Abstract

An optical levitation and translation method for a microscopic particle by use of the resultant force induced by multiple light beams is studied. We show dependence of the radiation pressure force on the illuminating distribution by numerical calculation, and we find that the strongest axial force is obtained by a specific spacing period of illuminating beams. Extending the optical manipulation technique by means of vertical-cavity surface-emitting laser (VCSEL) array sources [Appl. Opt. 40, 5430 (2001)], we are the first, to our knowledge, to demonstrate levitation of a particle and its translation while levitated by using a VCSEL array. The vertical position of the target particle can be controlled in a range of a few tens of micrometers with an accuracy of 2 µm or less. The analytical and experimental results suggest that use of multiple beams is an effective method to levitate a particle with low total illumination power. Some issues on the manipulation method that uses multiple beams are discussed.

© 2002 Optical Society of America

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  1. S. M. Block, “Making light work with optical tweezers,” Nature 360, 493–495 (1992).
    [CrossRef] [PubMed]
  2. A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
    [CrossRef] [PubMed]
  3. A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
    [CrossRef] [PubMed]
  4. S. C. Kuo, M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
    [CrossRef] [PubMed]
  5. P. Borowicz, J. Hotta, K. Sasaki, H. Masuhara, “Laser-controlled association of poly(N-vinylcarbazole) in organic solvents; radiation pressure effect of a focused near-infrared laser beam,” J. Phys. Chem. B 101, 5900–5904 (1997).
    [CrossRef]
  6. Z. P. Luo, Y. L. Sun, K. N. An, “An optical spin micromotor,” Appl. Phys. Lett. 76, 1779–1781 (2000).
    [CrossRef]
  7. M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, “Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap,” Opt. Lett. 26, 863–865 (2001).
    [CrossRef]
  8. M. M. Burns, J. M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
    [CrossRef] [PubMed]
  9. K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
    [CrossRef]
  13. K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys. 30, L907–L909 (1991).
    [CrossRef]
  14. Y. Hayasaki, M. Itoh, T. Yatagai, N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
    [CrossRef]
  15. J. Liesener, M. Reicherter, T. Haist, H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
    [CrossRef]
  16. Y. Ogura, K. Kagawa, J. Tanida, “Optical manipulation of microscopic objects by means of vertical-cavity surface-emitting laser array sources,” Appl. Opt. 40, 5430–5435 (2001).
    [CrossRef]
  17. R. C. Gauthier, S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of the force equations,” J. Opt. Soc. Am. B 12, 1680–1686 (1995).
    [CrossRef]
  18. N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 12, 1943–1949 (1998).
    [CrossRef]
  19. J. Noordmans, P. J. Wit, H. C. van der Mei, H. J. Busscher, “Detachment of polystyrene particles from collector surfaces by surface tension forces induced by air-bubble passage through a parallel plate flow chamber,” J. Adhes. Sci. Technol. 11, 957–970 (1997).
    [CrossRef]
  20. Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
    [CrossRef] [PubMed]
  21. B. H. Weigl, P. Yager, “Microfluidic diffusion-based separation and detection,” Science 283, 346–347 (1999).
    [CrossRef]
  22. J. B. Knight, A. Vishwanath, J. P. Brody, R. H. Austin, “Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds,” Phys. Rev. Lett. 80, 3863–3866 (1998).
    [CrossRef]

2001 (3)

2000 (2)

Z. P. Luo, Y. L. Sun, K. N. An, “An optical spin micromotor,” Appl. Phys. Lett. 76, 1779–1781 (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)

Y. Hayasaki, M. Itoh, T. Yatagai, N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[CrossRef]

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
[CrossRef] [PubMed]

B. H. Weigl, P. Yager, “Microfluidic diffusion-based separation and detection,” Science 283, 346–347 (1999).
[CrossRef]

1998 (3)

J. B. Knight, A. Vishwanath, J. P. Brody, R. H. Austin, “Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds,” Phys. Rev. Lett. 80, 3863–3866 (1998).
[CrossRef]

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 12, 1943–1949 (1998).
[CrossRef]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

1997 (2)

P. Borowicz, J. Hotta, K. Sasaki, H. Masuhara, “Laser-controlled association of poly(N-vinylcarbazole) in organic solvents; radiation pressure effect of a focused near-infrared laser beam,” J. Phys. Chem. B 101, 5900–5904 (1997).
[CrossRef]

J. Noordmans, P. J. Wit, H. C. van der Mei, H. J. Busscher, “Detachment of polystyrene particles from collector surfaces by surface tension forces induced by air-bubble passage through a parallel plate flow chamber,” J. Adhes. Sci. Technol. 11, 957–970 (1997).
[CrossRef]

1996 (1)

1995 (2)

R. C. Gauthier, S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of the force equations,” J. Opt. Soc. Am. B 12, 1680–1686 (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]

1993 (1)

S. C. Kuo, M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
[CrossRef] [PubMed]

1992 (1)

S. M. Block, “Making light work with optical tweezers,” Nature 360, 493–495 (1992).
[CrossRef] [PubMed]

1991 (1)

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys. 30, L907–L909 (1991).
[CrossRef]

1990 (1)

M. M. Burns, J. M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

1987 (2)

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

Akashi, K.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
[CrossRef] [PubMed]

Allen, L.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 12, 1943–1949 (1998).
[CrossRef]

An, K. N.

Z. P. Luo, Y. L. Sun, K. N. An, “An optical spin micromotor,” Appl. Phys. Lett. 76, 1779–1781 (2000).
[CrossRef]

Arai, Y.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
[CrossRef] [PubMed]

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]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

Austin, R. H.

J. B. Knight, A. Vishwanath, J. P. Brody, R. H. Austin, “Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds,” Phys. Rev. Lett. 80, 3863–3866 (1998).
[CrossRef]

Block, S. M.

S. M. Block, “Making light work with optical tweezers,” Nature 360, 493–495 (1992).
[CrossRef] [PubMed]

Borowicz, P.

P. Borowicz, J. Hotta, K. Sasaki, H. Masuhara, “Laser-controlled association of poly(N-vinylcarbazole) in organic solvents; radiation pressure effect of a focused near-infrared laser beam,” J. Phys. Chem. B 101, 5900–5904 (1997).
[CrossRef]

Brody, J. P.

J. B. Knight, A. Vishwanath, J. P. Brody, R. H. Austin, “Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds,” Phys. Rev. Lett. 80, 3863–3866 (1998).
[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]

Burns, M. M.

M. M. Burns, J. M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

Busscher, H. J.

J. Noordmans, P. J. Wit, H. C. van der Mei, H. J. Busscher, “Detachment of polystyrene particles from collector surfaces by surface tension forces induced by air-bubble passage through a parallel plate flow chamber,” J. Adhes. Sci. Technol. 11, 957–970 (1997).
[CrossRef]

Dholakia, K.

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, “Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap,” Opt. Lett. 26, 863–865 (2001).
[CrossRef]

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]

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 12, 1943–1949 (1998).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

Fournier, J. M.

M. M. Burns, J. M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[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]

Gahagan, K. T.

Gauthier, R. C.

Golovchenko, J. A.

M. M. Burns, J. M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

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]

Harada, Y.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
[CrossRef] [PubMed]

Hayasaki, Y.

Y. Hayasaki, M. Itoh, T. Yatagai, N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[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]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[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]

Hotta, J.

P. Borowicz, J. Hotta, K. Sasaki, H. Masuhara, “Laser-controlled association of poly(N-vinylcarbazole) in organic solvents; radiation pressure effect of a focused near-infrared laser beam,” J. Phys. Chem. B 101, 5900–5904 (1997).
[CrossRef]

Itoh, H.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
[CrossRef] [PubMed]

Itoh, M.

Y. Hayasaki, M. Itoh, T. Yatagai, N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[CrossRef]

Kagawa, K.

Kinosita, K.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
[CrossRef] [PubMed]

Kitamura, N.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys. 30, L907–L909 (1991).
[CrossRef]

Knight, J. B.

J. B. Knight, A. Vishwanath, J. P. Brody, R. H. Austin, “Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds,” Phys. Rev. Lett. 80, 3863–3866 (1998).
[CrossRef]

Koshioka, M.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys. 30, L907–L909 (1991).
[CrossRef]

Kuo, S. C.

S. C. Kuo, M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
[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]

Luo, Z. P.

Z. P. Luo, Y. L. Sun, K. N. An, “An optical spin micromotor,” Appl. Phys. Lett. 76, 1779–1781 (2000).
[CrossRef]

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]

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, “Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap,” Opt. Lett. 26, 863–865 (2001).
[CrossRef]

Masuhara, H.

P. Borowicz, J. Hotta, K. Sasaki, H. Masuhara, “Laser-controlled association of poly(N-vinylcarbazole) in organic solvents; radiation pressure effect of a focused near-infrared laser beam,” J. Phys. Chem. B 101, 5900–5904 (1997).
[CrossRef]

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys. 30, L907–L909 (1991).
[CrossRef]

McGloin, D.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 12, 1943–1949 (1998).
[CrossRef]

Misawa, H.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys. 30, L907–L909 (1991).
[CrossRef]

Miyata, H.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
[CrossRef] [PubMed]

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

Nishida, N.

Y. Hayasaki, M. Itoh, T. Yatagai, N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[CrossRef]

Noordmans, J.

J. Noordmans, P. J. Wit, H. C. van der Mei, H. J. Busscher, “Detachment of polystyrene particles from collector surfaces by surface tension forces induced by air-bubble passage through a parallel plate flow chamber,” J. Adhes. Sci. Technol. 11, 957–970 (1997).
[CrossRef]

Ogura, Y.

Padgett, M. J.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 12, 1943–1949 (1998).
[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]

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, “Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap,” Opt. Lett. 26, 863–865 (2001).
[CrossRef]

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]

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[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]

Sasaki, K.

P. Borowicz, J. Hotta, K. Sasaki, H. Masuhara, “Laser-controlled association of poly(N-vinylcarbazole) in organic solvents; radiation pressure effect of a focused near-infrared laser beam,” J. Phys. Chem. B 101, 5900–5904 (1997).
[CrossRef]

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys. 30, L907–L909 (1991).
[CrossRef]

Sheetz, M. P.

S. C. Kuo, M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
[CrossRef] [PubMed]

Sibbett, W.

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, “Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap,” Opt. Lett. 26, 863–865 (2001).
[CrossRef]

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, D. McGloin, K. Dholakia, L. Allen, M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 12, 1943–1949 (1998).
[CrossRef]

Sun, Y. L.

Z. P. Luo, Y. L. Sun, K. N. An, “An optical spin micromotor,” Appl. Phys. Lett. 76, 1779–1781 (2000).
[CrossRef]

Swartzlander, G. A.

Tanida, J.

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]

van der Mei, H. C.

J. Noordmans, P. J. Wit, H. C. van der Mei, H. J. Busscher, “Detachment of polystyrene particles from collector surfaces by surface tension forces induced by air-bubble passage through a parallel plate flow chamber,” J. Adhes. Sci. Technol. 11, 957–970 (1997).
[CrossRef]

Vishwanath, A.

J. B. Knight, A. Vishwanath, J. P. Brody, R. H. Austin, “Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds,” Phys. Rev. Lett. 80, 3863–3866 (1998).
[CrossRef]

Wallace, S.

Weigl, B. H.

B. H. Weigl, P. Yager, “Microfluidic diffusion-based separation and detection,” Science 283, 346–347 (1999).
[CrossRef]

Wit, P. J.

J. Noordmans, P. J. Wit, H. C. van der Mei, H. J. Busscher, “Detachment of polystyrene particles from collector surfaces by surface tension forces induced by air-bubble passage through a parallel plate flow chamber,” J. Adhes. Sci. Technol. 11, 957–970 (1997).
[CrossRef]

Yager, P.

B. H. Weigl, P. Yager, “Microfluidic diffusion-based separation and detection,” Science 283, 346–347 (1999).
[CrossRef]

Yamane, T.

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

Yasuda, R.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399, 446–448 (1999).
[CrossRef] [PubMed]

Yatagai, T.

Y. Hayasaki, M. Itoh, T. Yatagai, N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Z. P. Luo, Y. L. Sun, K. N. An, “An optical spin micromotor,” Appl. Phys. Lett. 76, 1779–1781 (2000).
[CrossRef]

J. Adhes. Sci. Technol. (1)

J. Noordmans, P. J. Wit, H. C. van der Mei, H. J. Busscher, “Detachment of polystyrene particles from collector surfaces by surface tension forces induced by air-bubble passage through a parallel plate flow chamber,” J. Adhes. Sci. Technol. 11, 957–970 (1997).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Model and the coordinate system used for numerical calculation. (a) Incident beams and (b) propagation path of a photon. The dielectric particle is illuminated by multiple beams from below. The calculated radiation pressure force is resolved into axial and transverse forces.

Fig. 2
Fig. 2

Illuminating distributions assumed in numerical calculation. (a) 1 beam, (b) 2 × 2 beams, (c) 3 × 3 beams, and (d) 4 × 4 beams. Individual beams focus at z = 0.

Fig. 3
Fig. 3

Relationship between the particle position and the axial force under W 0 = 0.26r s and beam-spacing period 0.75r s . (a) 1 beam, (b) 2 × 2 beams, (c) 3 × 3 beams, and (d) 4 × 4 beams. The particle position (x, y) is normalized by r s . The maximum forces are (a) 0.688 pN, (b) 1.503 pN, (c) 3.482 pN, and (d) 3.483 pN, by which the the strengths of the forces are normalized and shown as eight-bit gray-scale images.

Fig. 4
Fig. 4

Dependence of the axial force on z when the particle moves along the z axis. The axial displacement z is normalized by z 0.

Fig. 5
Fig. 5

Relationship between the transverse force and the particle position under W 0 = 0.26r s and beam-spacing period 0.75r s . (a) 1 beam, (b) 2 × 2 beams, (c) 3 × 3 beams, and (d) 4 × 4 beams. The particle position (x, y) is normalized by r s . The maximum forces are (a) 1.781, (b) 3.323, (c) 3.367, and (d) 3.372 pN, by which the strengths of the forces are normalized and shown as eight-bit gray-scale images.

Fig. 6
Fig. 6

Dependence of the transverse force on the particle position when the particle moves along (a) the x axis and (b) y = x, z = 0. The transverse displacement is normalized by r s .

Fig. 7
Fig. 7

Dependence of the maximum transverse force on z when the particle moves toward the +x direction. The axial displacement z is normalized by z 0.

Fig. 8
Fig. 8

Dependence of the levitation height and the translation velocity toward the +x direction on the total optical power. The illuminating distribution is 2 × 2 beams with a spacing period of 3.75 µm and W 0 = 1.3 µm. The radius of the particle is 5 µm.

Fig. 9
Fig. 9

Dependence of the radiation pressure force on the spacing period of the illuminating beams. (a) Maximum axial force when the particle moves along the z axis and (b) maximum transverse force when the particle moves along the x axis. W 0 = 0.26r s , and the spacing period is varied from 0 to 1.60r s at 0.02r s intervals.

Fig. 10
Fig. 10

Experimental setup. 60× (OBJ #1) and 100× (OBJ #2) objective lens are selectively used as the focusing lens of the VCSELs. The lower side of the sample stage is the manipulation system, and the upper side of the sample stage is the observation system. A microlens array is located just behind the VCSEL array to increase light efficiency. The sample chamber can be observed by a CCD and captured by a video recorder. The focusing plane of the observation system is changed when the objective lens of the observation system is moved. D/A, digital to analog.

Fig. 11
Fig. 11

(a) VCSELs used in the experiment for levitation and translation of the particle and (b) an emission sequence for nonmechanical manipulation. The illuminating distribution is switched manually while the target particle is observed. The averaged illumination power of the 2 × 2 beams is approximately 3.5 mW.

Fig. 12
Fig. 12

Experimental result for levitation of the particle and its translation with levitation. The focus of the observation system is moved to observe different planes. The target particle and its initial position are indicated by a circle and a dot, respectively. 1–3: The particle is levitated. 4–5: The particle is translated downward then toward the right. 6–7: The particle falls down on the glass slide.

Fig. 13
Fig. 13

Dependence of the vertical position of the particle on the total illumination power. The error bar is the standard deviation of three measurements, and the data points are fitted by the line. The illuminating distribution is 2 × 2 beams with a spacing period of 3.75 µm. The radius of the particle is approximately 5 µm.

Fig. 14
Fig. 14

Dependence of the power required for levitation on the beam-spacing period. Curves, calculation results; squares and circles, experimental results. The illuminating distribution is 2 × 2 beams. For spacing periods of 2.25, 6.75, and 7.50 µm, the particle could not be levitated under condition (i).

Tables (3)

Tables Icon

Table 1 Calculation Results of the Maximum Axial Force on za

Tables Icon

Table 2 Calculation Result of the Levitation Height for Different Total Illumination Powersa

Tables Icon

Table 3 Calculation Result of the Maximum Transverse Force on z a

Equations (9)

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

F=-IincΔE ΔPdS.
ΔE=hcλ0,
IGaussx, y, z; Xc, Yc=2PGaussπWz2exp-2x-Xc2+y-Yc2Wz2,
Wz=W01+z2z021/2,
z0=πW02λ0.
Imultix, y, z=c=1N IGaussx, y, z; Xc, Yc.
z=αz0.
Fg=43πrs3ρs-ρ0g,
Ftrans=6πηrsv,

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