Abstract

We propose a design for producing a conveyable quasi-periodic optical chain that can stably trap and deliver multiple individual particles in three dimensions at different planes near the focus. A diffractive optical element (DOE) is designed to spatially modulate the phase of an incoming radially polarized beam. For a tighly focused beam, a three-dimensional (3D) optical chain can be formed because of the difference in the Gouy phase shift from two concentric regions of the DOE. A desired number of particles can be stably tweezed one by one with individual 3D volumes in this trapping structure. By controlling the phase modulation of the incident beam, one can manipulate the interference pattern to accelerate and transport trapped particles along the optical axis in a prescribed way.

© 2005 Optical Society of America

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    [CrossRef]
  2. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2004 (4)

R. B. Case, Y. P. Chang, S. B. Smith, J. Gore, N. R. Cozzarelli, and C. Bustamante, Science 305, 222 (2004).
[CrossRef] [PubMed]

X. Zhuang, Science 305, 188 (2004).
[CrossRef] [PubMed]

Q. Zhan, Opt. Commun. 242, 351 (2004).
[CrossRef]

Q. Zhan, Opt. Express 12, 3377 (2004), http://www.opticsexpress.org.
[CrossRef] [PubMed]

2003 (2)

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, Science 299, 1892 (2003).
[CrossRef] [PubMed]

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, Science 301, 1914 (2003).
[CrossRef] [PubMed]

2002 (2)

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

R. L. Eriksen, P. C. Mogensen, and J. Glückstad, Opt. Lett. 27, 267 (2002).
[CrossRef]

2001 (4)

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, Science 293, 278 (2001).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

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

2000 (2)

A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. 85, 1762 (2000).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000), http://www.opticsexpress.org.
[CrossRef] [PubMed]

1999 (1)

1998 (2)

R. C. Gauthier and M. Ashiman, Appl. Opt. 37, 6421 (1998).
[CrossRef]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

1997 (1)

1995 (1)

T. Pellizzari, S. A. Gardiner, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 75, 3788 (1995).
[CrossRef] [PubMed]

1994 (1)

C. Bustamante, J. F. Marko, E. D. Siggia, and S. Smith, Science 265, 1599 (1994).
[CrossRef] [PubMed]

1993 (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

1987 (1)

1970 (1)

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

Allen, L.

Alt, W.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, Science 293, 278 (2001).
[CrossRef] [PubMed]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, 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]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Ashiman, M.

Ashkin, A.

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

Beige, A.

A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. 85, 1762 (2000).
[CrossRef] [PubMed]

Block, S. M.

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, Science 301, 1914 (2003).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Braun, D.

A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. 85, 1762 (2000).
[CrossRef] [PubMed]

Brown, T. G.

Bryant, P. E.

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

Bustamante, C.

R. B. Case, Y. P. Chang, S. B. Smith, J. Gore, N. R. Cozzarelli, and C. Bustamante, Science 305, 222 (2004).
[CrossRef] [PubMed]

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, Science 299, 1892 (2003).
[CrossRef] [PubMed]

C. Bustamante, J. F. Marko, E. D. Siggia, and S. Smith, Science 265, 1599 (1994).
[CrossRef] [PubMed]

Case, R. B.

R. B. Case, Y. P. Chang, S. B. Smith, J. Gore, N. R. Cozzarelli, and C. Bustamante, Science 305, 222 (2004).
[CrossRef] [PubMed]

Chang, Y. P.

R. B. Case, Y. P. Chang, S. B. Smith, J. Gore, N. R. Cozzarelli, and C. Bustamante, Science 305, 222 (2004).
[CrossRef] [PubMed]

Cirac, J. I.

T. Pellizzari, S. A. Gardiner, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 75, 3788 (1995).
[CrossRef] [PubMed]

Cozzarelli, N. R.

R. B. Case, Y. P. Chang, S. B. Smith, J. Gore, N. R. Cozzarelli, and C. Bustamante, Science 305, 222 (2004).
[CrossRef] [PubMed]

Dalal, R. V.

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, Science 301, 1914 (2003).
[CrossRef] [PubMed]

Dholakia, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, 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]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef] [PubMed]

Dumont, S.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, Science 299, 1892 (2003).
[CrossRef] [PubMed]

Durnin, J.

Eriksen, R. L.

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Galajda, P.

P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Gardiner, S. A.

T. Pellizzari, S. A. Gardiner, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 75, 3788 (1995).
[CrossRef] [PubMed]

Gauthier, R. C.

Glückstad, J.

Gomer, V.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, Science 293, 278 (2001).
[CrossRef] [PubMed]

Gore, J.

R. B. Case, Y. P. Chang, S. B. Smith, J. Gore, N. R. Cozzarelli, and C. Bustamante, Science 305, 222 (2004).
[CrossRef] [PubMed]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Jonas, A.

Knight, P. L.

A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. 85, 1762 (2000).
[CrossRef] [PubMed]

Kuhr, S.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, Science 293, 278 (2001).
[CrossRef] [PubMed]

Liphardt, J.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, Science 299, 1892 (2003).
[CrossRef] [PubMed]

Liska, M.

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, 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]

Marko, J. F.

C. Bustamante, J. F. Marko, E. D. Siggia, and S. Smith, Science 265, 1599 (1994).
[CrossRef] [PubMed]

Meschede, D.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, Science 293, 278 (2001).
[CrossRef] [PubMed]

Mitsis, P. G.

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, Science 301, 1914 (2003).
[CrossRef] [PubMed]

Mogensen, P. C.

Müller, M.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, Science 293, 278 (2001).
[CrossRef] [PubMed]

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Onoa, B.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, Science 299, 1892 (2003).
[CrossRef] [PubMed]

Ormos, P.

P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

Padgett, M. J.

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, 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]

Pellizzari, T.

T. Pellizzari, S. A. Gardiner, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 75, 3788 (1995).
[CrossRef] [PubMed]

Perkins, T. T.

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, Science 301, 1914 (2003).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Schmidt, C. F.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Schrader, D.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, Science 293, 278 (2001).
[CrossRef] [PubMed]

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, 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]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Siggia, E. D.

C. Bustamante, J. F. Marko, E. D. Siggia, and S. Smith, Science 265, 1599 (1994).
[CrossRef] [PubMed]

Simpson, N. B.

Smith, S.

C. Bustamante, J. F. Marko, E. D. Siggia, and S. Smith, Science 265, 1599 (1994).
[CrossRef] [PubMed]

Smith, S. B.

R. B. Case, Y. P. Chang, S. B. Smith, J. Gore, N. R. Cozzarelli, and C. Bustamante, Science 305, 222 (2004).
[CrossRef] [PubMed]

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, Science 299, 1892 (2003).
[CrossRef] [PubMed]

Sramek, L.

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Tinoco, I.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, Science 299, 1892 (2003).
[CrossRef] [PubMed]

Tregenna, B.

A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. 85, 1762 (2000).
[CrossRef] [PubMed]

Volke-Sepulveda, K.

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

Youngworth, K. S.

Zemanek, P.

Zhan, Q.

Zhuang, X.

X. Zhuang, Science 305, 188 (2004).
[CrossRef] [PubMed]

Zoller, P.

T. Pellizzari, S. A. Gardiner, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 75, 3788 (1995).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

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

Nature (2)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Opt. Commun. (2)

Q. Zhan, Opt. Commun. 242, 351 (2004).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

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

T. Pellizzari, S. A. Gardiner, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 75, 3788 (1995).
[CrossRef] [PubMed]

A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. 85, 1762 (2000).
[CrossRef] [PubMed]

Science (8)

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

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, Science 293, 278 (2001).
[CrossRef] [PubMed]

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, Science 299, 1892 (2003).
[CrossRef] [PubMed]

R. B. Case, Y. P. Chang, S. B. Smith, J. Gore, N. R. Cozzarelli, and C. Bustamante, Science 305, 222 (2004).
[CrossRef] [PubMed]

X. Zhuang, Science 305, 188 (2004).
[CrossRef] [PubMed]

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

C. Bustamante, J. F. Marko, E. D. Siggia, and S. Smith, Science 265, 1599 (1994).
[CrossRef] [PubMed]

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, Science 301, 1914 (2003).
[CrossRef] [PubMed]

Other (1)

H.-K. Lo, S. Popescu, and T. Spiller, eds., Introduction to Quantum Computation and Information (World Scientific, Singapore, 1998).

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Figures (5)

Fig. 1
Fig. 1

(a) Radial polarization and (b) transmission functions of three regions of the DOE: I, exp ( j φ 1 ) ; II, 0; and III, exp ( j φ 3 ) .

Fig. 2
Fig. 2

(a) Total field strength distributions and (b) axial Poynting vector S z near the focus.

Fig. 3
Fig. 3

Longitude component of the field strength (circles) and the Gouy phase difference δ gouy from two concentric regions of the DOE along the optical axis near the focus (solid). The maximal field strength appears close to the locations where δ gouy = 2 n π ( n = 0 , 1 , 2 ) .

Fig. 4
Fig. 4

Moving the interference pattern conveyor chain by changing Δ φ from 0 to 2 π . The white line is at the focus plane z = 0 . With increasing Δ φ , the chain moves along the z direction. (a) Δ φ = 0 (downward-facing white arrow) [ Δ φ = 2 π (upward-facing white arrow)], (b) Δ φ = π 2 , (c) Δ φ = π , (d) Δ φ = 3 π 2 .

Fig. 5
Fig. 5

 Illustration of the interference pattern moving with particles trapped in each individual volume. When Δ φ is increased gradually, the operation of the chain begins with trapping of particles from end 1 and then moves them along the axial direction, whereas when Δ φ is decreased, particles are trapped from end 2 and moved in the reverse direction.

Equations (1)

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E ( z ) 2 = [ E I ( z ) + E III ( z ) ] [ E I * ( z ) + E III * ( z ) ] = E I ( z ) 2 + E III ( z ) 2 + 2 E I ( z ) E III ( z ) cos δ = E I ( z ) 2 + E III ( z ) 2 + 2 E I ( z ) E III ( z ) cos ( Δ k z z + Δ φ ) ,

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