Abstract

We describe a method for projecting holographic optical traps that are extended along arbitrary curves in three dimensions, and whose amplitude and phase profiles are specified independently. This approach can be used to create bright optical traps with knotted optical force fields.

© 2011 OSA

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References

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  1. Y. Roichman and D. G. Grier, “Projecting extended optical traps with shape-phase holography,” Opt. Lett. 31, 1675–1677 (2006).
    [CrossRef] [PubMed]
  2. Y. Roichman and D. G. Grier, “Three-dimensional holographic ring traps,” Proc. SPIE 6483, 64830F (2007).
    [CrossRef]
  3. Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
    [CrossRef] [PubMed]
  4. S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express 18, 6988–6993 (2010).
    [CrossRef] [PubMed]
  5. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [CrossRef] [PubMed]
  6. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
    [CrossRef]
  7. N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
    [CrossRef]
  8. K. T. Gahagan and G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [CrossRef] [PubMed]
  9. K. Ladavac and D. G. Grier, “Microoptomechanical pump assembled and driven by holographic optical vortex arrays,” Opt. Express 12, 1144–1149 (2004).
    [CrossRef] [PubMed]
  10. K. Ladavac and D. G. Grier, “Colloidal hydrodynamic coupling in concentric optical vortices,” Europhys. Lett. 70, 548–554 (2005).
    [CrossRef]
  11. 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]
  12. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).
  13. G. C. Sherman, “Application of the convolution theorem to Rayleigh’s integral formulas,” J. Opt. Soc. Am. 57, 546–547 (1967).
    [CrossRef] [PubMed]
  14. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
    [CrossRef]
  15. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
    [CrossRef]
  16. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
    [CrossRef]
  17. J. Leach, K. Wulff, G. Sinclair, P. Jordan, J. Courial, L. Thomson, G. Gibson, K. Karunwi, J. Cooper, Z. J. Laczik, and M. Padgett, “Interactive approach to optical tweezers control,” Appl. Opt. 45, 897–903 (2006).
    [CrossRef] [PubMed]
  18. Y. Roichman, I. Cholis, and D. G. Grier, “Volumetric imaging of holographic optical traps,” Opt. Express 14, 10907–10912 (2006).
    [CrossRef] [PubMed]
  19. M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, “Optimized holographic optical traps,” Opt. Express 13, 5831–5845 (2005).
    [CrossRef] [PubMed]
  20. J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
    [CrossRef]
  21. 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, 8185–8189 (1992).
    [CrossRef] [PubMed]
  22. 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,” Phys. Rev. Lett. 88, 053601 (2002).
    [CrossRef] [PubMed]
  23. J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
    [CrossRef] [PubMed]
  24. S. Sundbeck, I. Gruzberg, and D. G. Grier, “Structure and scaling of helical modes of light,” Opt. Lett. 30, 477–479 (2005).
    [CrossRef] [PubMed]
  25. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
    [CrossRef] [PubMed]
  26. M. R. Dennis, R. P. King, J. Barry, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 53–56 (2010).
    [CrossRef]
  27. W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Phys. 4, 716–720 (2008).
    [CrossRef]
  28. L. Faddeev and A. J. Niemi, “Stable knot-like structures in classical field theory,” Nature 387, 58–61 (1997).
    [CrossRef]

2010 (2)

M. R. Dennis, R. P. King, J. Barry, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 53–56 (2010).
[CrossRef]

S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express 18, 6988–6993 (2010).
[CrossRef] [PubMed]

2008 (2)

W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Phys. 4, 716–720 (2008).
[CrossRef]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

2007 (1)

Y. Roichman and D. G. Grier, “Three-dimensional holographic ring traps,” Proc. SPIE 6483, 64830F (2007).
[CrossRef]

2006 (3)

2005 (3)

2004 (2)

2003 (1)

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

2002 (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,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

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

2000 (1)

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

1999 (1)

1997 (1)

L. Faddeev and A. J. Niemi, “Stable knot-like structures in classical field theory,” Nature 387, 58–61 (1997).
[CrossRef]

1996 (3)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

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

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

1995 (2)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

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]

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,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

1986 (1)

1967 (1)

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,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[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,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Amato-Grill, J.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Ashkin, A.

Barry, J.

M. R. Dennis, R. P. King, J. Barry, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 53–56 (2010).
[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, 8185–8189 (1992).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Bouwmeester, D.

W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Phys. 4, 716–720 (2008).
[CrossRef]

Cholis, I.

Chu, S.

Cooper, J.

Courial, J.

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

Crocker, J. C.

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Curtis, J. E.

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

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

Dennis, M. R.

M. R. Dennis, R. P. King, J. Barry, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 53–56 (2010).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

Dziedzic, J. M.

Faddeev, L.

L. Faddeev and A. J. Niemi, “Stable knot-like structures in classical field theory,” Nature 387, 58–61 (1997).
[CrossRef]

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]

Gahagan, K. T.

Gibson, G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

Grier, D. G.

S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express 18, 6988–6993 (2010).
[CrossRef] [PubMed]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, “Three-dimensional holographic ring traps,” Proc. SPIE 6483, 64830F (2007).
[CrossRef]

Y. Roichman and D. G. Grier, “Projecting extended optical traps with shape-phase holography,” Opt. Lett. 31, 1675–1677 (2006).
[CrossRef] [PubMed]

Y. Roichman, I. Cholis, and D. G. Grier, “Volumetric imaging of holographic optical traps,” Opt. Express 14, 10907–10912 (2006).
[CrossRef] [PubMed]

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, “Optimized holographic optical traps,” Opt. Express 13, 5831–5845 (2005).
[CrossRef] [PubMed]

S. Sundbeck, I. Gruzberg, and D. G. Grier, “Structure and scaling of helical modes of light,” Opt. Lett. 30, 477–479 (2005).
[CrossRef] [PubMed]

K. Ladavac and D. G. Grier, “Colloidal hydrodynamic coupling in concentric optical vortices,” Europhys. Lett. 70, 548–554 (2005).
[CrossRef]

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

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

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

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Gruzberg, I.

Haist, T.

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

He, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

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]

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

Irvine, W. T. M.

W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Phys. 4, 716–720 (2008).
[CrossRef]

Jordan, P.

Karunwi, K.

King, R. P.

M. R. Dennis, R. P. King, J. Barry, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 53–56 (2010).
[CrossRef]

Koss, B. A.

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

Laczik, Z. J.

Ladavac, K.

Leach, J.

Lee, S.-H.

Liesener, J.

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

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,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Niemi, A. J.

L. Faddeev and A. J. Niemi, “Stable knot-like structures in classical field theory,” Nature 387, 58–61 (1997).
[CrossRef]

O’Holleran, K.

M. R. Dennis, R. P. King, J. Barry, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 53–56 (2010).
[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,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Padgett, M.

Padgett, M. J.

M. R. Dennis, R. P. King, J. Barry, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 53–56 (2010).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

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,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

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

Polin, M.

Reicherter, M.

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

Roichman, Y.

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]

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

Sherman, G. C.

Simpson, N. B.

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

Sinclair, G.

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Sun, B.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Sundbeck, S.

Swartzlander, G. A.

Thomson, L.

Tiziani, H. J.

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

Wagemann, E. U.

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Wulff, K.

Appl. Opt. (1)

Europhys. Lett. (1)

K. Ladavac and D. G. Grier, “Colloidal hydrodynamic coupling in concentric optical vortices,” Europhys. Lett. 70, 548–554 (2005).
[CrossRef]

J. Colloid Interface Sci. (1)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

J. Mod. Opt. (2)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

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

J. Opt. Soc. Am. (1)

Nat. Phys. (2)

M. R. Dennis, R. P. King, J. Barry, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 53–56 (2010).
[CrossRef]

W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Phys. 4, 716–720 (2008).
[CrossRef]

Nature (2)

L. Faddeev and A. J. Niemi, “Stable knot-like structures in classical field theory,” Nature 387, 58–61 (1997).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

Opt. Commun. (2)

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

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

Opt. Express (4)

Opt. Lett. (5)

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

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,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

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

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]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Proc. SPIE (1)

Y. Roichman and D. G. Grier, “Three-dimensional holographic ring traps,” Proc. SPIE 6483, 64830F (2007).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

Supplementary Material (1)

» Media 1: MPG (520 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Projecting three-dimensionally extended holographic traps. A laser beam is imprinted with a hologram in the input pupil of an objective lens. The hologram is projected through the objective’s focal plane, and comes to a focus along a three-dimensional curve parameterized by its arc length, s.

Fig. 2.
Fig. 2.

(a) Volumetric reconstruction of a tilted ring trap. (b) Horizontal section near the midplane showing tilt around the ŷ axis. (c) Vertical section along the axis. (d) Vertical section along the ŷ axis.

Fig. 3.
Fig. 3.

(a) Bright-field microscope image of 5.17 μm diameter colloidal silica spheres trapped on an inclined ring. (b) Schematic representation of the geometry in (a). Media 1 shows particles circulating around the inclined ring under the influence of phase-gradient forces.

Fig. 4.
Fig. 4.

(a) Intensity in the focal plane of the microscope of two tilted ring traps projected simultaneously with opposite inclination, β = ±π/8. (b) Colloidal silica spheres trapped in three dimensions within the focused Hopf link. (c) Schematic representation of the three-dimensional intensity distribution responsible for the image in (a).

Equations (10)

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u h ( ρ ) = k 2 π i Ω u f ( r ) exp ( i k f r · ρ ) d 2 r ,
u h ( ρ ) = i λ u ˜ f ( q )
u ( r , z ) = exp ( ikz ) H z ( q ) u ˜ f ( q ) exp ( i q · r ) d 2 q ,
H Z ( q ) = exp ( iz ( k 2 q 2 ) 1 / 2 )
u ˜ f ( q ) a 0 ( s ) exp ( φ 0 ( s ) ) exp ( ikz 0 ( s ) ) H z 0 ( s ) ( q ) exp ( i q · r 0 ( s ) ) ds
R 0 ( s ) = R ( cos ( s R ) cos β , sin ( s R ) , cos ( s R ) sin β ) ,
u h ( ρ ) = J 0 ( A ( ρ ) )
( 2 f A ( ρ ) kR ) 2 = ξ 2 + [ η cos β + ( 4 f 2 + ρ 2 ) 1 / 2 sin β ] 2 .
u h ( ρ ) = J 0 ( kR 2 f ρ )
u h ( ρ ) = J ( A ( ρ ) ) exp ( 2 π i s R )

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