Abstract

We analyze a method for efficiently generating optical vortices by use of annular computer-generated holograms and a spatial light modulator. We found that there exists an optimal annular width by which the reconstructed vortex ring in the focal plane has the steepest gradient and the worthless subbright rings can be largely suppressed. We fitted a general formula for determining the value of this optimal annular width and propose a method for designing a multiring structure of optical vortices and specialized interferometric vortex patterns. Finally, we discuss the situation of a Gaussian beam as illuminated light and find that there exists an optimal beam waist that results in the best energy efficiency.

© 2005 Optical Society of America

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  1. H. He, M. E. J. Friese, N. R. Heckenberg, 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]
  2. N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
    [CrossRef]
  3. K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [CrossRef] [PubMed]
  4. K. T. Gahagan, G. A. Swartzlander, “Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap,” J. Opt. Soc. Am. B 16, 533–537 (1999).
    [CrossRef]
  5. J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
    [CrossRef] [PubMed]
  6. J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28, 872–874 (2003).
    [CrossRef] [PubMed]
  7. M. J. Padgett, L. Allen, “The Poynting vector in Laguerre–Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
    [CrossRef]
  8. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
    [CrossRef] [PubMed]
  9. L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
    [CrossRef]
  10. A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
    [CrossRef] [PubMed]
  11. J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
    [CrossRef]
  12. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
    [CrossRef] [PubMed]
  13. D. G. Grier, “A revolution in optical manipulation,” Nature (London) 424, 810–816 (2003).
    [CrossRef]
  14. K. Ladavac, D. G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express 12, 1144–1149 (2004); www.opticsexpress.org .
    [CrossRef] [PubMed]
  15. A. Terray, J. Oakey, D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841–1844 (2002).
    [CrossRef] [PubMed]
  16. G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
    [CrossRef] [PubMed]
  17. G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
    [CrossRef]
  18. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wave-front laser-beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  19. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
    [CrossRef]
  20. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
    [CrossRef]
  21. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef] [PubMed]
  22. J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
    [CrossRef]
  23. C.-S. Guo, X. Liu, J.-L. He, H.-T. Wang, “Optimal annular structure of optical vortices,” Opt. Express 12, 4625–4634 (2004); www.opticsexpress.org .
    [CrossRef] [PubMed]
  24. M. Reicherter, T. Haist, E. U. Wagemann, H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
    [CrossRef]
  25. J. Liesener, M. Reicherter, T. Haist, H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
    [CrossRef]

2004 (2)

2003 (3)

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

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28, 872–874 (2003).
[CrossRef] [PubMed]

2002 (3)

A. Terray, J. Oakey, D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841–1844 (2002).
[CrossRef] [PubMed]

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

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

2001 (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

2000 (2)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

J. Liesener, M. Reicherter, T. Haist, H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

1999 (3)

1998 (1)

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

1996 (3)

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
[CrossRef] [PubMed]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

1995 (2)

M. J. Padgett, L. Allen, “The Poynting vector in Laguerre–Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, 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 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wave-front laser-beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

1992 (3)

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

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

Allen, L.

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

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

M. J. Padgett, L. Allen, “The Poynting vector in Laguerre–Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

Babiker, M.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wave-front laser-beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Bomzon, Z.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wave-front laser-beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Curtis, J. E.

J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28, 872–874 (2003).
[CrossRef] [PubMed]

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

Firth, W. J.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

Friese, M. E. J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, 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]

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Gahagan, K. T.

Grier, D. G.

K. Ladavac, D. G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express 12, 1144–1149 (2004); www.opticsexpress.org .
[CrossRef] [PubMed]

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

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28, 872–874 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Guo, C.-S.

Haist, T.

J. Liesener, M. Reicherter, T. Haist, H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[CrossRef]

Hasman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, 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]

He, J.-L.

Heckenberg, N. R.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, 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]

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

Koss, B. A.

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wave-front laser-beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Ladavac, K.

Law, C. T.

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

Liu, X.

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

MacVicar, I.

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

Marr, D. W. M.

A. Terray, J. Oakey, D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841–1844 (2002).
[CrossRef] [PubMed]

McDonald, G. S.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

McDuff, R.

O’Neil, A. T.

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

Oakey, J.

A. Terray, J. Oakey, D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841–1844 (2002).
[CrossRef] [PubMed]

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Padgett, M. J.

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

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

M. J. Padgett, L. Allen, “The Poynting vector in Laguerre–Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[CrossRef]

Rubinsztein-Dunlop, H.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, 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]

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Simpson, N. B.

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

Smith, C. P.

Swartzlander, G. A.

Syed, K. S.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

Terray, A.

A. Terray, J. Oakey, D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841–1844 (2002).
[CrossRef] [PubMed]

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[CrossRef]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Wagemann, E. U.

Wang, H.-T.

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wave-front laser-beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Appl. Phys. Lett. (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

J. Mod. Opt. (2)

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

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

Nature (London) (1)

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

Opt. Commun. (6)

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Conventional circular CGH used to generate an optical vortex ring with a helical wave front and (b) its reconstructed intensity distribution in the Fourier plane. The parameters of the CGH are set as topological charge, l=40; outer radius of the CGH, R0=256 pixels.

Fig. 2
Fig. 2

Radial intensity distribution of the reconstructed field in the Fourier plane when the inner radius R1 of the annular CGH is set to be (a) 0, (b) 125, (c) 200, and (d) 230 pixels. The outside radius R0 is taken as 256 pixels, and the topological charge l is 40.

Fig. 3
Fig. 3

(a) Peak intensity of the vortex ring in the back focal plane versus the annular width of the CGH. The maximum radius R0 is 256 pixels. (b) Relative peak intensity (the maximum intensity divided by the annular area) versus the annular width. The dashed curve shows the positions of the optimal annular width with different topological charges.

Fig. 4
Fig. 4

(a) Example of the annular CGH designed according to Eq. (4); (b) and (c) simulated intensity and phase distribution at the focal plane, respectively; (d) experimental result.

Fig. 5
Fig. 5

(a) and (c) Two examples of biannular CGHs with helical wave fronts. Their reconstructed results in our experiments are shown in (b) and (d), respectively.

Fig. 6
Fig. 6

Peak intensity of the reconstructed vortex ring as a function of the input Gaussian beam waist w.

Equations (8)

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T(r, θ)=T0 expiα coslθ-2πΛr cos θ,
u1th(ρ, ϕ, l)=circρRfFcircrR0T(r, θ)×exp2πΛr cos θA circrR0×expilθ-i2πλfρr cos(θ-ϕ)rdrdθ=2π(-i)lA exp(ilϕ)0R0rdrJl2πλfρr,
λf2πR0xma2l+xmi2l2=λf2π(R0-ΔRopt)xma1l;
ΔRopt=1-2xma1lxma2l+xmi2lR0,
l1=1b2πR0Rf1λf-a,
R1=R0-ΔRopt=2xma1l1xma2l1+xmi2l1 R0.
u0(r, w)=A0wexp-r2w2,
wopt=2RmΔRopt/ln2Rm+ΔRopt2Rm-ΔRopt1/2,

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