Abstract

Partially coherent beams hold much promise in free-space optical communications for their resistance to the deleterious effects of atmospheric turbulence. We describe the basic theoretical and computational tools used to investigate these effects, and review the research to date.

© 2014 Optical Society of America

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  76. G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, “Suppression of intensity fluctuations in free space high-speed optical communication based on spectral encoding of a partially coherent beam,” Opt. Commun. 280, 264–270 (2007).
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  85. P. Polynki, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. 32, 885–887 (2007).
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  86. O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281, 2342–2348 (2008).
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  87. Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008).
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    [CrossRef]
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  92. Y. Gu and G. Gbur, “Reduction of turbulence-induced scintillation by nonuniformly polarized beam arrays,” Opt. Lett. 37, 1553–1555 (2012).
    [CrossRef]

2013

2012

2011

2010

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18, 10777–10785 (2010).
[CrossRef]

Y. Gu and G. Gbur, “Scintillation of Airy beam arrays in atmospheric turbulence,” Opt. Lett. 35, 3456–3458 (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]

C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of J0- and I0-Bessel Gaussian beams propagating in turbulent atmosphere,” Appl. Phys. B 98, 195–202 (2010).
[CrossRef]

Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283, 1209–1212 (2010).
[CrossRef]

2009

2008

2007

W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue,” Opt. Commun. 270, 474–478 (2007).
[CrossRef]

A. Peleg and J. V. Moloney, “Scintillation reduction by use of multiple Gaussian laser beams with different wavelengths,” IEEE Photon. Technol. Lett. 19, 883–885 (2007).
[CrossRef]

G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, “Suppression of intensity fluctuations in free space high-speed optical communication based on spectral encoding of a partially coherent beam,” Opt. Commun. 280, 264–270 (2007).
[CrossRef]

G. A. Sililoglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32, 3531–3533 (2007).
[CrossRef]

G. Gbur and O. Korotkova, “Angular spectrum representation for the propagation of arbitrary coherent and partially coherent beams through atmospheric turbulence,” J. Opt. Soc. Am. A 24, 745–752 (2007).
[CrossRef]

P. Polynki, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. 32, 885–887 (2007).
[CrossRef]

O. Korotkova and G. Gbur, “Angular spectrum representation for propagation of random electromagnetic beams in turbulent atmosphere,” J. Opt. Soc. Am. A 24, 2728–2736 (2007).
[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of elliptical Gaussian beam in turbulent atmosphere,” Opt. Lett. 32, 2405–2407 (2007).
[CrossRef]

2006

2005

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
[CrossRef]

E. Baleine and A. Dogariu, “Variable coherence scattering microscopy,” Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef]

J. Recolons and F. Dios, “Accurate calculation of phase screens for the modelling of laser beam propagation through atmospheric turbulence,” Proc. SPIE 5891, 589107 (2005).
[CrossRef]

Y. Baykal, “Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium,” J. Opt. Soc. Am. A 22, 672–679 (2005).
[CrossRef]

T. J. Schulz, “Optimal beams for propagation through random media,” Opt. Lett. 30, 1093–1095 (2005).
[CrossRef]

2004

E. Baleine and A. Dogariu, “Variable-coherence tomography for inverse scattering problems,” J. Opt. Soc. Am. A 21, 1917–1923 (2004).
[CrossRef]

T. J. Schulz, “Iterative transform algorithm for the computation of optimal beams,” J. Opt. Soc. Am. A 21, 1970–1974 (2004).
[CrossRef]

Y. Baykal, “Average transmittance in turbulence for partially coherent sources,” Opt. Commun. 231, 129–136 (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]

F. E. Strömqvist Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).
[CrossRef]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Complex Media 14, 513–523 (2004).
[CrossRef]

D. Voelz and K. Fitzhenry, “Pseudo-partially coherent beam for free-space laser communication,” Proc. SPIE 5550, 218–224 (2004).

2003

2002

2000

1992

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

1991

J. Wu and A. D. Boardman, “Coherence length of a Gaussian-Schell beam and atmospheric turbulence,” J. Mod. Opt. 38, 1355–1363 (1991).
[CrossRef]

1990

J. Wu, “Propagation of a Gaussian-Schell beam through turbulent media,” J. Mod. Opt. 37, 671–684 (1990).
[CrossRef]

1988

1983

V. A. Banach, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

V. A. Banakh and V. M. Buldakov, “Effect of the initial degree of spatial coherence of a light beam on intensity fluctuations in a turbulent atmosphere,” Opt. Spectrosc. 54, 423–427 (1983).

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
[CrossRef]

1982

1981

R. L. Fante, “Two-position, two-frequency mutual-coherence function in turbulence,” J. Opt. Soc. Am. 71, 1446–1451 (1981).
[CrossRef]

R. L. Fante, “Intensity fluctuations of an optical wave in a turbulent medium; effect of source coherence,” Opt. Acta 28, 1203–1207 (1981).
[CrossRef]

1980

1979

1978

1977

M. S. Belen’kii, A. I. Kon, and V. L. Mironov, “Turbulent distortions of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

V. A. Banakh and V. L. Mironov, “Phase approximation of the Huygens-Kirchhoff method in problems of laser-beam propagation in the turbulent atmosphere,” Opt. Lett. 1, 172–174 (1977).
[CrossRef]

1974

1972

H. T. Yura, “Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,” Appl. Opt. 11, 1399–1406 (1972).
[CrossRef]

A. I. Kon and V. I. Tatarskii, “On the theory of the propagation of partially coherent light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 15, 1187–1192 (1972).
[CrossRef]

1971

1967

L. S. Taylor, “Decay of mutual coherence in turbulent media,” J. Opt. Soc. Am. 57, 304–308 (1967).
[CrossRef]

Z. I. Feizulin and Y. A. Kravtsov, “Broadening of a laser beam in a turbulent medium,” Radiophys. Quantum Electron. 10, 33–35 (1967).
[CrossRef]

1966

1964

Alonso, M. A.

Amarande, S.

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, 330–341 (2004).
[CrossRef]

F. E. Strömqvist Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Baleine, E.

E. Baleine and A. Dogariu, “Variable coherence scattering microscopy,” Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef]

E. Baleine and A. Dogariu, “Variable-coherence tomography for inverse scattering problems,” J. Opt. Soc. Am. A 21, 1917–1923 (2004).
[CrossRef]

Banach, V. A.

V. A. Banach, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

Banakh, V. A.

Baykal, Y.

H. Gerçekcioğlu and Y. Baykal, “Scintillation index of flat-topped Gaussian laser beam in strongly turbulent medium,” J. Opt. Soc. Am. A 28, 1540–1544 (2011).
[CrossRef]

C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of J0- and I0-Bessel Gaussian beams propagating in turbulent atmosphere,” Appl. Phys. B 98, 195–202 (2010).
[CrossRef]

H. T. Eyyuboğlu, Y. Baykal, E. Sermutlu, O. Korotkova, and Y. Cai, “Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media,” J. Opt. Soc. Am. A 26, 387–394 (2009).
[CrossRef]

Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Scintillations of partially coherent multiple Gaussian beams in turbulence,” Appl. Opt. 48, 1943–1954 (2009).
[CrossRef]

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16, 7665–7673 (2008).
[CrossRef]

H. T. Eyyuboğlu, Y. Baykal, E. Sermutlu, and Y. Cai, “Scintillation advantages of lowest order Bessel-Gaussian beams,” Appl. Phys. B 92, 229–235 (2008).
[CrossRef]

Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008).
[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of elliptical Gaussian beam in turbulent atmosphere,” Opt. Lett. 32, 2405–2407 (2007).
[CrossRef]

Y. Baykal, “Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium,” J. Opt. Soc. Am. A 22, 672–679 (2005).
[CrossRef]

Y. Baykal, “Average transmittance in turbulence for partially coherent sources,” Opt. Commun. 231, 129–136 (2004).
[CrossRef]

Beckley, A. M.

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Figures (3)

Fig. 1.
Fig. 1.

Illustration of the geometry of beam propagation through the atmosphere.

Fig. 2.
Fig. 2.

Simple illustration of a model for atmospheric turbulence.

Fig. 3.
Fig. 3.

Simple illustration of the turbulence resistance of PC beams. A PC beam will simultaneously “sample” multiple paths through the turbulence, and the mutually incoherent beams will not produce interference speckle at the detector. Figure adapted from [37].

Equations (32)

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U(r,L,ω)=ik2πLexp(ikL)U0(ρ,ω)exp[ik|ρr|22L+ψ(r,ρ,L)]d2ρ,
W2(r1,r2,L)=U(r1,L)U*(r2,L)=U0(ρ1)U0*(ρ2)G0(ρ1,r1)G0*(ρ2,r2)×M2[{ri,ρi},L]d2ρ1d2ρ2
W4(r1,r2,r3,r4,L)=U(r1,L)U*(r2,L)U(r3,L)U*(r4,L)=U0(ρ1)U0*(ρ2)U0(ρ3)U0*(ρ4)×G0(ρ1,r1)G0*(ρ2,r2)G0(ρ3,r3)G0*(ρ4,r4)×M4[{ri,ρi},L]d2ρ1d2ρ2d2ρ3d2ρ4,
M2[{ri,ρi},L]=exp[ψ(r1,ρ1,L)+ψ*(r2,ρ2,L)],
M4[{ri,ρi},L]=exp[ψ(r1,ρ1,L)+ψ*(r2,ρ2,L)+ψ(r3,ρ3,L)+ψ*(r4,ρ4,L)],
G0(ρ,r)=ik2πLexp(ikL)exp[ik|ρr|22L]
exp[Ψ(r,L)]=exp[K1+12K2],
K1=Ψ(r,L),
K2=Ψ2(r,L)Ψ(r,L)2.
M2[{ri,ρi},L]=exp[2E1(0,0;0,0)+E2(r1,r2;ρ1,ρ2)],
M4[{ri,ρi},L]=exp[4E1(0,0;0,0)+E2(r1,r2;ρ1,ρ2)+E2(r1,r4;ρ1,ρ4)+E2(r3,r2;ρ3,ρ2)+E2(r2,r4;ρ2,ρ4)+E3(r1,r3;ρ1,ρ3)+E3*(r2,r4;ρ2,ρ4)],
E1(0,0;0,0)=2π2k2L0κΦn(κ)dκ,
E2(r1,r2;ρ1,ρ2)=4π2k2L010κΦn(κ)J0[κ|(1ξ)Δr+ξΔρ|]dκdξ,
E3(r1,r2;ρ1,ρ2)=4π2k2L010κΦn(κ)J0[κ|(1ξ)Δr+ξΔρ|]exp[iLκ2ξ(1ξ)/k]dκdξ.
Φn(κ)=0.033Cn2κ11/3,1/L0κ1/l0.
Φn(κ)=0.033Cn2κ11/3exp(κ2/κm2),1/L0κ,
Φn(κ)=0.033Cn2exp(κ2/κm2)(κ2+κ02)11/6,
W0(ρ1,ρ2,ω)=U0(ρ1,ω)U0*(ρ2,ω)ω,
W(r1,r2,ω)=nλn(ω)ϕn(r1,ω)ϕn*(r2,ω),
W(r1,r2,ω)ϕn(r2,ω)d2r2=λn(ω)ϕn(r1,ω),
σI2=I2I21,
σ12=1.23Cn2k7/6z11/6,
U0(ρ1)U0*(ρ2)U0(ρ3)U0*(ρ4)=W0(ρ1,ρ2)W0(ρ3,ρ4),
U0(ρ1)U0*(ρ2)U0(ρ3)U0*(ρ4)=W0(ρ1,ρ2)W0(ρ3,ρ4)+W0(ρ1,ρ4)W0(ρ3,ρ2).
τcτdτbτt.
[2+n2(r)k2]U(r)=0,
U(r)=V(r)eikz,
2ikzV+2V+k2(n21)V=0,
2ikzV+2V+2k2ΔnV=0.
Φθ(κ)=2πk2δzΦn(κ).
W(r1,r2)=I(r1)I(r2)μ(r2r1),
μ(r2r1)=μ˜(K)exp[iK·r2]exp[iK·r1]d2K.

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