Abstract

A technique for generating dark-hollow optical beams (DHOBs) with a controllable cross-sectional intensity distribution is proposed and studied both theoretically and experimentally. Superimposed Bessel beams were used to generate such DHOBs. Variation of individual beam parameters enables the generation of Bessel-like non-diffracting beams. This technique allows the design of transmission functions for elements that shape both non-rotating and rotating DHOBs. We demonstrate photophoresis-based optical trapping and manipulation of absorbing air-borne nanoclusters with such beams.

© 2015 Optical Society of America

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References

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
    [Crossref]
  2. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [Crossref] [PubMed]
  3. D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
    [Crossref]
  4. N. Eckerskorn, L. Li, R. A. Kirian, J. Küpper, D. P. DePonte, W. Krolikowski, W. M. Lee, H. N. Chapman, and A. V. Rode, “Hollow Bessel-like beam as an optical guide for a stream of microscopic particles,” Opt. Express 21(25), 30492–30499 (2013).
    [Crossref] [PubMed]
  5. V. G. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
    [Crossref]
  6. V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, “Optical guiding of absorbing nanoclusters in air,” Opt. Express 17(7), 5743–5757 (2009).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. R. Ling-Ling, G. Zhong-Yi, and Q. Shi-Liang, “Rotational motions of optically trapped microscopic particles by a vortex femtosecond laser,” Chin. Phys. B. 21(10), 104206 (2012).
    [Crossref]
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    [Crossref]
  13. A. Dudley and A. Forbes, “From stationary annular rings to rotating Bessel beams,” J. Opt. Soc. Am. A 29(4), 567–573 (2012).
    [Crossref] [PubMed]
  14. A. P. Porfirev and R. V. Skidanov, “A simple method of the formation nondiffracting hollow optical beams with intensity distribution in form of a regular polygon contour,” Comput. Opt. 38(2), 243–248 (2014).
  15. V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images,” J. Mod. Opt. 44(7), 1409–1416 (1997).
    [Crossref]
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    [Crossref] [PubMed]
  18. H. Rohatschek, “Direction, magnitude and causes of photophoretic forces,” J. Aerosol Sci. 16(1), 29–42 (1985).
    [Crossref]
  19. O. Jovanovic, “Photophoresis: light-induced motion of particles suspended in gas,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 889–901 (2009).
    [Crossref]
  20. H. Rohatschek, “Semi-empirical model of photophoretic forces for the entire range of pressures,” J. Aerosol Sci. 26(5), 717–734 (1995).
    [Crossref]

2014 (2)

V. G. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

A. P. Porfirev and R. V. Skidanov, “A simple method of the formation nondiffracting hollow optical beams with intensity distribution in form of a regular polygon contour,” Comput. Opt. 38(2), 243–248 (2014).

2013 (2)

2012 (3)

R. Ling-Ling, G. Zhong-Yi, and Q. Shi-Liang, “Rotational motions of optically trapped microscopic particles by a vortex femtosecond laser,” Chin. Phys. B. 21(10), 104206 (2012).
[Crossref]

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt. 59(3), 259–267 (2012).
[Crossref]

A. Dudley and A. Forbes, “From stationary annular rings to rotating Bessel beams,” J. Opt. Soc. Am. A 29(4), 567–573 (2012).
[Crossref] [PubMed]

2010 (1)

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

2009 (3)

2005 (1)

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
[Crossref]

2003 (2)

1998 (1)

1997 (1)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images,” J. Mod. Opt. 44(7), 1409–1416 (1997).
[Crossref]

1995 (1)

H. Rohatschek, “Semi-empirical model of photophoretic forces for the entire range of pressures,” J. Aerosol Sci. 26(5), 717–734 (1995).
[Crossref]

1985 (1)

H. Rohatschek, “Direction, magnitude and causes of photophoretic forces,” J. Aerosol Sci. 16(1), 29–42 (1985).
[Crossref]

1974 (1)

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Ashkin, A.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Businaro, L.

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
[Crossref]

Chapman, H. N.

Chávez-Cerda, S.

Cojoc, D.

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
[Crossref]

Davoyan, A. R.

V. G. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

DePonte, D. P.

Desyatnikov, A. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, “Optical guiding of absorbing nanoclusters in air,” Opt. Express 17(7), 5743–5757 (2009).
[Crossref] [PubMed]

Dholakia, K.

Di Fabrizio, E.

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
[Crossref]

Dudley, A.

Eckerskorn, N.

Engheta, N.

V. G. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Fedotowsky, A.

Ferrari, E.

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
[Crossref]

Forbes, A.

Garbin, V.

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
[Crossref]

Garcés-Chávez, V.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Hickmann, J. M.

Hnatovsky, C.

V. G. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Izdebskaya, Y. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

Jovanovic, O.

O. Jovanovic, “Photophoresis: light-induced motion of particles suspended in gas,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 889–901 (2009).
[Crossref]

Khilo, N.

Khonina, S. N.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images,” J. Mod. Opt. 44(7), 1409–1416 (1997).
[Crossref]

Kirian, R. A.

Kivshar, Y. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, “Optical guiding of absorbing nanoclusters in air,” Opt. Express 17(7), 5743–5757 (2009).
[Crossref] [PubMed]

Kotlyar, V. V.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images,” J. Mod. Opt. 44(7), 1409–1416 (1997).
[Crossref]

Krolikowski, W.

V. G. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

N. Eckerskorn, L. Li, R. A. Kirian, J. Küpper, D. P. DePonte, W. Krolikowski, W. M. Lee, H. N. Chapman, and A. V. Rode, “Hollow Bessel-like beam as an optical guide for a stream of microscopic particles,” Opt. Express 21(25), 30492–30499 (2013).
[Crossref] [PubMed]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, “Optical guiding of absorbing nanoclusters in air,” Opt. Express 17(7), 5743–5757 (2009).
[Crossref] [PubMed]

Küpper, J.

Lee, W. M.

Lehovec, K.

Li, L.

Ling-Ling, R.

R. Ling-Ling, G. Zhong-Yi, and Q. Shi-Liang, “Rotational motions of optically trapped microscopic particles by a vortex femtosecond laser,” Chin. Phys. B. 21(10), 104206 (2012).
[Crossref]

Lopez-Mariscal, C.

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt. 59(3), 259–267 (2012).
[Crossref]

McGloin, D.

Meneses-Nava, M. A.

Porfirev, A. P.

A. P. Porfirev and R. V. Skidanov, “A simple method of the formation nondiffracting hollow optical beams with intensity distribution in form of a regular polygon contour,” Comput. Opt. 38(2), 243–248 (2014).

A. P. Porfirev and R. V. Skidanov, “Generation of an array of optical bottle beams using a superposition of Bessel beams,” Appl. Opt. 52(25), 6230–6238 (2013).
[Crossref] [PubMed]

Rode, A. V.

Rohatschek, H.

H. Rohatschek, “Semi-empirical model of photophoretic forces for the entire range of pressures,” J. Aerosol Sci. 26(5), 717–734 (1995).
[Crossref]

H. Rohatschek, “Direction, magnitude and causes of photophoretic forces,” J. Aerosol Sci. 16(1), 29–42 (1985).
[Crossref]

Romanato, F.

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
[Crossref]

Rop, R.

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt. 59(3), 259–267 (2012).
[Crossref]

Shi-Liang, Q.

R. Ling-Ling, G. Zhong-Yi, and Q. Shi-Liang, “Rotational motions of optically trapped microscopic particles by a vortex femtosecond laser,” Chin. Phys. B. 21(10), 104206 (2012).
[Crossref]

Shvedov, V. G.

V. G. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, “Optical guiding of absorbing nanoclusters in air,” Opt. Express 17(7), 5743–5757 (2009).
[Crossref] [PubMed]

Skidanov, R. V.

A. P. Porfirev and R. V. Skidanov, “A simple method of the formation nondiffracting hollow optical beams with intensity distribution in form of a regular polygon contour,” Comput. Opt. 38(2), 243–248 (2014).

A. P. Porfirev and R. V. Skidanov, “Generation of an array of optical bottle beams using a superposition of Bessel beams,” Appl. Opt. 52(25), 6230–6238 (2013).
[Crossref] [PubMed]

Soifer, V. A.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images,” J. Mod. Opt. 44(7), 1409–1416 (1997).
[Crossref]

Vasilyeu, R.

Zhong-Yi, G.

R. Ling-Ling, G. Zhong-Yi, and Q. Shi-Liang, “Rotational motions of optically trapped microscopic particles by a vortex femtosecond laser,” Chin. Phys. B. 21(10), 104206 (2012).
[Crossref]

Appl. Opt. (2)

Chin. Phys. B. (1)

R. Ling-Ling, G. Zhong-Yi, and Q. Shi-Liang, “Rotational motions of optically trapped microscopic particles by a vortex femtosecond laser,” Chin. Phys. B. 21(10), 104206 (2012).
[Crossref]

Comput. Opt. (1)

A. P. Porfirev and R. V. Skidanov, “A simple method of the formation nondiffracting hollow optical beams with intensity distribution in form of a regular polygon contour,” Comput. Opt. 38(2), 243–248 (2014).

J. Aerosol Sci. (2)

H. Rohatschek, “Direction, magnitude and causes of photophoretic forces,” J. Aerosol Sci. 16(1), 29–42 (1985).
[Crossref]

H. Rohatschek, “Semi-empirical model of photophoretic forces for the entire range of pressures,” J. Aerosol Sci. 26(5), 717–734 (1995).
[Crossref]

J. Mod. Opt. (2)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images,” J. Mod. Opt. 44(7), 1409–1416 (1997).
[Crossref]

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt. 59(3), 259–267 (2012).
[Crossref]

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

J. Quant. Spectrosc. Radiat. Transf. (1)

O. Jovanovic, “Photophoresis: light-induced motion of particles suspended in gas,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 889–901 (2009).
[Crossref]

Microelectron. Eng. (1)

D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, “Laser trapping and micro-manipulation using optical vortices,” Microelectron. Eng. 78–79, 125–131 (2005).
[Crossref]

Nat. Photonics (1)

V. G. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Supplementary Material (1)

» Media 1: AVI (3007 KB)     

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Figures (13)

Fig. 1
Fig. 1 The intensity (top row) and phase (bottom row) distributions of two superimposed Bessel beams (n = 8, m = 3, kr = 51996 m−1, and α = 0.2): (a), (e) z = 100 mm; (b), (f) z = 300 mm; (c), (g) z = 500 mm; and (d), (h) z = 700 mm. Mesh step is 200 μm.
Fig. 2
Fig. 2 The intensity (top row) and phase (bottom row) distributions of two superimposed Bessel beams (n = 4, m = −2, kr = 51996 m−1, and α = 0.4): (a), (e) z = 100 mm; (b), (f) z = 300 mm; (c), (g) z = 500 mm; and (d), (h) z = 700 mm. Mesh step is 100 μm.
Fig. 3
Fig. 3 The intensity (the top row) and phase (the bottom row) distributions of two superimposed Bessel beams (n = 4, m = −2, k r 1 =51996 m−1, k r 2 =48296 m−1, and α = 0.4): (a), (e) z = 100 mm; (b), (f) z = 300 mm; (c), (g) z = 500 mm; and (d), (h) z = 700 mm. Mesh step is 100 μm.
Fig. 4
Fig. 4 The phase function of the DOE forming an intensity distribution with a regular pentagon contour.
Fig. 5
Fig. 5 Experimental optical setup: L is a solid-state laser, F is a neutral density filter, MO is a microobjective (40x, NA = 0.6), PH is a pinhole (40-µm aperture),L1, L2, and L3 are the lenses with focal lengths f 1 =350 mm, f 2 =350 mm, and f 3 =150 mm, respectively, BS is a beam splitter, SLM is a spatial light modulator (PLUTO Spatial Light Modulator, 1920x1080), RP is a rectangular prism, D is a diaphragm, CMOS is a video camera (VSTT-252), and Rail is an optical rail.
Fig. 6
Fig. 6 Experimental intensity distribution for two superimposed Bessel beams (n = 8, m = 3, kr = 51996 m−1, and α = 0.2).
Fig. 7
Fig. 7 Experimental intensity distribution for two superimposed Bessel beams (n = 4, m = −2, k r 1 =51996 m−1, k r 2 =48296 m−1, and α=0.4 ).
Fig. 8
Fig. 8 Experimental setup for optical trapping experiments: L is a solid-state laser (λ = 532 nm), L1, L2 are lenses with f1 = 15 mm and f2 = 35 mm, respectively, MO1 is a microobjective (20 × , NA = 0.4), MO2 is a microobjective (10 × , NA = 0.3), DOE is a diffractive optical element with the phase function shown in Fig. 4, C is a cuvette, and Cam1 is a video camera (MDCE-5, 1280 × 1024 pixels).
Fig. 9
Fig. 9 Carbon nanoparticle agglomerations used in the experiments.
Fig. 10
Fig. 10 Experimental optical trapping and holding of absorbing microparticles with the DHOB generated by DOE (Media 1). Three particles are trapped stable (in the bottom right of the images). One particle (denoted by an arrow) keeps on moving inside volume defined by DHOB structure.
Fig. 11
Fig. 11 Illustration of trapping mechanism involved in DHOB trapping. (a) shows possible forces acting on a particle in our experimental system; (b-e) show directions of the forces depending on the position of the particles inside the minimum intensity region of the DHOB.
Fig. 12
Fig. 12 Motion stages of a carbon nanoparticle agglomeration trapped by the DHOB with an intensity distribution in the form of a regular pentagon contour.
Fig. 13
Fig. 13 The points in which trapped particle was located during observation.

Equations (10)

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

E( r,φ,z )= A 0 exp( i k z z ) J n ( k r r )exp( inφ ),
E( r,φ,z )= A 0n J n ( k r r )exp( inφ )+ A 0m J m ( k r r )exp( imφ ).
I( r,φ )= | A on J n ( k r r )exp( inφ )+ A 0m J m ( k r r )exp( imφ ) | 2 = A 0n 2 J n 2 ( k r r )+ A 0m 2 J m 2 ( k r r )+2 A 0n A 0m J n ( k r r ) J m ( k r r )cos[ ( nm )φ ].
P( r,φ )=arg{ A 0n J n ( k r r )exp( inφ )+ A 0m J m ( k r r )exp( imφ ) }= arctan{ A 0n J n ( k r r )sin( nφ )+ A 0m J m ( k r r )sin( mφ ) A 0n J n ( k r r )cos( nφ )+ A 0m J m ( k r r )cos( mφ ) }.
I( r,φ )= A 0n 2 J n 2 ( k r r )+2 A 0n A 0m J n ( k r r ) J m ( k r r )cos[ ( nm )φ ].
| m || n |,m>0,n<0,| | m || n | |=2,and0.3α0.6
τ( r,φ )=sgn( J n ( k r r ) )×exp( inφ ).
z max = R k z / k r
τ( r,φ )= p=1 N C p sgn( J n p ( k r p r ) )×exp( i n p φ )
τ( r,φ )= C 1 sgn( J n ( k r r ) )×exp( inφ )+ C 2 sgn( J m ( k r r ) )×exp( imφ )

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