Abstract

The structure of an optical vortex formed in a partially coherent Laguerre–Gauss laser beam was considered. The main object of study was the recorded vector field of wavefront tilts that consisted of the vortical and potential components. It was found that the vortical motion weakened as the coherence decreased. Main regularities in the behavior of the vortical component can be described by the Scully vortex model of vortical liquid flow. In the spatial evolution, the potential component of tilts may alternate the sign, thus determining the direction of energy flow to the center or to the periphery of the vortex. Energy flow lines in the beam demonstrate the pattern of decay of an optical vortex similar to the pattern of decaying vortical motion in viscous liquid.

© 2012 Optical Society of America

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References

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2008 (2)

2007 (2)

G. A Swartzlander and R. I. Hernandes-Aranda, “Optical Rankine vortex and anomalous circulation of light,” Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 307–310 (2007).
[CrossRef]

2006 (1)

2005 (1)

2004 (1)

2002 (2)

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Wave and ray spatial dynamics of the light field in the generation, evolution, and annihilation of phase dislocations,” Opt. Spectrosc. 92, 409–418 (2002).
[CrossRef]

V. P. Aksenov and O. V. Tikhomirova, “Theory of singular-phase reconstruction for an optical speckle field in the turbulent atmosphere,” J. Opt. Soc. Am. A 19, 345–355 (2002).
[CrossRef]

2001 (1)

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Spatial ray dynamics at forming of optical speckle-field,” Proc. SPIE 4403, 108–114 (2001).
[CrossRef]

Aksenov, V.

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Wave and ray spatial dynamics of the light field in the generation, evolution, and annihilation of phase dislocations,” Opt. Spectrosc. 92, 409–418 (2002).
[CrossRef]

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Spatial ray dynamics at forming of optical speckle-field,” Proc. SPIE 4403, 108–114 (2001).
[CrossRef]

Aksenov, V. P.

Alekseenko, S. V.

S. V. Alekseenko, P. A. Kuibin, and V. L. Okulov, Theory of Concentrated Vortices: An Introduction (Springer, 2007).

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[CrossRef]

Bekshaev, A.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[CrossRef]

Gbur, G.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes(Oxford University, 1998).

Hernandes-Aranda, R. I.

G. A Swartzlander and R. I. Hernandes-Aranda, “Optical Rankine vortex and anomalous circulation of light,” Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

Izmailov, I.

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Wave and ray spatial dynamics of the light field in the generation, evolution, and annihilation of phase dislocations,” Opt. Spectrosc. 92, 409–418 (2002).
[CrossRef]

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Spatial ray dynamics at forming of optical speckle-field,” Proc. SPIE 4403, 108–114 (2001).
[CrossRef]

Keen, S.

Kolosov, V.

Kuibin, P. A.

S. V. Alekseenko, P. A. Kuibin, and V. L. Okulov, Theory of Concentrated Vortices: An Introduction (Springer, 2007).

Leach, J.

Maleev, I. D.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Marathay, A. S.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 307–310 (2007).
[CrossRef]

Okulov, V. L.

S. V. Alekseenko, P. A. Kuibin, and V. L. Okulov, Theory of Concentrated Vortices: An Introduction (Springer, 2007).

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[CrossRef]

Padgett, M. J.

Palacios, D. M.

Poizner, B.

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Wave and ray spatial dynamics of the light field in the generation, evolution, and annihilation of phase dislocations,” Opt. Spectrosc. 92, 409–418 (2002).
[CrossRef]

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Spatial ray dynamics at forming of optical speckle-field,” Proc. SPIE 4403, 108–114 (2001).
[CrossRef]

Soskin, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

Swartzlander, G. A

G. A Swartzlander and R. I. Hernandes-Aranda, “Optical Rankine vortex and anomalous circulation of light,” Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

Swartzlander, G. A.

Tikhomirova, O.

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Wave and ray spatial dynamics of the light field in the generation, evolution, and annihilation of phase dislocations,” Opt. Spectrosc. 92, 409–418 (2002).
[CrossRef]

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Spatial ray dynamics at forming of optical speckle-field,” Proc. SPIE 4403, 108–114 (2001).
[CrossRef]

Tikhomirova, O. V.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 307–310 (2007).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 307–310 (2007).
[CrossRef]

Vasnetsov, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

Vorontsov, M.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Laser Photon. Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[CrossRef]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 307–310 (2007).
[CrossRef]

Opt. Express (1)

Opt. Spectrosc. (1)

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Wave and ray spatial dynamics of the light field in the generation, evolution, and annihilation of phase dislocations,” Opt. Spectrosc. 92, 409–418 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

G. A Swartzlander and R. I. Hernandes-Aranda, “Optical Rankine vortex and anomalous circulation of light,” Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

Proc. SPIE (1)

V. Aksenov, I. Izmailov, B. Poizner, and O. Tikhomirova, “Spatial ray dynamics at forming of optical speckle-field,” Proc. SPIE 4403, 108–114 (2001).
[CrossRef]

Other (4)

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

S. V. Alekseenko, P. A. Kuibin, and V. L. Okulov, Theory of Concentrated Vortices: An Introduction (Springer, 2007).

J. W. Hardy, Adaptive Optics for Astronomical Telescopes(Oxford University, 1998).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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Figures (2)

Fig. 1.
Fig. 1.

Normalized circulation of average wavefront tilts (curve 1) and distribution of αφ over the beam cross-section (curve 2) calculated at z=zd; a=0.05m; lc=0,354 m; λ=1.69μm.

Fig. 2.
Fig. 2.

Average energy flow lines LG01 of the beam at a=0.05m, λ=1.69μm.

Equations (22)

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{rjc}={MFj1}/{MFj0},j=1,,N
{rjc}={MFj1}/{MFj0},
{αj}={rjc}/F=(1/F){MFj1}/{MFj0}.
α(R,z)=(ik)1ρlnΓ2,1(R,ρ0,z),
Γ2,1(R,ρ,z)=u(R+ρ/2,z,t)u*(Rρ/2,z,t)
Γ2,1(R,ρ,0)=u021a2(R2ρ2/4+i(RxρyRyρx))exp{R2a2ρ24a2ρ2lC2},
Γ2,1(R,ρ,z)=u02a2ae2exp{R2ae2ρ24ρa12+iχae2Rρ}×{1g2(g2+4a2/lC2)1[1R2ae2]ρ24ρa22i4Ω(g2+4a2/lC2)1a2lC2Rρae2iRxρyRyρxae2}.
ae=a[1+Ω2(1+4a2/lC2)]1/2,ρa12=ae2(1+4a2/lC2)1,χ=Ω1(1+4a2/lC2)Ω,ρa2=ae[1+4a2/lC2(1a2/ae2)]1/2,g2=1+Ω2,Ω=ka2z.
Γ2,1(0,ρ,z)=u02a2ae2exp{ρ24ρa12}{4(g2+4a2/lC2)1a2lC2ρ24ρa22}.
Rpd=alC2ρa2(g2+4a2/lC2)1/2
α(R,ϕ,z)=αRr^+αϕφ^,
αR=Rz{12ΩCΩ[1zkΩCε2(12a2lC2g2(R/ε)2)][1+(R/ε)2]1},
αϕ=RzΩC1+(R/ε)2
Ωz(R,z)=lC2k2z2[1+(R/ε)2]2.
Γ(R,z)=2π0RΩz(R,z)RdR,
Γ(R,z)=2πΩczR21+(R/ε)2,
Γ(,z)=2πk(1+4a2lC2g2).
αϕ=Γ(R,z)2πR.
Rpd=4zklCε(ε2+a2g2(1+4a2/lC2)ΩC2)1/2.
α(R,z)=I(R,z,t)S(R,z,t)kI(R,z,t),
Rs=ε[Ω214a2lC2]1/2[1+4a2lC2]1/2.
dR(z)dz=αRr^+αϕφ^,R(0)=R0.

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