σ lnI 2 ] 2 2 σ lnI 2 } dI
P out = Q ( y th )
y th = ln I th ln I ¯ + 0.5 σ lnI 2 σ lnI ,
y th ln I th ln I ¯ + 0.5 σ lnI 2 σ lnI 1 σ lnI ln ( I th / I ¯ )
φ ( l c ) = 1 σ I ln ( I th I ¯ )
σ I 2 = 4.42 σ R 2 z e 5 / 6 [ σ pe 2 W 0 2 ( r 0 2 + ξ s z 0 2 ) + 0.8733 g ( x ) ]
g ( x ) = 0.7127 ( 1 + 5 72 x 2 455 4 ! 6 4 x 4 + 43225 144 × 6 6 x 6 ) 11 / 16
g ( x ) = 0.7127 ( x 2 ) 5 12 { cos ( 5 π 12 ) [ 1 + 5 72 ( 1 x ) 2 455 24 × 6 4 ( 1 x ) 4 ] ± sin ( 5 π 12 ) [ 5 6 ( 1 x ) 35 6 4 ( 1 x ) 3 + ] } 11 16
d σ I 2 dl c = ( 1 W r 2 ) [ I ¯ σ I 2 ln ( I / I th ) ] 32 z 2 k 2 l c 3
d I ¯ dl c = ( W 0 W r ) 2 I ¯ 2 z 0 2 4 W 0 2 l c 3
d dl c σ I 2 = 3.6833 σ R 2 z e 1 / 6 ( d z e d l c ) [ σ p e 2 W 0 2 ( r 0 2 + ξ s z 0 2 ) + 0.8733 g ( x ) ] + 4.42 σ R 2 z e 5 / 6 [ 4 σ pe 2 z 0 2 ( r 0 2 + ξ s z 0 2 ) 2 l c 3 + 0.8733 g ( x ) ]
g ( x ) = 0.7127 ( 10 72 x 4 × 455 4 ! 6 4 x 3 + 6 × 43225 144 × 6 6 x 5 + ) ( dx dl c )
g ( x ) = 0.7127 [ ( 5 6 ) ( x 2 ) 7 12 x { cos ( 5 π 12 ) [ 1 + 5 72 ( 1 x ) 2 455 24 × 6 4 ( 1 x ) 4 ] ± sin ( 5 π 12 ) [ 5 6 ( 1 x ) 35 6 4 ( 1 x ) 3 + ] } + ( x 2 ) 5 12 { cos ( 5 π 12 ) [ 10 72 ( 1 x ) 3 + 4 × 455 24 × 6 4 ( 1 x ) 5 ] ± sin ( 5 π 12 ) [ 5 6 ( 1 x ) 2 + 3 × 35 6 4 ( 1 x ) 4 ] } ] ( dx dl c )
dz e dl c = 8 zr 0 2 kl c 3 ( r 0 2 + ξ s z 0 2 ) 2 ,
dx dl c = π ( 3 4 z F 0 + z 2 F 0 2 ) 2 λ z l c ( 1 + l c 2 2 W 0 2 ) 2
l c 0 = [ k 2 W 0 2 8 z 2 { W r 2 W 0 2 I th [ r 0 2 + ( 1 + 2 W 0 2 ρ 0 2 ) z 0 2 ] } ] 1
d σ I 2 d F 0 = ( W 0 W r ) 2 4 z σ I 2 I ¯ ln ( I th / I ¯ ) ( 1 z F 0 ) 1 F 0 2
d σ I 2 dW 0 = 4 σ I 2 W 0 ln ( I th / I ¯ ) [ 1 8 z 2 I ¯ k 2 W r 2 ( 1 l c 2 + 1 ρ 0 2 + 1 W 0 2 ) ]
W 0 4 4 z 2 ξ s k 2
W 0 2 4 z 2 k 2 l c 2 + 16 z 4 k 4 l c 4 + 4 z 2 k 2
z e = 2 z / k W 0 2 ξ s ( 1 + 4 z 2 ξ s k 2 W 0 4 ) 2 z ξ s kW 0 2 ( 1 4 z 2 ξ s k 2 W 0 4 )
x = 3 kW 0 2 4 z ξ s ( 1 + 4 z 2 ξ s 3 k 2 W 0 4 )
z e 3 2 x
σ I 2 3.86 σ R 2 z e 5 / 6 g ( x )
x = 3 k 4 z ( 1 / W 0 2 + 2 / l c 2 )
W 0 4 4 z 2 ξ s k 2
W 0 2 4 z 2 k 2 l c 2 + 16 z 4 k 4 l c 4 + 4 z 2 k 2
z e kW 0 2 2 z ( 1 k 2 W 0 4 4 ξ s z 2 )
x = z kW 0 2 ( 1 + 3 k 2 W 0 4 4 z 2 ξ s )
z e 1 2 x kW 0 2 2 z
tan 1 x = 1 2 j ln ( 1 + jx 1 jx )
cos { 5 6 tan 1 ( 1 + 2 r e 2 z e ) } = 1 2 [ exp ( j 5 6 tan 1 x ) + exp ( j 5 6 tan 1 x ) ] = 1 2 { exp [ 5 12 ln ( 1 + jx 1 jx ) ] + exp [ 5 12 ln ( 1 + jx 1 jx ) ] } = ( 1 + jx ) 5 / 6 + ( 1 jx ) 5 / 6 2 ( 1 + x 2 ) 5 / 12
σ I , nw 2 = 3.86 σ R 2 z e 5 / 6 [ 0.7127 ( 1 + 5 72 x 2 455 4 ! 6 4 x 4 + 43225 144 × 6 6 x 6 ) 11 / 16 ]
tan 1 x = ± π 2 + 1 2 j ln ( 1 jy 1 + jy )
cos [ 5 6 tan 1 ( 1 + 2 r e 2 z e ) ] = 1 2 [ e ± j 5 π 12 ( 1 jy 1 + jy ) 5 / 12 + e j 5 π 12 ( 1 + jy 1 jy ) 5 / 12 ]
σ I , nw 2 = 3.86 σ R 2 z e 5 / 6 [ 0.7127 ( x 2 ) 5 / 12 { cos ( 5 π 12 ) [ 1 + 5 72 ( 1 x ) 2 455 24 × 6 4 ( 1 x ) 4 ] ± sin ( 5 π 12 ) [ 5 6 ( 1 x ) 35 6 4 ( 1 x ) 3 + ] } 11 16 ]

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