Abstract

We describe novel optical doughnuts for optical tweezers. With new phase functions, the proposed doughnut beams have dark cores in specified shapes. The technique can offer a simple method for creating a variety of beam shapes to match the trapped objects. One can rotate the beams directly by revolving their phase structures about their axes on the initial plane. The technique for generating the traditional Laguerre–Gaussian beam can be used to create these novel beams.

© 2003 Optical Society of America

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  1. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
    [CrossRef]
  2. J. T. Finer, R. M. Simmons, and J. A. Spudich, Nature 368, 113 (1996).
    [CrossRef]
  3. W. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, Biophys. J. 72, 1335 (1997).
    [CrossRef] [PubMed]
  4. A. T. O’Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601-1 (2002).
    [CrossRef]
  5. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  6. V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnesov, J. Mod. Opt. 39, 985 (1992).
    [CrossRef]
  7. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
    [CrossRef]
  8. H. He, M. E. J. Friese, N. R. Heckenburg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [CrossRef] [PubMed]
  9. A. T. O’Neil and M. J. Padgett, Opt. Lett. 27, 743 (2002).
    [CrossRef]
  10. M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
    [CrossRef] [PubMed]
  11. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
    [CrossRef] [PubMed]
  12. J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 67.
  15. J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
    [CrossRef]

2002 (6)

A. T. O’Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601-1 (2002).
[CrossRef]

A. T. O’Neil and M. J. Padgett, Opt. Lett. 27, 743 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002); http://www.opticsexpress.org .
[CrossRef] [PubMed]

R. L. Eriksen, V. R. Daria, and J. Glückstad, Opt. Express 10, 597 (2002); http://www.opticsexpress.org .
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

2001 (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

1999 (1)

1997 (1)

W. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, Biophys. J. 72, 1335 (1997).
[CrossRef] [PubMed]

1996 (1)

J. T. Finer, R. M. Simmons, and J. A. Spudich, Nature 368, 113 (1996).
[CrossRef]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenburg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnesov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

1970 (1)

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Allen, L.

A. T. O’Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601-1 (2002).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002); http://www.opticsexpress.org .
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Bazhenov, V. Y.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnesov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Block, S. M.

W. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, Biophys. J. 72, 1335 (1997).
[CrossRef] [PubMed]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Daria, V. R.

Dholakia, K.

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002); http://www.opticsexpress.org .
[CrossRef] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Eriksen, R. L.

Finer, J. T.

J. T. Finer, R. M. Simmons, and J. A. Spudich, Nature 368, 113 (1996).
[CrossRef]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenburg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Gelles, J.

W. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, Biophys. J. 72, 1335 (1997).
[CrossRef] [PubMed]

Glückstad, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 67.

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Haist, T.

He, H.

H. He, M. E. J. Friese, N. R. Heckenburg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Heckenburg, N. R.

H. He, M. E. J. Friese, N. R. Heckenburg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Landick, R.

W. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, Biophys. J. 72, 1335 (1997).
[CrossRef] [PubMed]

Mac Vicar, I.

A. T. O’Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601-1 (2002).
[CrossRef]

MacDonald, M.

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

O’Neil, A. T.

A. T. O’Neil and M. J. Padgett, Opt. Lett. 27, 743 (2002).
[CrossRef]

A. T. O’Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601-1 (2002).
[CrossRef]

Padgett, M. J.

A. T. O’Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601-1 (2002).
[CrossRef]

A. T. O’Neil and M. J. Padgett, Opt. Lett. 27, 743 (2002).
[CrossRef]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002); http://www.opticsexpress.org .
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Reicherter, M.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenburg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002); http://www.opticsexpress.org .
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Simmons, R. M.

J. T. Finer, R. M. Simmons, and J. A. Spudich, Nature 368, 113 (1996).
[CrossRef]

Soskin, M. S.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnesov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Spudich, J. A.

J. T. Finer, R. M. Simmons, and J. A. Spudich, Nature 368, 113 (1996).
[CrossRef]

Tiziani, H. J.

Vasnesov, M. V.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnesov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

Volke-Sepulaveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Volke-Sepulveda, K.

Wagemann, E. U.

Wang, W. D.

W. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, Biophys. J. 72, 1335 (1997).
[CrossRef] [PubMed]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Yin, H.

W. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, Biophys. J. 72, 1335 (1997).
[CrossRef] [PubMed]

Biophys. J. (1)

W. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, Biophys. J. 72, 1335 (1997).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnesov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

Nature (1)

J. T. Finer, R. M. Simmons, and J. A. Spudich, Nature 368, 113 (1996).
[CrossRef]

Opt. Commun. (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

H. He, M. E. J. Friese, N. R. Heckenburg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

A. T. O’Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601-1 (2002).
[CrossRef]

Science (2)

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 67.

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Figures (3)

Fig. 1
Fig. 1

Phase function in Cartesian coordinates.

Fig. 2
Fig. 2

Intensity profiles of the various mode lights: (a) the Gaussian mode, Φx,y=0; (b) the conventional circular doughnut mode, Φx,y=ϕ; (c) the square doughnut mode, Φx,y=ΦSx,y; (d) the triangular doughnut mode, Φx,y=Φtx,y.

Fig. 3
Fig. 3

White dots and the arrows indicate the rotation of the intensity pattern as a result of the revolving phase of the triangular doughnut beam.

Equations (7)

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

ur,ϕ=E0 expjlϕexp-jkzz,
ux,y=E0 expjlΦx,yexp-jkzz
ur=0=DE0 expjlΦx,yexp-jkzzdxdy=0,
Φsx,y=πy4xx>0, y>0, y<xπ2-πx4yyx, y0, x0π+πy4xx<0, y<x3π2-πx4yyx<02π+πy4xx>0, y<0, y<x.
Φtx,y=yπ3y+x cotπ6cos2π6
ux,y,z=-iλz--dxdyux,y,z×expik/2zx-x2+y-y2.
E0x,y,z=0=exp-πx2+y2/ω02.

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