Abstract

A general formulation is presented that describes the propagation of the rotational field correlation of an optical beam through atmospheric turbulence. The associated influence on the orbital angular momentum (OAM) of a single photon is described analytically. The analysis predicts the probability of change in the OAM state due to the process of propagating through turbulence. The probability of a change in an OAM state depends on the Fresnel number and on the ratio of the beam diameter to the Fried parameter.

© 2014 Optical Society of America

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References

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    [CrossRef]
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2012 (1)

2011 (2)

2009 (1)

2005 (1)

C. Paterson, Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

1983 (1)

1976 (1)

Andrew, L.

L. Andrew and R. Philips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Andrews, L.

Boyd, R.

Ishimaru, A.

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

Lavery, M.

Malik, M.

Mirhosseni, M.

Noll, R.

O’Sullivan, M.

Oesch, D.

Padgett, M.

Paterson, C.

C. Paterson, Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

Philips, R.

L. Andrew and R. Philips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Phillips, R.

Robertson, D.

Rodenburg, B.

Sanchez, D.

Tyler, G.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

C. Paterson, Phys. Rev. Lett. 94, 153901 (2005).
[CrossRef]

Other (2)

L. Andrew and R. Philips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

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

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram for OAM analysis.

Fig. 2.
Fig. 2.

Probability of change in the OAM state of a vortex beam of uniform amplitude versus the ratio D/ro.

Fig. 3.
Fig. 3.

Probability of change in the OAM states as a function of Fresnel number. Solid curves represent a vortex beam with uniform amplitude, and dashed curves represent a Laguerre–Gaussian beam of mode, LG01.

Fig. 4.
Fig. 4.

Probability of change in the OAM state of as a function of D/r0.

Equations (17)

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Cψ(ρ⃗,z)=d2rCψ(r⃗,0)G(r⃗,ρ⃗,k,z)exp(D(r⃗,ρ⃗)),
G(r⃗,ρ⃗,k,z)=(k2πz)2exp[ikzrρcos(ΔϕΔθ)],
D(r⃗,ρ⃗)=3.44r05/301|(1ν)(ρ⃗ρ⃗)ν(r⃗r⃗)|5/3dν,
D(r⃗,ρ⃗)=3.44(2r0)5/3(ρsin(Δϕ/2))8/3(rsin(Δθ/2))8/3ρsin(Δϕ/2)rsin(Δθ/2).
Cψ(r⃗,0)=ψ(r,0,0)ψ*(r,Δθ,0)δ(Δθ).
Cψ(r⃗,0)=|R(r)|2exp(imΔθ)δ(Δθ/2π).
Cψ(ρ,Δϕ,z)=12π(kz)2exp[3.44(2ρr0sin(Δϕ/2))5/3]×dr|R(r)|2rexp[ikzrρcosΔϕ].
n=ineinΔθ(kz)2dr|R(r)|2rJn(ikrρ/z)=n=ineinΔθHn(|R(r)|2),
Cψ(ρ,Δϕ,z)=IB{|R(r)|2}exp[3.44(2ρrosin(Δϕ/2))5/3].
Cψ(ρ,Δϕ,z)=2J1(wkρ/z)wkρ/zexp[3.44(2ρrosin(Δϕ/2))5/3],
P(Δm)=2πα01dρJ1(αρ)×02πdΔϕexp[3.44(2wr0ρsin(Δϕ/2))5/3]exp(iΔmΔϕ),
IB{|R(r)01|2}=(1w2k24z2ρ2)exp(w2k24z2ρ2).
P(Δm)=2πα01dρρ(1α24ρ2)exp(α24ρ2)×02πdΔϕexp[3.44(2wr0ρsin(Δϕ/2))5/3]exp(iΔmΔϕ).
σs/a2=2πk20ζdζFs/a(ζ)Φ(ζ),
Fs/a(ζ)=1±sin(ζ2L/k)(ζ2L/k).
σs2=1.02(D/ro)5/3,
σa2=exp(4σr2)1.

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