Abstract

We experimentally demonstrate optical rotation and manipulation of microscopic particles by use of optical vortex beams with fractional topological charges, namely fractional optical vortex beams, which are coupled in an optical tweezers system. Like the vortex beams with integer topological charges, the fractional optical vortex beams are also capable of rotating particles induced by the transfer of orbital angular momentum. However, the unique radial opening (low-intensity gap) in the intensity ring encompassing the dark core, due to the fractional nature of the beam, hinders the rotation significantly. The fractional vortex beam’s orbital angular momentum and radial opening are exploited to guide and transport microscopic particles.

©2005 Optical Society of America

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References

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  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,” Phy. Rev. A 45, 8185–8190 (1992).
    [Crossref]
  2. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
    [Crossref] [PubMed]
  3. K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt, and K Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum and Semiclass Opt. 4, S82–S89 (2002).
    [Crossref]
  4. M V Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6, 259–268 (2004).
    [Crossref]
  5. Jonathan Leach, Eric Yao, and Miles J Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
    [Crossref]
  6. S. S. R. Oemrawsingh, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices,” J. Opt. Soc. Am. A 21, 2089–2096 (2004).
    [Crossref]
  7. M.W. Beijersbergen, R. P.C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [Crossref]
  8. I V Basistiy, V A Pas’ko, V V Slyusa, M S Soskin, and M V Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A: Pure Appl. Opt. 6, S166–S169 (2004).
    [Crossref]
  9. W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129 (2004).
    [Crossref]
  10. S. H. Tao, W. M. Lee, and X.-C. Yuan, “Dynamic optical manipulation using higher order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
    [Crossref] [PubMed]
  11. S. H. Tao, W. M. Lee, and X.-C. Yuan, “Experimental study of holographic generation of fractional Bessel beams,” Appl. Opt. 43, 122–126(2004).
    [Crossref] [PubMed]
  12. A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phy. Rev. Lett. 88, 053601 (2002).
    [Crossref]
  13. S M Barnett and L Allen, “Orbital angular momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
    [Crossref]
  14. S. H. Tao, X.-C. Yuan, H. B. Niu, and X. Peng, “Dynamic optical manipulation using intensity patterns directly projected by a reflective spatial light modulator,” Rev. Sci. Instrum. 76, 056103 (2005).
    [Crossref]
  15. Jennifer E. Curtis and David G. Grier, “Structure of optical vortices,” Phy. Rev. Lett. 90, 133901 (2003).
    [Crossref]
  16. K. Ladavac and D. G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express 12, 1144–1149 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1144.
    [Crossref] [PubMed]

2005 (1)

S. H. Tao, X.-C. Yuan, H. B. Niu, and X. Peng, “Dynamic optical manipulation using intensity patterns directly projected by a reflective spatial light modulator,” Rev. Sci. Instrum. 76, 056103 (2005).
[Crossref]

2004 (7)

S. H. Tao, W. M. Lee, and X.-C. Yuan, “Experimental study of holographic generation of fractional Bessel beams,” Appl. Opt. 43, 122–126(2004).
[Crossref] [PubMed]

K. Ladavac and D. G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express 12, 1144–1149 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1144.
[Crossref] [PubMed]

S. S. R. Oemrawsingh, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices,” J. Opt. Soc. Am. A 21, 2089–2096 (2004).
[Crossref]

M V Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6, 259–268 (2004).
[Crossref]

Jonathan Leach, Eric Yao, and Miles J Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

I V Basistiy, V A Pas’ko, V V Slyusa, M S Soskin, and M V Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A: Pure Appl. Opt. 6, S166–S169 (2004).
[Crossref]

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129 (2004).
[Crossref]

2003 (2)

2002 (2)

K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt, and K Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum and Semiclass Opt. 4, S82–S89 (2002).
[Crossref]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phy. Rev. Lett. 88, 053601 (2002).
[Crossref]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

1994 (2)

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

S M Barnett and L Allen, “Orbital angular momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
[Crossref]

1992 (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,” Phy. Rev. A 45, 8185–8190 (1992).
[Crossref]

Allen, L

S M Barnett and L Allen, “Orbital angular momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
[Crossref]

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phy. Rev. Lett. 88, 053601 (2002).
[Crossref]

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,” Phy. Rev. A 45, 8185–8190 (1992).
[Crossref]

Arlt, J

K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt, and K Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum and Semiclass Opt. 4, S82–S89 (2002).
[Crossref]

Barnett, S M

S M Barnett and L Allen, “Orbital angular momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
[Crossref]

Basistiy, I V

I V Basistiy, V A Pas’ko, V V Slyusa, M S Soskin, and M V Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A: Pure Appl. Opt. 6, S166–S169 (2004).
[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,” Phy. Rev. A 45, 8185–8190 (1992).
[Crossref]

Beijersbergen, M.W.

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

Berry, M V

M V Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6, 259–268 (2004).
[Crossref]

Chávez-Cerda, S

K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt, and K Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum and Semiclass Opt. 4, S82–S89 (2002).
[Crossref]

Coerwinkel, R. P.C.

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

Curtis, Jennifer E.

Jennifer E. Curtis and David G. Grier, “Structure of optical vortices,” Phy. Rev. Lett. 90, 133901 (2003).
[Crossref]

Dholakia, K

K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt, and K Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum and Semiclass Opt. 4, S82–S89 (2002).
[Crossref]

Dholakia, K.

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129 (2004).
[Crossref]

Eliel, E. R.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Garcés-Chávez, V

K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt, and K Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum and Semiclass Opt. 4, S82–S89 (2002).
[Crossref]

Grier, D. G.

Grier, David G.

Jennifer E. Curtis and David G. Grier, “Structure of optical vortices,” Phy. Rev. Lett. 90, 133901 (2003).
[Crossref]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Kristensen, M.

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

Ladavac, K.

Leach, Jonathan

Jonathan Leach, Eric Yao, and Miles J Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Lee, W. M.

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phy. Rev. Lett. 88, 053601 (2002).
[Crossref]

Nienhuis, G.

Niu, H. B.

S. H. Tao, X.-C. Yuan, H. B. Niu, and X. Peng, “Dynamic optical manipulation using intensity patterns directly projected by a reflective spatial light modulator,” Rev. Sci. Instrum. 76, 056103 (2005).
[Crossref]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phy. Rev. Lett. 88, 053601 (2002).
[Crossref]

Oemrawsingh, S. S. R.

Padgett, M. J.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phy. Rev. Lett. 88, 053601 (2002).
[Crossref]

Padgett, Miles J

Jonathan Leach, Eric Yao, and Miles J Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Pas’ko, V A

I V Basistiy, V A Pas’ko, V V Slyusa, M S Soskin, and M V Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A: Pure Appl. Opt. 6, S166–S169 (2004).
[Crossref]

Peng, X.

S. H. Tao, X.-C. Yuan, H. B. Niu, and X. Peng, “Dynamic optical manipulation using intensity patterns directly projected by a reflective spatial light modulator,” Rev. Sci. Instrum. 76, 056103 (2005).
[Crossref]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Slyusa, V V

I V Basistiy, V A Pas’ko, V V Slyusa, M S Soskin, and M V Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A: Pure Appl. Opt. 6, S166–S169 (2004).
[Crossref]

Soskin, M S

I V Basistiy, V A Pas’ko, V V Slyusa, M S Soskin, and M V Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A: Pure Appl. Opt. 6, S166–S169 (2004).
[Crossref]

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,” Phy. Rev. A 45, 8185–8190 (1992).
[Crossref]

Tao, S. H.

Vasnetsov, M V

I V Basistiy, V A Pas’ko, V V Slyusa, M S Soskin, and M V Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A: Pure Appl. Opt. 6, S166–S169 (2004).
[Crossref]

Volke-Sepulveda, K

K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt, and K Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum and Semiclass Opt. 4, S82–S89 (2002).
[Crossref]

Woerdman, J. P.

S. S. R. Oemrawsingh, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices,” J. Opt. Soc. Am. A 21, 2089–2096 (2004).
[Crossref]

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

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,” Phy. Rev. A 45, 8185–8190 (1992).
[Crossref]

Yao, Eric

Jonathan Leach, Eric Yao, and Miles J Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Yuan, X.-C.

S. H. Tao, X.-C. Yuan, H. B. Niu, and X. Peng, “Dynamic optical manipulation using intensity patterns directly projected by a reflective spatial light modulator,” Rev. Sci. Instrum. 76, 056103 (2005).
[Crossref]

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129 (2004).
[Crossref]

S. H. Tao, W. M. Lee, and X.-C. Yuan, “Experimental study of holographic generation of fractional Bessel beams,” Appl. Opt. 43, 122–126(2004).
[Crossref] [PubMed]

S. H. Tao, W. M. Lee, and X.-C. Yuan, “Dynamic optical manipulation using higher order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
[Crossref] [PubMed]

Appl. Opt. (1)

J. Opt. A: Pure Appl. Opt. (2)

M V Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6, 259–268 (2004).
[Crossref]

I V Basistiy, V A Pas’ko, V V Slyusa, M S Soskin, and M V Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A: Pure Appl. Opt. 6, S166–S169 (2004).
[Crossref]

J. Opt. B: Quantum and Semiclass Opt. (1)

K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt, and K Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum and Semiclass Opt. 4, S82–S89 (2002).
[Crossref]

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

New J. Phys. (1)

Jonathan Leach, Eric Yao, and Miles J Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Opt. Commun. (3)

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

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129 (2004).
[Crossref]

S M Barnett and L Allen, “Orbital angular momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phy. 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,” Phy. Rev. A 45, 8185–8190 (1992).
[Crossref]

Phy. Rev. Lett. (2)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phy. Rev. Lett. 88, 053601 (2002).
[Crossref]

Jennifer E. Curtis and David G. Grier, “Structure of optical vortices,” Phy. Rev. Lett. 90, 133901 (2003).
[Crossref]

Phys. Rev. Lett. (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

S. H. Tao, X.-C. Yuan, H. B. Niu, and X. Peng, “Dynamic optical manipulation using intensity patterns directly projected by a reflective spatial light modulator,” Rev. Sci. Instrum. 76, 056103 (2005).
[Crossref]

Supplementary Material (4)

» Media 1: AVI (847 KB)     
» Media 2: AVI (586 KB)     
» Media 3: AVI (1339 KB)     
» Media 4: AVI (1320 KB)     

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Figures (6)

Fig. 1.
Fig. 1. Schematic setup for the optical tweezers system.
Fig. 2.
Fig. 2. Patterns of the vortex beams on the sample stage of the microscope.
Fig. 3.
Fig. 3. Frames demonstrate that particles are rotating induced by: (a) (847 KB, movie for optical rotation) a vortex beam with l=3.3, and (b) (587 KB, movie for optical rotation) a vortex beam with l=3.4.
Fig. 4.
Fig. 4. Plot of the time for one cycle of rotation versus the topological charge of vortex beams.
Fig. 5.
Fig. 5. (1.3 MB, video for optical rotation) particles are rotating intrinsically, controlled by a vortex beam of l=-3.5.
Fig. 6.
Fig. 6. (a) (1.28 MB, video for optical aligning and guiding) with its OAM and opening slit, the vortex beam of l=3.5 is used for aligning and transporting particles. (b) Schematic illustration explaining the mechanism of the aligning and guiding with the vortex beam of l=3.5.

Equations (2)

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j z = 1 c 2 ( r × S ) z = [ r × iw ε 0 2 ( u * u u u * ) ] z
Γ z = P 2 πv l

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