Abstract

Based on Zernike-model expansion of turbulence phase aberrations and non-Kolmogorov spectrum model of index-of-refraction fluctuation, we analyze the effects of low-order Zernike turbulence aberrations on orbital angular momentum (OAM) entanglement states in a weak fluctuation region. The signal photon detection probability of OAM entanglement states propagating in a slant turbulence channel with non-Kolmogorov turbulence Z-tilt, defocus, astigmatism, and coma aberrations are modeled, respectively. The results demonstrate that turbulence Z-tilt aberration is the dominant aberration, coma is the second, and astigmatism is the third, but that the defocus aberration has no impact on the detection probability. As the power-law exponent of the non-Kolmogorov spectrum increases from 3 to 4, the detection probability decreases.

© 2012 Optical Society of America

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  1. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
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  11. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
    [CrossRef]

2011 (3)

F. S. Roux, Phys. Rev. A 83, 053822 (2011).
[CrossRef]

B. J. Pors, C. H. Monken, E. R. Eliel, and J. P. Woerdman, Opt. Express 19, 6671 (2011).
[CrossRef]

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, Opt. Commun. 284, 1132 (2011).
[CrossRef]

2008 (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

2007 (2)

A. Tunick, Proc. SPIE 6708, 670802 (2007).
[CrossRef]

C. Gopaul and R. Andrews, New J. Phys. 9, 94 (2007).
[CrossRef]

2006 (1)

B. J. Smith and M. G. Raymer, Phys. Rev. A 74, 062104 (2006).
[CrossRef]

2004 (1)

1995 (1)

B. E. Stribling, B. M. Welsh, and C. Roggemann, Proc. SPIE 2472, 181 (1995).
[CrossRef]

1976 (1)

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005).

Andrews, R.

C. Gopaul and R. Andrews, New J. Phys. 9, 94 (2007).
[CrossRef]

Barnett, S. M.

Courtial, J.

Eliel, E. R.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Franke-Arnold, S.

Gibson, G.

Gopaul, C.

C. Gopaul and R. Andrews, New J. Phys. 9, 94 (2007).
[CrossRef]

Jia, J.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, Opt. Commun. 284, 1132 (2011).
[CrossRef]

Monken, C. H.

Padgett, M. J.

Pas’ko, V.

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005).

Pors, B. J.

Raymer, M. G.

B. J. Smith and M. G. Raymer, Phys. Rev. A 74, 062104 (2006).
[CrossRef]

Robert, J. N.

Roggemann, C.

B. E. Stribling, B. M. Welsh, and C. Roggemann, Proc. SPIE 2472, 181 (1995).
[CrossRef]

Roux, F. S.

F. S. Roux, Phys. Rev. A 83, 053822 (2011).
[CrossRef]

Smith, B. J.

B. J. Smith and M. G. Raymer, Phys. Rev. A 74, 062104 (2006).
[CrossRef]

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and C. Roggemann, Proc. SPIE 2472, 181 (1995).
[CrossRef]

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Tunick, A.

A. Tunick, Proc. SPIE 6708, 670802 (2007).
[CrossRef]

Vasnetsov, M.

Wang, J.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, Opt. Commun. 284, 1132 (2011).
[CrossRef]

Wang, Y.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, Opt. Commun. 284, 1132 (2011).
[CrossRef]

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and C. Roggemann, Proc. SPIE 2472, 181 (1995).
[CrossRef]

Woerdman, J. P.

Xu, J.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, Opt. Commun. 284, 1132 (2011).
[CrossRef]

Zhang, Y.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, Opt. Commun. 284, 1132 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

New J. Phys. (1)

C. Gopaul and R. Andrews, New J. Phys. 9, 94 (2007).
[CrossRef]

Opt. Commun. (1)

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, Opt. Commun. 284, 1132 (2011).
[CrossRef]

Opt. Eng. (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (2)

F. S. Roux, Phys. Rev. A 83, 053822 (2011).
[CrossRef]

B. J. Smith and M. G. Raymer, Phys. Rev. A 74, 062104 (2006).
[CrossRef]

Proc. SPIE (2)

A. Tunick, Proc. SPIE 6708, 670802 (2007).
[CrossRef]

B. E. Stribling, B. M. Welsh, and C. Roggemann, Proc. SPIE 2472, 181 (1995).
[CrossRef]

Other (1)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005).

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Figures (5)

Fig. 1.
Fig. 1.

Detection probability versus propagation distance at total turbulent fluctuation (solid curve), turbulence Z-tilt (dash-dotted curve), astigmatism (dashed curve), and coma (dotted curve) aberrations. (a) lp=l1=0, (b) lp=l1=5.

Fig. 2.
Fig. 2.

Detection probability versus refractive-index structure parameter on the ground at total turbulent fluctuation (solid curve), turbulence Z-tilt (dash-dotted curve), astigmatism (dashed curve), and coma (dotted curve) aberrations, for lp=l1=1.

Fig. 3.
Fig. 3.

Detection probability versus channel zenith angle at total turbulent fluctuation (solid curve), turbulence Z-tilt (dash-dotted curve), astigmatism (dashed curve), and coma (dotted curve) aberrations, for lp=l1=1 and θ<π/3.

Fig. 4.
Fig. 4.

Detection probability versus diameter of circular sampling aperture at turbulence Z-tilt (dash-dotted curve), astigmatism (dashed curve), and coma (dotted curve) aberrations, for lp=l1=1.

Fig. 5.
Fig. 5.

Detection probability versus the power-law exponent of non-Kolmogorov spectrum α at total turbulent fluctuation (solid curve), turbulence Z-tilt (dash-dotted curve), astigmatism (dashed curve), and coma (dotted curve) aberrations, for lp=l1=1.

Equations (14)

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P(l1,l2)=Rlp(r)Rlp*(r)Rl1(r,z)Rl2(r,z)×expi[S(r,φ,z)S(r,φ,z)]×Rl1*(r,z)Rl2*(r,z)exp[iΔlΔφ]rdrrdrdΔφ,
Rli(r,z)=1wi1(|li|)!(rwi)|li|exp(r22wi2)exp(ikr24Ri),i=1,2,
expi[S(r,φ,z)S*(r,φ,z)]=exp[12DS(rr,Δφ)],
P(l1)=Rlp(r)Rlp*(r)Rl1(r,z)Rl1*(r,z)×exp[12DS(r,Δφ)]exp[i(l1lp)Δφ]rdrdΔφ.
ϕn(α,κ)=A(α)Cn2(z,α)κα,0κ<,3<α<5,
Cn2(z,α)=0.033(kz)α11/3[0.00594(υ/27)2(zcosθ×105)10×exp(zcosθ/1000)+2.7×1016exp(zcosθ/1500)+Cn2(0)exp(zcosθ/100)]/A(α),
DS(r,Δφ)2[2(1cosΔφ)r2/ρ02](α2)/2
Dtilt(r,Δφ)=8a2,32r2[1cosΔφ]
Ddef(r,Δφ)0
Dastig(r,Δφ)=24a5,62r4sin2Δφ
Dcoma(r,Δφ)=16a7,82(3r22r)2[1cosΔφ]
ρ0(α)={2Γ(3α2)π1/2k2Γ(2α2)z01Cn2(ξz,α)(1ξ)α2dξ}1/(α2),3<α<4,
|a2,3|2=(Dr0(α))α22Γ(4α2)Γ(α+42)Γ(α2)sin(πα22)πΓ(6+α2),|a5,6|2=(Dr0(α))α23Γ(6α2)Γ(α+42)Γ(α2)sin(πα22)πΓ(8+α2),|a7,8|2=(Dr0(α))α24Γ(8α2)Γ(α+42)Γ(α2)sin(πα22)πΓ(10+α2)
r0(α)={2Γ(3α2)(8α2Γ(2α2))(α2)/2π1/2k2Γ(2α2)0zCn2(ξ)(1ξz)α2dξ}1/(α2),3<α<4.

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