Abstract

The temporal covariance function of irradiance-flux fluctua-tions for Gaussian Schell-model (GSM) beams propagating in atmospheric turbulence is theoretically formulated by making use of the method of effective beam parameters. Based on this formulation, new expressions for the root-mean-square (RMS) bandwidth of the irradiance-flux temporal spectrum due to GSM beams passing through atmospheric turbulence are derived. With the help of these expressions, the temporal fade statistics of the irradiance flux in free-space optical (FSO) communication systems, using spatially partially coherent sources, impaired by atmospheric turbulence are further calculated. Results show that with a given receiver aperture size, the use of a spatially partially coherent source can reduce both the fractional fade time and average fade duration of the received light signal; however, when atmospheric turbulence grows strong, the reduction in the fractional fade time becomes insignificant for both large and small receiver apertures and in the average fade duration turns inconsiderable for small receiver apertures. It is also illustrated that if the receiver aperture size is fixed, changing the transverse correlation length of the source from a larger value to a smaller one can reduce the average fade frequency of the received light signal only when a threshold parameter in decibels greater than the critical threshold level is specified.

© 2013 Optical Society of America

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References

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2013 (1)

2011 (1)

K. Drexler, M. Roggemann, and D. Voelz, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng.50,025002 (2011).
[CrossRef]

2010 (2)

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Scintillation calculations for partially coherent general beams via extended Huygens-Fresnel integral and self-designed Matlab function,” Appl. Phys. B100, 597–609 (2010).
[CrossRef]

D. K. Borah and D. G. Voelz, “Spatially partially coherent beam parameter optimization for free space optical communications,” Opt. Express18, 20746–20758 (2010).
[CrossRef] [PubMed]

2009 (3)

2007 (1)

2004 (2)

O. Korotkova, L. C. Andrews, and R. L. Phillips, “The effect of partially coherent quasi-monochromatic Gaussian-beam on the probability of fade,”Proc. SPIE5160, 68–77 (2004).
[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, 330–341 (2004).
[CrossRef]

2002 (3)

1991 (1)

M. Silberstein, “Application of a generalized Leibniz rule for calculating electromagnetic fields within continuous source regions,” Radio Sci.26, 183–190 (1991).
[CrossRef]

1983 (1)

1980 (1)

1973 (1)

H. Flanders, “Differentiation under the integral sign,” Am. Math. Mon.80, 615–627 (1973).
[CrossRef]

Andrews, L.

Andrews, L. C.

O. Korotkova, L. C. Andrews, and R. L. Phillips, “The effect of partially coherent quasi-monochromatic Gaussian-beam on the probability of fade,”Proc. SPIE5160, 68–77 (2004).
[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, 330–341 (2004).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

Baykal, Y.

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Scintillation calculations for partially coherent general beams via extended Huygens-Fresnel integral and self-designed Matlab function,” Appl. Phys. B100, 597–609 (2010).
[CrossRef]

Borah, D. K.

Cai, Y.

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Scintillation calculations for partially coherent general beams via extended Huygens-Fresnel integral and self-designed Matlab function,” Appl. Phys. B100, 597–609 (2010).
[CrossRef]

Chen, C.

Dan, Y.

Davidson, F. M.

Drexler, K.

K. Drexler, M. Roggemann, and D. Voelz, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng.50,025002 (2011).
[CrossRef]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Scintillation calculations for partially coherent general beams via extended Huygens-Fresnel integral and self-designed Matlab function,” Appl. Phys. B100, 597–609 (2010).
[CrossRef]

Feng, X.

Flanders, H.

H. Flanders, “Differentiation under the integral sign,” Am. Math. Mon.80, 615–627 (1973).
[CrossRef]

Gbur, G.

Ghassemlooy, Z.

Hemmati, H.

H. Hemmati, Near-Earth Laser Communications (Taylor & Francis Group, 2008).

Holmes, J. F.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

Kerr, J. R.

Khalighi, M.

Kiasaleh, K.

K. Kiasaleh, “Performance analysis of free-space, on-off-keying optical communication systems impaired by turbulence,” Proc. SPIE4635, 150–161 (2002).
[CrossRef]

Korotkova, O.

O. Korotkova, L. C. Andrews, and R. L. Phillips, “The effect of partially coherent quasi-monochromatic Gaussian-beam on the probability of fade,”Proc. SPIE5160, 68–77 (2004).
[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, 330–341 (2004).
[CrossRef]

Lee, I. E.

Lee, M. H.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[CrossRef]

McKinley, W. G.

Ng, W. P.

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, 330–341 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, “The effect of partially coherent quasi-monochromatic Gaussian-beam on the probability of fade,”Proc. SPIE5160, 68–77 (2004).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[CrossRef]

Ricklin, J. C.

Roggemann, M.

K. Drexler, M. Roggemann, and D. Voelz, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng.50,025002 (2011).
[CrossRef]

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms, (SPIE, 2007).
[CrossRef]

Silberstein, M.

M. Silberstein, “Application of a generalized Leibniz rule for calculating electromagnetic fields within continuous source regions,” Radio Sci.26, 183–190 (1991).
[CrossRef]

Vetelino, F. S.

Voelz, D.

K. Drexler, M. Roggemann, and D. Voelz, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng.50,025002 (2011).
[CrossRef]

X. Xiao and D. Voelz, “On-axis probability density function and fade behavior of partially coherent beams propagating through turbulence,” Appl. Opt.48, 167–175 (2009).
[CrossRef] [PubMed]

Voelz, D. G.

Wang, H.

Wolf, E.

Xiao, X.

Yang, H.

Young, C.

Yura, H. T.

Zhang, B.

Am. Math. Mon. (1)

H. Flanders, “Differentiation under the integral sign,” Am. Math. Mon.80, 615–627 (1973).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (1)

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Scintillation calculations for partially coherent general beams via extended Huygens-Fresnel integral and self-designed Matlab function,” Appl. Phys. B100, 597–609 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (2)

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, 330–341 (2004).
[CrossRef]

K. Drexler, M. Roggemann, and D. Voelz, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng.50,025002 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (2)

K. Kiasaleh, “Performance analysis of free-space, on-off-keying optical communication systems impaired by turbulence,” Proc. SPIE4635, 150–161 (2002).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, “The effect of partially coherent quasi-monochromatic Gaussian-beam on the probability of fade,”Proc. SPIE5160, 68–77 (2004).
[CrossRef]

Radio Sci. (1)

M. Silberstein, “Application of a generalized Leibniz rule for calculating electromagnetic fields within continuous source regions,” Radio Sci.26, 183–190 (1991).
[CrossRef]

Other (5)

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms, (SPIE, 2007).
[CrossRef]

H. Hemmati, Near-Earth Laser Communications (Taylor & Francis Group, 2008).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

RMS bandwidth of the irradiance-flux temporal spectrum, scaled by the Fresnel frequency ωt, as a function of σc/W0.

Fig. 2
Fig. 2

Fractional fade time in terms of the threshold parameter in decibels. (a) σ R 2 = 0.3; (b) σ R 2 = 1; (c) σ R 2 = 10.

Fig. 3
Fig. 3

Average fade frequency, scaled by the Fresnel frequency ωt, as a function of the threshold parameter in decibels. (a) σ R 2 = 0.3; (b) σ R 2 = 1; (c) σ R 2 = 10.

Fig. 4
Fig. 4

Average fade duration, multiplied by the Fresnel frequency ωt, as a function of the threshold parameter in decibels. (a) σ R 2 = 0.3; (b) σ R 2 = 1; (c) σ R 2 = 10.

Equations (26)

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B I ( τ ) = exp [ B ln X ( τ ) + B ln Y ( τ ) ] 1
B ln X ( τ ) = 8 π 2 k 2 L 0 1 0 κ Φ n ( κ ) G X ( κ ) J 0 ( κ v τ ) × exp { L κ 2 k ( Λ 1 + Ω G ) [ ( 1 Θ ¯ 1 ξ ) 2 + Λ 1 Ω G ξ 2 ] } × { 1 cos [ L κ 2 k Ω G Λ 1 Ω G + Λ 1 ξ ( 1 Θ ¯ 1 ξ ) ] } d κ d ξ
B ln Y ( τ ) = 8 π 2 k 2 L 0 1 0 κ Φ n ( κ ) G Y ( κ ) J 0 ( κ v τ ) × exp { L κ 2 k ( Λ 1 + Ω G ) [ ( 1 Θ ¯ 1 ξ ) 2 + Λ 1 Ω G ξ 2 ] } × { 1 cos [ L κ 2 k Ω G Λ 1 Ω G + Λ 1 ξ ( 1 Θ ¯ 1 ξ ) ] } d κ d ξ ,
B ln X ( τ ) 0.53 σ R 2 ( Ω G Λ 1 Ω G + Λ 1 ) 2 0 1 ξ 2 ( 1 Θ ¯ 1 ξ ) 2 0 η 1 / 6 J 0 ( ω t τ η ) × exp ( η η X ) exp { η Λ 1 + Ω G [ ( 1 Θ ¯ 1 ξ ) 2 + Λ 1 Ω G ξ 2 ] } d η d ξ ,
0 x u exp ( a 2 x 2 ) J p ( b x ) d x = b p Γ ( p + u + 1 2 ) 2 p + 1 a p + u + 1 Γ ( p + 1 ) F 1 1 ( p + u + 1 2 ; p + 1 ; b 2 4 a 2 ) ,
B ln X ( τ ) = 0.49 σ R 2 ( Ω G Λ 1 Ω G + Λ 1 ) 2 0 1 ξ 2 ( 1 Θ ¯ 1 ξ ) 2 R 7 / 6 ( ξ ) F 1 1 [ 7 6 ; 1 ; ω t 2 τ 2 R ( ξ ) 4 ] d ξ
R ( ξ ) = η X { 1 + η X Λ 1 + Ω G [ ( 1 Θ ¯ 1 ξ ) 2 + Λ 1 Ω G ξ 2 ] } 1 .
B ln Y ( τ ) 1.06 σ R 2 0 1 0 J 0 ( ω t τ η ) ( η + η Y ) 11 / 6 exp { ( 1 Θ ¯ 1 ξ ) 2 η Λ 1 + Ω G } d η d ξ ,
B ln Y ( τ ) = 1.06 π 1 / 2 σ R 2 Λ 1 + Ω G Θ ¯ 1 0 J 0 ( ω t τ x ) ( x 2 + η Y ) 11 / 6 × [ erf ( x Λ 1 + Ω G ) + erf ( x ( Θ ¯ 1 1 ) Λ 1 + Ω G ) ] d x ,
Λ e = Λ 1 N S 1 + 4 Λ 1 q c , Θ ¯ e = Θ ¯ 1 + 4 Λ 1 q c 1 + 4 Λ 1 q c ,
η X = ( 1 3 Θ ¯ e 2 + Θ ¯ e 2 5 ) 6 / 7 ( σ B σ R ) 12 / 7 [ 1 + 0.56 ( 2 Θ ¯ e ) σ B 12 / 5 ] 1
η Y = 3 ( σ R σ B ) 12 / 5 + 2.07 σ R 12 / 5 ,
σ B 2 = 3.86 σ R 2 Re [ i 5 / 6 F 1 2 ( 5 6 , 11 6 , 17 6 ; Θ ¯ e + i Λ e ) 11 16 Λ e 5 / 6 ] ,
B RMS = 1 2 π [ 0 ω 2 S I ( ω ) d ω 0 S I ( ω ) d ω ] 1 / 2 ,
B RMS = 1 2 π [ B I ( 0 ) B I ( 0 ) ] 1 / 2
B I ( τ ) = exp [ B ln X ( τ ) + B ln Y ( τ ) ] { [ B ln X ( τ ) + B ln Y ( τ ) ] 2 + B ln X ( τ ) + B ln Y ( τ ) } ,
C 1 = 0.29 σ R 2 ( Ω G Λ e Ω G + Λ e ) 2 0 1 ξ 2 ( 1 Θ ¯ e ξ ) 2 R e 13 / 6 ( ξ ) d ξ ,
C 2 = 0.53 π 1 / 2 σ R 2 Λ e + Ω G Θ ¯ e 0 x 2 ( x 2 + η Y ) 11 / 6 × [ erf ( x Λ e + Ω G ) + erf ( x ( Θ ¯ e 1 ) Λ e + Ω G ) ] d x ,
B RMS = C 3 ω t 2 π ,
B I ( 0 ) = σ I 2 = exp ( σ ln X 2 + σ ln Y 2 ) 1
σ ln X 2 0.49 σ R 2 ( Ω G Λ e Ω G + Λ e ) 2 ( 1 3 Θ ¯ e 2 + Θ ¯ e 2 5 ) [ η X 1 + 0.4 η X ( 2 Θ ¯ e ) / ( Λ e + Ω G ) ] 7 / 6 ,
σ ln Y 2 1.27 σ R 2 η Y 5 / 6 1 + 0.4 η Y / ( Λ e + Ω G ) .
C 2 = 0.53 σ R 2 { 3 π ( Λ e + Ω G ) 1 / 6 Θ ¯ e Γ ( 5 / 6 ) [ F 2 2 ( 11 6 , 1 3 , 4 3 , 5 6 ; η Y Λ e + Ω G ) | 1 Θ ¯ e | 2 / 3 × F 2 2 ( 11 6 , 1 3 ; 4 3 , 5 6 ; η Y ( 1 Θ ¯ e ) 2 Λ e + Ω G ) ] 36 η Y 1 / 6 5 Θ ¯ e [ F 2 2 ( 2 , 1 2 ; 7 6 , 3 2 ; η Y Λ e + Ω G ) ( 1 Θ ¯ e ) F 2 2 ( 2 , 1 2 ; 7 6 , 3 2 ; η Y ( 1 Θ ¯ e ) 2 Λ e + Ω G ) ] } ,
p fade ( μ th ) = 0 μ th p I ( μ ) d μ ,
f fade ( μ th ) = 2 2 π α β σ I B RMS Γ ( α ) Γ ( β ) ( α β μ th ) ( α + β 1 ) / 2 K α β ( 2 α β μ th ) .
t fade ( μ th ) = p fade ( μ th ) f fade ( μ th ) .

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