Abstract

In an optical communication link between an optical ground station and a geostationary satellite the main problems appear in the uplink and are due to beam wander and to scintillation. Reliable methods for modeling both effects simultaneously are needed to provide an accurate tool with which the robustness of the communication channel can be tested. Numerical tools, especially the split-step method (also referred to as the fast-Fourier-transform beam propagation method), have demonstrated their ability to deal with problems of optical propagation during atmospheric turbulence. However, obtaining statistically significant results with this technique is computationally intensive. We present an analytical-numerical hybrid technique that provides good information on the variance in optical irradiance with an important saving of time and computational resources.

© 2004 Optical Society of America

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References

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  1. J. W. Strohbehn, “Line-of-sight wave propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
    [CrossRef]
  2. V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translation-NOAA, Jerusalem, 1971).
  3. S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).
    [CrossRef]
  4. A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
    [CrossRef]
  5. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
    [CrossRef]
  6. J. W. Strohbehn, ed., Laser Beam Propagation in the Atmosphere (Springer-Verlag, Berlin, 1978).
    [CrossRef]
  7. R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
    [CrossRef]
  8. J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
    [CrossRef] [PubMed]
  9. I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Free-Space Laser Communication Technologies IX, G. S. Mercherle, ed., Proc. SPIE2990, 102–113 (1997).
    [CrossRef]
  10. L. C. Andrews, R. L. Phillips, Laser Beam Propagation through Random Media, Vol. PM53 of SPIE Press Monograph Series (SPIE Press, Bellingham, Wash., 1998).
  11. L. C. Andrews, R. L. Phillips, C. Y. Hopen, M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. A 16, 1417–1429 (1999).
    [CrossRef]
  12. J. H. Churnside, R. J. Lataitis, “Wander of an optical beam in the turbulent atmosphere,” Appl. Opt. 29, 926–930 (1990).
    [CrossRef] [PubMed]
  13. R. A. Schmeltzer, “Means, variances and covariances for laser beam propagation through a random medium,” Q. Appl. Math. 24, 339–354 (1966).
  14. A. Ishimaru, “Fluctuations of a focused beam wave for atmospheric turbulence probing,” Proc. IEEE 57, 407–414 (1969).
    [CrossRef]
  15. L. Andrews, Department of Mathematics, University of Central Florida, Orlando, Fla. (personal communication, 22January2004).
  16. R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (U.S. Office of Naval Research, Washington, D.C., 1978), Chap. 6.
  17. P. J. Titterton, “Power reduction and fluctuations caused by narrow laser beam motion in the far field,” Appl. Opt. 12, 423–425 (1973).
    [CrossRef] [PubMed]
  18. T. Chiba, “Spot dancing of the laser beam propagated through the turbulent atmosphere,” Appl. Opt. 10, 2456–2461 (1971).
    [CrossRef] [PubMed]
  19. D. H. Tofsted, “Outer-scale effects on beam-wander and angle-of-arrival variances,” Appl. Opt. 31, 5865–5870 (1992).
    [CrossRef] [PubMed]
  20. L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillation and fade statistics for a satellite-communication system,” Appl. Opt. 34, 7742–7751 (1995).
    [CrossRef] [PubMed]
  21. H. T. Yura, C. C. Sung, S. F. Clifford, R. J. Hill, “Second-order Rytov approximation,” J. Opt. Soc. Am. 73, 500–502 (1983).
    [CrossRef]
  22. H. T. Yura, “Short-term average optical-beam spread in a turbulent medium,” J. Opt. Soc. Am. 63, 567–572 (1973).
    [CrossRef]
  23. A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39, 5426–5445 (2000).
    [CrossRef]
  24. J. W. Goodman, Statistical Optics (Wiley, New York, 2000).
  25. R. G. Lane, A. Glindeman, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
    [CrossRef]
  26. C. M. Harding, R. A. Johnston, R. G. Lane, “Fast formulation of a Kolmogorov phase screen,” Appl. Opt. 38, 2161–2170 (1999).
    [CrossRef]

2000 (1)

1999 (2)

1995 (1)

1992 (2)

R. G. Lane, A. Glindeman, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

D. H. Tofsted, “Outer-scale effects on beam-wander and angle-of-arrival variances,” Appl. Opt. 31, 5865–5870 (1992).
[CrossRef] [PubMed]

1991 (1)

1990 (1)

1983 (1)

1980 (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[CrossRef]

1975 (2)

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

1974 (1)

1973 (2)

1971 (1)

1969 (1)

A. Ishimaru, “Fluctuations of a focused beam wave for atmospheric turbulence probing,” Proc. IEEE 57, 407–414 (1969).
[CrossRef]

1968 (1)

J. W. Strohbehn, “Line-of-sight wave propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

1966 (1)

R. A. Schmeltzer, “Means, variances and covariances for laser beam propagation through a random medium,” Q. Appl. Math. 24, 339–354 (1966).

Adhikari, P.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Free-Space Laser Communication Technologies IX, G. S. Mercherle, ed., Proc. SPIE2990, 102–113 (1997).
[CrossRef]

Al-Habash, M. A.

Andrews, L.

L. Andrews, Department of Mathematics, University of Central Florida, Orlando, Fla. (personal communication, 22January2004).

Andrews, L. C.

Belmonte, A.

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Chiba, T.

Churnside, J. H.

Clifford, S. F.

Dainty, J. C.

R. G. Lane, A. Glindeman, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[CrossRef]

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Glindeman, A.

R. G. Lane, A. Glindeman, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Gochelashvily, K. S.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 2000).

Hakakha, H.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Free-Space Laser Communication Technologies IX, G. S. Mercherle, ed., Proc. SPIE2990, 102–113 (1997).
[CrossRef]

Harding, C. M.

Hill, R. J.

Hopen, C. Y.

Hufnagel, R. E.

R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (U.S. Office of Naval Research, Washington, D.C., 1978), Chap. 6.

Ishimaru, A.

A. Ishimaru, “Fluctuations of a focused beam wave for atmospheric turbulence probing,” Proc. IEEE 57, 407–414 (1969).
[CrossRef]

Johnston, R. A.

Kim, I. I.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Free-Space Laser Communication Technologies IX, G. S. Mercherle, ed., Proc. SPIE2990, 102–113 (1997).
[CrossRef]

Korevaar, E.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Free-Space Laser Communication Technologies IX, G. S. Mercherle, ed., Proc. SPIE2990, 102–113 (1997).
[CrossRef]

Lane, R. G.

C. M. Harding, R. A. Johnston, R. G. Lane, “Fast formulation of a Kolmogorov phase screen,” Appl. Opt. 38, 2161–2170 (1999).
[CrossRef]

R. G. Lane, A. Glindeman, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Lataitis, R. J.

Lawrence, R. S.

Majumdar, A. K.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Free-Space Laser Communication Technologies IX, G. S. Mercherle, ed., Proc. SPIE2990, 102–113 (1997).
[CrossRef]

Ochs, G. R.

Phillips, R. L.

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Schmeltzer, R. A.

R. A. Schmeltzer, “Means, variances and covariances for laser beam propagation through a random medium,” Q. Appl. Math. 24, 339–354 (1966).

Shishov, V. I.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Strohbehn, J. W.

J. W. Strohbehn, “Line-of-sight wave propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

Sung, C. C.

Tatarski, V. I.

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translation-NOAA, Jerusalem, 1971).

Titterton, P. J.

Tofsted, D. H.

Yu, P. T.

Yura, H. T.

Appl. Opt. (8)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Proc. IEEE (5)

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[CrossRef]

A. Ishimaru, “Fluctuations of a focused beam wave for atmospheric turbulence probing,” Proc. IEEE 57, 407–414 (1969).
[CrossRef]

J. W. Strohbehn, “Line-of-sight wave propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

Q. Appl. Math. (1)

R. A. Schmeltzer, “Means, variances and covariances for laser beam propagation through a random medium,” Q. Appl. Math. 24, 339–354 (1966).

Waves Random Media (1)

R. G. Lane, A. Glindeman, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Other (7)

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translation-NOAA, Jerusalem, 1971).

J. W. Goodman, Statistical Optics (Wiley, New York, 2000).

L. Andrews, Department of Mathematics, University of Central Florida, Orlando, Fla. (personal communication, 22January2004).

R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (U.S. Office of Naval Research, Washington, D.C., 1978), Chap. 6.

I. I. Kim, H. Hakakha, P. Adhikari, E. Korevaar, A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Free-Space Laser Communication Technologies IX, G. S. Mercherle, ed., Proc. SPIE2990, 102–113 (1997).
[CrossRef]

L. C. Andrews, R. L. Phillips, Laser Beam Propagation through Random Media, Vol. PM53 of SPIE Press Monograph Series (SPIE Press, Bellingham, Wash., 1998).

J. W. Strohbehn, ed., Laser Beam Propagation in the Atmosphere (Springer-Verlag, Berlin, 1978).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Long-term beam spread at the reception plane situated in a geostationary orbit. Three methods were used for the calculation, as shown.

Fig. 2
Fig. 2

Short-term beam width in a stationary orbit. The differences between the classic expression given by Yura22 and the FFT-BPM simulations are apparent.

Fig. 3
Fig. 3

Second-order moment of the beam wander.

Fig. 4
Fig. 4

Intrinsic error in the preceding calculations, following Eq. (29).

Fig. 5
Fig. 5

Log-amplitude variance in the uplink of a geostationary satellite as a function of the initial waist of a collimated beam, obtained by the semianalytical method presented in this paper. The wavelength was 0.84 μm. The correspondence with the numerical calculations (the asterisk curves) is good enough until the appearance of the saturation effect.

Fig. 6
Fig. 6

(a) Pdf of the log amplitude, deduced from a high number of simulations with the semianalytical method presented in this paper. The normal value of the pdf holds only for small values of the log-amplitude variance. (b) Corresponding pdf of the irradiance. For small variances in irradiance it is a log-normal function, but it loses this characteristic when the influence of beam wander appears.

Fig. 7
Fig. 7

Effect of beam wander on the uplink’s log-amplitude variance as a function of beam waist and wavelength.

Equations (29)

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WLT2z=WST2z+2β2,
WLT2z=L=W021+L2Z02+24Lk0r0,s2,
r0,s=0.42k20L Cn2zL-zL5/3dz-3/5
WLTL=WL1+Gu,
Gu=4π2k020L0 κΦnz, κ×1-exp-ΛLκ2k01-zL2dκdz,
Λ=2Lk0W2L.
WST2z=L=W021+L2Z02+2×4.2Lkr0,s1-0.26r0,sW01/32,
σβX2=σβY2=βx2=βy2.
β=βx2+βy2
βx2=βy2=½β2.
β2=2.07 0L Cn2zL-z21Wsz1/3dz.
σI2=I2-I2I2,
σI2r, L=σI20, L+σI,r2r, L.
σI20, L=8π2k020L0 κΦnz, κ×exp-ΛLκ2k0L-zL2×1-cosLκ2k0L-zL×Θ+1-ΘzLdκdz,
Λ=2Lk0W2L, Θ=1+LZ02-1,
σI20, L=4π2k02Γ-56×0.033 0L Cn2z×Az5/61-1+BzAz25/12×cos56arctanBzAzdz,
Az=ΛLk0L-zL2,
Bz=Lk0L-zLΘ+1-ΘzL.
σI,r2r, L=8π2k020L0 κΦnz, κ×exp-ΛLκ2k0L-zL2×I02ΛκrL-zL-1dκdz,
σI,r2r, L=4π2k02Γ-560.033 0L Cn2zAz5/6×1F1-56, 1, 2r2W2L-1dz,
Ix, y, L=I0 exp-2 x-βx2+y-βy2WST2L,
I0=exp2χβ,
I0, 0, L=exp2χβexp-2 β2WST2L.
Ir, L=exp-2 r2WLT2L,
σI,Gb2=σI2+σI,r2I2,
χ=-σχ2,σχ2=¼ln1+σI,Gb2,
I=exp2χexp-2β2WST2L
Cn2h=0.00594v/272h×10-510 exp-h/1000+2.7×10-16exp-h/1500+Aexp-h/100,
ε=1-WST2+2β2WLT2.

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