Abstract

When a phase singularity is suddenly imprinted on the axis of an ordinary Gaussian beam, an optical vortex appears and starts to grow radially, by effect of diffraction. This radial growth and the subsequent evolution of the optical vortex under focusing or imaging can be well described in general within the recently introduced theory of circular beams, which generalize the hypergeometric-Gaussian beams and which obey novel kinds of ABCD rules. Here, we investigate experimentally these vortex propagation phenomena and test the validity of circular-beam theory. Moreover, we analyze the difference in radial structure between the newly generated optical vortex and the vortex obtained in the image plane, where perfect imaging would lead to complete closure of the vortex core.

© 2016 Optical Society of America

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References

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  1. J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. A 336, 165–190 (1974).
    [Crossref]
  2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
    [Crossref] [PubMed]
  3. M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [Crossref]
  4. N. R. Heckenberg, R. McDuff, C. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [Crossref] [PubMed]
  5. L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
    [Crossref] [PubMed]
  6. B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
    [Crossref]
  7. V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
    [Crossref]
  8. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  21. A. Y. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction gratings with embedded phase singularity,” Opt. Commun. 281, 1366–1374 (2008).
    [Crossref]

2016 (1)

2015 (2)

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
[Crossref]

G. Vallone, “On the properties of circular beams: normalization, Laguerre Gauss expansion, and free-space divergence,” Opt. Lett. 40, 1717–1720 (2015).
[Crossref] [PubMed]

2014 (1)

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

2012 (1)

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

2011 (1)

2010 (1)

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

2008 (3)

2007 (1)

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

2005 (2)

1998 (1)

1994 (1)

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

1992 (2)

N. R. Heckenberg, R. McDuff, C. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref] [PubMed]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref] [PubMed]

Aolita, L.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Baccari, F.

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
[Crossref]

Bandres, M. A.

Beijersbergen, M.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref] [PubMed]

Bekshaev, A. Y.

A. Y. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction gratings with embedded phase singularity,” Opt. Commun. 281, 1366–1374 (2008).
[Crossref]

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

Coerwinkel, R.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

D’Ambrosio, V.

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

Gbur, Greg

Grier, D. G.

Gruzberg, I.

Gutiérrez-Vega, J. C.

Heckenberg, N. R.

Karamoch, A. I.

A. Y. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction gratings with embedded phase singularity,” Opt. Commun. 281, 1366–1374 (2008).
[Crossref]

Karimi, E.

Kotlyar, V. V.

Kristensen, M.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Mari, E.

G. Vallone, G. Parisi, F. Spinello, E. Mari, F. Tamburini, and P. Villoresi, “A general theorem on the divergence of vortex beams,” [arXiv:1601.02350] (2016).

Marrucci, L.

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Improved focusing with Hypergeometric-Gaussian type-II optical modes,” Opt. Express 16, 21069–21075 (2008).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

McDuff, R.

Nagali, E.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

Padgett, M. J.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Parisi, G.

G. Vallone, G. Parisi, F. Spinello, E. Mari, F. Tamburini, and P. Villoresi, “A general theorem on the divergence of vortex beams,” [arXiv:1601.02350] (2016).

Piccirillo, B.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Improved focusing with Hypergeometric-Gaussian type-II optical modes,” Opt. Express 16, 21069–21075 (2008).
[Crossref] [PubMed]

Rozas, D.

Sacks, Z. S.

Santamato, E.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Improved focusing with Hypergeometric-Gaussian type-II optical modes,” Opt. Express 16, 21069–21075 (2008).
[Crossref] [PubMed]

Sciarrino, F.

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers, (University Science, 1986).

Slussarenko, S.

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

Smith, C.

Spinello, F.

G. Vallone, G. Parisi, F. Spinello, E. Mari, F. Tamburini, and P. Villoresi, “A general theorem on the divergence of vortex beams,” [arXiv:1601.02350] (2016).

Sponselli, A.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref] [PubMed]

Sundbeck, S.

Swartzlander, G. A.

Tamburini, F.

G. Vallone, G. Parisi, F. Spinello, E. Mari, F. Tamburini, and P. Villoresi, “A general theorem on the divergence of vortex beams,” [arXiv:1601.02350] (2016).

Vallone, G.

G. Vallone, “On the properties of circular beams: normalization, Laguerre Gauss expansion, and free-space divergence,” Opt. Lett. 40, 1717–1720 (2015).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

G. Vallone, G. Parisi, F. Spinello, E. Mari, F. Tamburini, and P. Villoresi, “A general theorem on the divergence of vortex beams,” [arXiv:1601.02350] (2016).

Villoresi, P.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

G. Vallone, G. Parisi, F. Spinello, E. Mari, F. Tamburini, and P. Villoresi, “A general theorem on the divergence of vortex beams,” [arXiv:1601.02350] (2016).

Walborn, S. P.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

White, A. G.

Woerdman, J.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref] [PubMed]

Yao, A. M.

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Opt. Commun. (2)

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

A. Y. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction gratings with embedded phase singularity,” Opt. Commun. 281, 1366–1374 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (5)

Optica (1)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8190 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Proc. R. Soc. A (1)

J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

Sci. Rep. (1)

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
[Crossref]

Other (2)

G. Vallone, G. Parisi, F. Spinello, E. Mari, F. Tamburini, and P. Villoresi, “A general theorem on the divergence of vortex beams,” [arXiv:1601.02350] (2016).

A. E. Siegman, Lasers, (University Science, 1986).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. A Gaussian beam is sent through a q-plate that is placed at the beam waist location and generates the optical vortex. The obtained beam passes then through two lenses with focal lengths f1 and f2. This defines three interesting propagation zones which will be analyzed: (B) newly generated vortex in free propagation; (C) focused vortex; (D) controlled imaging of the vortex source plane.

Fig. 2
Fig. 2

“Birth” of the optical vortex. In the first row we show the experimental intensity patterns obtained after the q-plate placed at the beam waist location at various propagation distances d. The data should be compared with the theoretical CiB model shown in the second row. In the third row we show the corresponding Laguerre-Gauss mode with the same z0 and beam waist located at d = 0. The degree of agreement between the two models and the experiment is measured by the reported similarity values, S, given in each panel and shown in the right inset for different values of d.

Fig. 3
Fig. 3

Left: Focusing of an optical vortex by a lens. Experimental (upper row) and theoretical (lower row) intensity patterns obtained at various distances d from the focusing lens. Right: Quasi-closure of the optical vortex occurring when a real image of the vortex source is created by a lens system. Experimental (upper row) and theoretical (lower row) intensity patterns obtained at various distances d from the second lens. The medium panel for d = 200 mm corresponds to the image plane.

Equations (4)

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

CiB p , ( ξ , q 0 ) = N ( 1 + ξ q 0 * q 0 ) p 2 ( i k z 0 r q 0 )   | | G ( r ) 1 F 1 ( p 2 , | | + 1 ; r 2 χ 2 ) e i ϕ .
q 0 A q 0 + B C q 0 + D , ξ C q 0 * + D C q 0 + D ξ .
CiB | | , ( ξ , q 0 ) = Γ ( | | / 2 + 1 ) | | ! ( r 2 ξ χ 2 ) | | 2 G ( r ) 1 F 1 ( | | 2 , | | + 1 ; r 2 χ 2 ) e i ϕ , when | ξ | = 1 .
q 0 ( d ) = ( d + d 1 ) f 1 d d 1 + i z 0 ( f 1 d ) f d 1 i z 0 , ξ C = f 1 d 1 + i z 0 f 1 d 1 i z 0 .

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