Abstract

The root-mean-square (RMS) bandwidth of temporal light-flux fluctuations is formulated for both plane and spherical waves propagating in the turbulent atmosphere with location-dependent transverse wind. Two path weighting functions characterizing the joint contributions of turbulent eddies and transverse winds at various locations toward the RMS bandwidth are derived. Based on the developed formulations, the roles of variations in both the direction and magnitude of transverse wind velocity with locations over a path on the RMS bandwidth are elucidated. For propagation paths between ground and space, comparisons of the RMS bandwidth computed based on the Bufton wind profile with that calculated by assuming a nominal constant transverse wind velocity are made to exemplify the effect that location dependence of transverse wind velocity has on the RMS bandwidth. Moreover, an expression for the weighted RMS transverse wind velocity has been derived, which can be used as a nominal constant transverse wind velocity over a path for accurately determining the RMS bandwidth.

© 2017 Optical Society of America

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References

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2017 (1)

2015 (1)

2014 (1)

2013 (2)

2012 (4)

2011 (3)

2010 (2)

M. Charnotskii, “Coupling turbulence-distorted wave front to fiber: wave propagation theory perspective,” Proc. SPIE 7814, 78140I (2010).
[Crossref]

Y. Gu and G. Gbur, “Scintillation of pseudo-Bessel correlated beams in atmospheric turbulence,” J. Opt. Soc. Am. A 27, 2621–2629 (2010).
[Crossref]

2007 (2)

2006 (2)

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142-km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[Crossref]

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber Commun. Rep. 3, 111–158 (2006).
[Crossref]

2005 (1)

N. Perlot, J. Horwath, and R. Jüngling, “Modelling wind in simulations of atmospheric optical propagation,” Proc. SPIE 5712, 140–150 (2005).
[Crossref]

2002 (1)

K. Kiasaleh, “Performance analysis of free-space, on-off-keying optical communication systems impaired by turbulence,” Proc. SPIE 4635, 150–161 (2002).
[Crossref]

1993 (1)

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, and V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” Prog. Opt. 32, 203–266 (1993).
[Crossref]

1991 (1)

M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite-size source scintillations in random media,” Waves Random Media 1, 223–243 (1991).
[Crossref]

1973 (1)

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

1972 (1)

1970 (1)

A. I. Kon, “Focusing of light in a turbulent medium,” Radiophys. Quantum. Electron. 13, 43–50 (1970).
[Crossref]

Abad, G. G.

Andrews, L.

Andrews, L. C.

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

Anguita, J. A.

Baker, G. J.

M. I. Charnotskii and G. J. Baker, “Practical calculation of the beam scintillation index based on the rigorous asymptotic propagation theory,” Proc. SPIE 8038, 803804 (2011).
[Crossref]

Baykal, Y.

C. Kamacıoğlu, Y. Baykal, and E. Yazgan, “Averaging of receiver aperture for flat-topped incidence,” Opt. Laser Technol. 52, 91–95 (2013).
[Crossref]

Y. Baykal, “Sinusoidal Gaussian beam field correlations,” J. Opt. 14, 075707 (2012).
[Crossref]

Beck, S. M.

Beresnev, L. A.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Carhart, G. W.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Charnotskii, M.

M. Charnotskii, “Coupling turbulence-distorted wave front to fiber: wave propagation theory perspective,” Proc. SPIE 7814, 78140I (2010).
[Crossref]

Charnotskii, M. I.

M. I. Charnotskii and G. J. Baker, “Practical calculation of the beam scintillation index based on the rigorous asymptotic propagation theory,” Proc. SPIE 8038, 803804 (2011).
[Crossref]

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, and V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” Prog. Opt. 32, 203–266 (1993).
[Crossref]

M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite-size source scintillations in random media,” Waves Random Media 1, 223–243 (1991).
[Crossref]

Chen, C.

Cheon, Y.

Cisternas, J. E.

Eaton, F. D.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber Commun. Rep. 3, 111–158 (2006).
[Crossref]

Fedorova, O. V.

Flanders, H.

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

Fortus, M. I.

Frazier, B. W.

R. K. Tyson and B. W. Frazier, Field Guide to Adaptive Optics, 2nd ed. (SPIE, 2012), p. 11.

Gbur, G.

Gerbunov, M. E.

Giggenbach, D.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142-km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[Crossref]

Gorbunov, M. E.

Gozani, J.

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, and V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” Prog. Opt. 32, 203–266 (1993).
[Crossref]

Gu, Y.

Gudimetla, V. S. R.

Gurvich, A. S.

Hammel, S. M.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber Commun. Rep. 3, 111–158 (2006).
[Crossref]

Henniger, H.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142-km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[Crossref]

Holmes, R. B.

Horwath, J.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142-km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[Crossref]

N. Perlot, J. Horwath, and R. Jüngling, “Modelling wind in simulations of atmospheric optical propagation,” Proc. SPIE 5712, 140–150 (2005).
[Crossref]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

Jüngling, R.

N. Perlot, J. Horwath, and R. Jüngling, “Modelling wind in simulations of atmospheric optical propagation,” Proc. SPIE 5712, 140–150 (2005).
[Crossref]

Kamacioglu, C.

C. Kamacıoğlu, Y. Baykal, and E. Yazgan, “Averaging of receiver aperture for flat-topped incidence,” Opt. Laser Technol. 52, 91–95 (2013).
[Crossref]

Kavehrad, M.

Kiasaleh, K.

K. Kiasaleh, “Performance analysis of free-space, on-off-keying optical communication systems impaired by turbulence,” Proc. SPIE 4635, 150–161 (2002).
[Crossref]

Kirchengast, G.

Knapek, M.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142-km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[Crossref]

Kon, A. I.

A. I. Kon, “Focusing of light in a turbulent medium,” Radiophys. Quantum. Electron. 13, 43–50 (1970).
[Crossref]

Lachinova, S.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Lachinova, S. L.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber Commun. Rep. 3, 111–158 (2006).
[Crossref]

Liu, J. J.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Muschinski, A.

Needham, G.

Perlot, N.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142-km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[Crossref]

N. Perlot, J. Horwath, and R. Jüngling, “Modelling wind in simulations of atmospheric optical propagation,” Proc. SPIE 5712, 140–150 (2005).
[Crossref]

Phillips, R. L.

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

Proschek, V.

Rehder, K.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Ricklin, J. C.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber Commun. Rep. 3, 111–158 (2006).
[Crossref]

Riker, J. F.

V. S. R. Gudimetla, R. B. Holmes, and J. F. Riker, “Analytical expressions for the log-amplitude correlation function for plane wave propagation in anisotropic non-Kolmogorov refractive turbulence,” J. Opt. Soc. Am. A 29, 2622–2627 (2012).
[Crossref]

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Smith, C.

Stevenson, E.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Takayama, Y.

Takenaka, H.

Tatarskii, V. I.

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, and V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” Prog. Opt. 32, 203–266 (1993).
[Crossref]

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

Tereszchuk, K. A.

Tong, S.

Toyoshima, M.

Tyson, R. K.

R. K. Tyson and B. W. Frazier, Field Guide to Adaptive Optics, 2nd ed. (SPIE, 2012), p. 11.

Vetelino, F. S.

Vorontsov, M.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Wang, T.

Weyrauch, T.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

Yang, H.

Yazgan, E.

C. Kamacıoğlu, Y. Baykal, and E. Yazgan, “Averaging of receiver aperture for flat-topped incidence,” Opt. Laser Technol. 52, 91–95 (2013).
[Crossref]

Young, C.

Yura, H. T.

Zavorotny, V. U.

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, and V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” Prog. Opt. 32, 203–266 (1993).
[Crossref]

Zettl, K.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142-km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[Crossref]

Zhang, W.

Zhou, Z.

Am. Math. Mon. (1)

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

Appl. Opt. (4)

J. Opt. (1)

Y. Baykal, “Sinusoidal Gaussian beam field correlations,” J. Opt. 14, 075707 (2012).
[Crossref]

J. Opt. Fiber Commun. Rep. (1)

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber Commun. Rep. 3, 111–158 (2006).
[Crossref]

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

Opt. Express (4)

Opt. Laser Technol. (1)

C. Kamacıoğlu, Y. Baykal, and E. Yazgan, “Averaging of receiver aperture for flat-topped incidence,” Opt. Laser Technol. 52, 91–95 (2013).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (5)

M. I. Charnotskii and G. J. Baker, “Practical calculation of the beam scintillation index based on the rigorous asymptotic propagation theory,” Proc. SPIE 8038, 803804 (2011).
[Crossref]

M. Charnotskii, “Coupling turbulence-distorted wave front to fiber: wave propagation theory perspective,” Proc. SPIE 7814, 78140I (2010).
[Crossref]

K. Kiasaleh, “Performance analysis of free-space, on-off-keying optical communication systems impaired by turbulence,” Proc. SPIE 4635, 150–161 (2002).
[Crossref]

N. Perlot, J. Horwath, and R. Jüngling, “Modelling wind in simulations of atmospheric optical propagation,” Proc. SPIE 5712, 140–150 (2005).
[Crossref]

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142-km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[Crossref]

Prog. Opt. (1)

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, and V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” Prog. Opt. 32, 203–266 (1993).
[Crossref]

Radiophys. Quantum. Electron. (1)

A. I. Kon, “Focusing of light in a turbulent medium,” Radiophys. Quantum. Electron. 13, 43–50 (1970).
[Crossref]

Waves Random Media (1)

M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite-size source scintillations in random media,” Waves Random Media 1, 223–243 (1991).
[Crossref]

Other (5)

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

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

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. Lachinova, L. A. Beresnev, J. J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in AMOS Conference (2010), p. E18.

R. K. Tyson and B. W. Frazier, Field Guide to Adaptive Optics, 2nd ed. (SPIE, 2012), p. 11.

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Figures (4)

Fig. 1.
Fig. 1.

Scaled path weighting functions in terms of ξ for the plane-wave case with various qp. Blue and red curves correspond to w^1(ξ)=w1(ξ)/w1(0) and w^2(ξ)=w2(ξ)/w2(0), respectively.

Fig. 2.
Fig. 2.

Two path weighting functions scaled by peak values in terms of ξ for the spherical-wave case with various qm and qR. Blue and red curves, respectively, correspond to w^1(ξ)=w1(ξ)/w1(ξm,1) and w^2(ξ)=w2(ξ)/w2(ξm,2), where w1(ξm,1) and w2(ξm,2) denote the peak values of w1(ξ) and w2(ξ), respectively. (a) qm=102; (b) qm=1.

Fig. 3.
Fig. 3.

Ratio of the RMS bandwidth calculated based on valt(h) to that computed by assuming a nominal constant transverse wind velocity Vrms in terms of qR and H for plane-wave cases, where qm0 and A=1.7×1014  m2/3. (a) Downlink paths; (b) uplink paths.

Fig. 4.
Fig. 4.

Ratio of the RMS bandwidth calculated based on valt(h) to that computed by assuming a nominal constant transverse wind velocity Vrms in terms of qR and H for spherical-wave cases, where qm0 and A=1.7×1014  m2/3. (a) Downlink paths; (b) uplink paths.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

χ1(r)=k0Ldzdυ(κ,z)exp(iγκ·r)×sin[κ2γ(Lz)/(2k)],
P^=1SADI^(r)d2r,
I^(r)1+2[χ1(r)+χ12(r)+χ2(r)+],
P^2χ^1+1,
χ^1=1SADχ1(r)d2r
χ^1=k0Ldzdυ(κ,z)jinc(γκR)×sin[κ2γ(Lz)/(2k)]
Bflux(τ)4Bχ^(τ)=4χ^1(t=0)χ^1*(t=τ),
n1(s,z;t)=exp{iκ·[sv(z)t]}dυ(κ,z),
χ^1(t)=k0Ldzdυ(κ,z)exp[iκ·v(z)t]×jinc(γκR)sin[κ2γ(Lz)/(2k)].
Bflux(τ)0Ldzbflux(z,τ),
bflux(z,τ)=4πk2d2κϕn(κ,z)exp[iκ·v(z)τ]×jinc2(γκR){1cos[κ2γ(Lz)/k]},
bflux(z,τ)=8π2k20dκκϕn(κ,z)J0[κv(z)τ]×jinc2(γκR){1cos[κ2γ(Lz)/k]},
Δ=12πBflux(0)/Bflux(0),
Bflux(0)=4π2k20Ldzv2(z)0dκκ3ϕn(κ,z)×jinc2(γκR){1cos[κ2γ(Lz)/k]}.
Bflux(0)=01dξC^n2(ξL)w1(ξ),
Bflux(0)=01dξC^n2(ξL)ωv2(ξL)w2(ξ),
w1(ξ)=8.702×{cos[arctan(qp1γ(1ξ))×5/6]×[qp2+γ2(1ξ)2]5/12qp5/6},
w2(ξ)=3.626×{cos[arctan(qp1γ(1ξ))×1/6]×[qp2+γ2(1ξ)2]1/12+qp1/6},
Δ12πw2(0)/w1(0)ωv,rms,
ωv,rms=[01dξωv2(ξL)wv(ξ)]/[01dξwv(ξ)]
Δ12πw2(0.5)/w1(0.5)ωv,rms,
Cn,alt2(h)=5.94×1053(Vrms/27)2h10exp(h/103)+2.7×1016exp(h/1500)+Aexp(h/100),
Vrms=[115×103500020000valt2(h)dh]1/2
valt(h)=5+30exp[(h9400)2/48002]
ΔΔ¯={01dξvalt2(ζuH)C^n,alt2(ζuH)w2(ξ)Vrms201dξC^n,alt2(ζuH)w2(ξ)uplink,01dξvalt2(ζdH)C^n,alt2(ζdH)w2(ξ)Vrms201dξC^n,alt2(ζdH)w2(ξ)downlink
V˜rms=[01dξv2(ξL)wv(ξ)]/[01dξwv(ξ)],