Abstract

Optical-trapping forces exerted on polystyrene microspheres are predicted and measured as a function of sphere size, laser spot size, and laser beam polarization. Axial and transverse forces are in good and excellent agreement, respectively, with a ray-optics model when the sphere diameter is ≥ 10 μm. Results are compared with results from an electromagnetic model when the sphere size is ≤ 1 μm. Axial trapping performance is found to be optimum when the numerical aperture of the objective lens is as large as possible, and when the trapped sphere is located just below the chamber cover slip. Forces in the transverse direction are not as sensitive to parametric variations as are the axial forces. These results are important as a first-order approximation to the forces that can be applied either directly to biological objects or by means of microsphere handles attached to the biological specimen.

© 1994 Optical Society of America

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    [CrossRef] [PubMed]
  2. A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987);A. Ashkin, J. M. Dziedzic, T. M. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
    [CrossRef] [PubMed]
  3. T. N. Buican, M. J. Smith, H. A. Crissman, G. C. Salzman, C. C. Stewart, J. C. Martin, “Automated single-cell manipulation and sorting by light trapping,” Appl. Opt. 26, 5311–5316 (1987).
    [CrossRef] [PubMed]
  4. R. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser-induced cell fusion in combination with optical tweezers: the laser–cell fusion trap,” Cytometry 12, 505–510 (1991).
    [CrossRef] [PubMed]
  5. M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  12. K. Visscher, G. J. Brakenhoff, “Single-beam optical trapping integrated in a confocal microscope for biological applications,” Cytometry 12, 486–491 (1991).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  23. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
    [CrossRef]
  24. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  25. R. S. Afzal, E. B. Treacy, “Optical tweezers using a diode laser,” Rev. Sci. Instrum. 63, 2157–2163 (1992).
    [CrossRef]
  26. H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829–3836 (1991).
    [CrossRef]
  27. J. B. Bateman, E. J. Weneck, D. C. Eshler, “Determination of particle size and concentration from spectrophotometry transmission,” J. Colloid Sci. 14, 308–329 (1959).
    [CrossRef]
  28. A. H. Firester, M. E. Heller, P. Sheng, “Knife-edge scanning measurements of subwavelength focused light beams,” Appl. Opt. 16, 1971–1974 (1977).
    [CrossRef] [PubMed]
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  31. E. M. Bonder, J. M. Colon, J. M. Dziedzic, A. Ashkin, “Force production by swimming sperm: analysis using optical tweezers,” J. Cell Biol. 111, 421a (1990).
  32. S. M. Block, “Optical tweezers: a new tool for biophysics,” in Noninvasive Techniques in Cell Biology, J. K. Foskett, S. Grinstein, eds. (Wiley-Liss, New York, 1990), pp. 375–402.
  33. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986).
  34. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 478.

1993 (3)

H. Liang, W. H. Wright, S. Cheng, W. He, M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

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

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

1992 (2)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

R. S. Afzal, E. B. Treacy, “Optical tweezers using a diode laser,” Rev. Sci. Instrum. 63, 2157–2163 (1992).
[CrossRef]

1991 (6)

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829–3836 (1991).
[CrossRef]

S. Sato, M. Ohyumi, H. Shibata, H. Inaba, Y. Ogawa, “Optical trapping of small particles using a 1.3-μm compact InGaAsP diode laser,” Opt. Lett. 16, 282–284 (1991).
[CrossRef] [PubMed]

S. Chu, “Laser manipulation of atoms and particles,” Science 253, 861–866 (1991).
[CrossRef] [PubMed]

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometric optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

K. Visscher, G. J. Brakenhoff, “Single-beam optical trapping integrated in a confocal microscope for biological applications,” Cytometry 12, 486–491 (1991).
[CrossRef] [PubMed]

R. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser-induced cell fusion in combination with optical tweezers: the laser–cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

1990 (3)

A. Ashkin, K. Schultze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

E. M. Bonder, J. M. Colon, J. M. Dziedzic, A. Ashkin, “Force production by swimming sperm: analysis using optical tweezers,” J. Cell Biol. 111, 421a (1990).

1989 (4)

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

S. Block, L. S. B. Goldstein, B. J. Schnapp, “Using optical tweezers to investigate kinesin-based motility in vitro,” J. Cell Biol. 109, 81a (1989).

1988 (1)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

1987 (2)

T. N. Buican, M. J. Smith, H. A. Crissman, G. C. Salzman, C. C. Stewart, J. C. Martin, “Automated single-cell manipulation and sorting by light trapping,” Appl. Opt. 26, 5311–5316 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987);A. Ashkin, J. M. Dziedzic, T. M. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef] [PubMed]

1986 (1)

1983 (1)

1979 (1)

G. Roosen, “La levitation optique de spheres,” Can. J. Phys. 57, 1260–1279 (1979).
[CrossRef]

1977 (2)

G. Roosen, “A theoretical and experimental study of the stable equilibrium positions of spheres levitated by two horizontal laser beams,” Opt. Commun. 21, 189–194 (1977).
[CrossRef]

A. H. Firester, M. E. Heller, P. Sheng, “Knife-edge scanning measurements of subwavelength focused light beams,” Appl. Opt. 16, 1971–1974 (1977).
[CrossRef] [PubMed]

1975 (1)

1959 (1)

J. B. Bateman, E. J. Weneck, D. C. Eshler, “Determination of particle size and concentration from spectrophotometry transmission,” J. Colloid Sci. 14, 308–329 (1959).
[CrossRef]

Afzal, R. S.

R. S. Afzal, E. B. Treacy, “Optical tweezers using a diode laser,” Rev. Sci. Instrum. 63, 2157–2163 (1992).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Andrews, J. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

E. M. Bonder, J. M. Colon, J. M. Dziedzic, A. Ashkin, “Force production by swimming sperm: analysis using optical tweezers,” J. Cell Biol. 111, 421a (1990).

A. Ashkin, K. Schultze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987);A. Ashkin, J. M. Dziedzic, T. M. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

Bakker Schut, T. C.

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometric optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Bateman, J. B.

J. B. Bateman, E. J. Weneck, D. C. Eshler, “Determination of particle size and concentration from spectrophotometry transmission,” J. Colloid Sci. 14, 308–329 (1959).
[CrossRef]

Berns, M. W.

H. Liang, W. H. Wright, S. Cheng, W. He, M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

R. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser-induced cell fusion in combination with optical tweezers: the laser–cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Block, S.

S. Block, L. S. B. Goldstein, B. J. Schnapp, “Using optical tweezers to investigate kinesin-based motility in vitro,” J. Cell Biol. 109, 81a (1989).

Block, S. M.

S. M. Block, “Optical tweezers: a new tool for biophysics,” in Noninvasive Techniques in Cell Biology, J. K. Foskett, S. Grinstein, eds. (Wiley-Liss, New York, 1990), pp. 375–402.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 478.

Bonder, E. M.

E. M. Bonder, J. M. Colon, J. M. Dziedzic, A. Ashkin, “Force production by swimming sperm: analysis using optical tweezers,” J. Cell Biol. 111, 421a (1990).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Sec. 13.5.1.

Brakenhoff, G. J.

K. Visscher, G. J. Brakenhoff, “Single-beam optical trapping integrated in a confocal microscope for biological applications,” Cytometry 12, 486–491 (1991).
[CrossRef] [PubMed]

Brenner, H.

J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media (Prentice-Hall, Englewood Cliffs, N.J., 1965), p. 327.

Buican, T. N.

Cheng, S.

H. Liang, W. H. Wright, S. Cheng, W. He, M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

R. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser-induced cell fusion in combination with optical tweezers: the laser–cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

Chu, S.

Colon, J. M.

E. M. Bonder, J. M. Colon, J. M. Dziedzic, A. Ashkin, “Force production by swimming sperm: analysis using optical tweezers,” J. Cell Biol. 111, 421a (1990).

Crissman, H. A.

de Grooth, B. G.

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometric optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, K. Schultze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

E. M. Bonder, J. M. Colon, J. M. Dziedzic, A. Ashkin, “Force production by swimming sperm: analysis using optical tweezers,” J. Cell Biol. 111, 421a (1990).

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987);A. Ashkin, J. M. Dziedzic, T. M. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

Eshler, D. C.

J. B. Bateman, E. J. Weneck, D. C. Eshler, “Determination of particle size and concentration from spectrophotometry transmission,” J. Colloid Sci. 14, 308–329 (1959).
[CrossRef]

Euteneuer, U.

A. Ashkin, K. Schultze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

Firester, A. H.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986).

Goldstein, L. S. B.

S. Block, L. S. B. Goldstein, B. J. Schnapp, “Using optical tweezers to investigate kinesin-based motility in vitro,” J. Cell Biol. 109, 81a (1989).

Greve, J.

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometric optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Happel, J.

J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media (Prentice-Hall, Englewood Cliffs, N.J., 1965), p. 327.

He, W.

H. Liang, W. H. Wright, S. Cheng, W. He, M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

Heller, M. E.

Hesselink, G.

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometric optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 478.

Inaba, H.

Kim, J. S.

Kitamura, N.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829–3836 (1991).
[CrossRef]

Koshioka, M.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829–3836 (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]

Lee, S. S.

Liang, H.

H. Liang, W. H. Wright, S. Cheng, W. He, M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

Martin, J. C.

Masuhara, H.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829–3836 (1991).
[CrossRef]

Misawa, H.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829–3836 (1991).
[CrossRef]

Numajiri, Y.

R. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser-induced cell fusion in combination with optical tweezers: the laser–cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

Ogawa, Y.

Ohyumi, M.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986).

Profeta, G. A.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

Roosen, G.

G. Roosen, “La levitation optique de spheres,” Can. J. Phys. 57, 1260–1279 (1979).
[CrossRef]

G. Roosen, “A theoretical and experimental study of the stable equilibrium positions of spheres levitated by two horizontal laser beams,” Opt. Commun. 21, 189–194 (1977).
[CrossRef]

Salzman, G. C.

Sasaki, K.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829–3836 (1991).
[CrossRef]

Sato, S.

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Schliwa, M.

A. Ashkin, K. Schultze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

Schnapp, B. J.

S. Block, L. S. B. Goldstein, B. J. Schnapp, “Using optical tweezers to investigate kinesin-based motility in vitro,” J. Cell Biol. 109, 81a (1989).

Schultze, K.

A. Ashkin, K. Schultze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[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]

Sheng, P.

Shibata, H.

Smith, M. J.

Sonek, G. J.

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Steubing, R.

R. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser-induced cell fusion in combination with optical tweezers: the laser–cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

Stewart, C. C.

Suzaki, Y.

Tachibana, A.

Tadir, Y.

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986).

Treacy, E. B.

R. S. Afzal, E. B. Treacy, “Optical tweezers using a diode laser,” Rev. Sci. Instrum. 63, 2157–2163 (1992).
[CrossRef]

Tromberg, B. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Sec. 4.5.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986).

Visscher, K.

K. Visscher, G. J. Brakenhoff, “Single-beam optical trapping integrated in a confocal microscope for biological applications,” Cytometry 12, 486–491 (1991).
[CrossRef] [PubMed]

Walter, R. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

Weneck, E. J.

J. B. Bateman, E. J. Weneck, D. C. Eshler, “Determination of particle size and concentration from spectrophotometry transmission,” J. Colloid Sci. 14, 308–329 (1959).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Sec. 13.5.1.

Wright, W. H.

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

H. Liang, W. H. Wright, S. Cheng, W. He, M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

R. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser-induced cell fusion in combination with optical tweezers: the laser–cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Biophys. J. (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

Can. J. Phys. (1)

G. Roosen, “La levitation optique de spheres,” Can. J. Phys. 57, 1260–1279 (1979).
[CrossRef]

Cytometry (3)

R. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser-induced cell fusion in combination with optical tweezers: the laser–cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometric optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

K. Visscher, G. J. Brakenhoff, “Single-beam optical trapping integrated in a confocal microscope for biological applications,” Cytometry 12, 486–491 (1991).
[CrossRef] [PubMed]

Exp. Cell Res. (1)

H. Liang, W. H. Wright, S. Cheng, W. He, M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

J. Appl. Phys. (4)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829–3836 (1991).
[CrossRef]

J. Cell Biol. (2)

S. Block, L. S. B. Goldstein, B. J. Schnapp, “Using optical tweezers to investigate kinesin-based motility in vitro,” J. Cell Biol. 109, 81a (1989).

E. M. Bonder, J. M. Colon, J. M. Dziedzic, A. Ashkin, “Force production by swimming sperm: analysis using optical tweezers,” J. Cell Biol. 111, 421a (1990).

J. Colloid Sci. (1)

J. B. Bateman, E. J. Weneck, D. C. Eshler, “Determination of particle size and concentration from spectrophotometry transmission,” J. Colloid Sci. 14, 308–329 (1959).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (London) (1)

A. Ashkin, K. Schultze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

Opt. Commun. (1)

G. Roosen, “A theoretical and experimental study of the stable equilibrium positions of spheres levitated by two horizontal laser beams,” Opt. Commun. 21, 189–194 (1977).
[CrossRef]

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989);A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

R. S. Afzal, E. B. Treacy, “Optical tweezers using a diode laser,” Rev. Sci. Instrum. 63, 2157–2163 (1992).
[CrossRef]

Science (3)

S. Chu, “Laser manipulation of atoms and particles,” Science 253, 861–866 (1991).
[CrossRef] [PubMed]

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

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987);A. Ashkin, J. M. Dziedzic, T. M. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature (London) 330, 769–771 (1987).
[CrossRef] [PubMed]

Other (6)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Sec. 4.5.

J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media (Prentice-Hall, Englewood Cliffs, N.J., 1965), p. 327.

S. M. Block, “Optical tweezers: a new tool for biophysics,” in Noninvasive Techniques in Cell Biology, J. K. Foskett, S. Grinstein, eds. (Wiley-Liss, New York, 1990), pp. 375–402.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 478.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Sec. 13.5.1.

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Figures (7)

Fig. 1
Fig. 1

Ray-optics (RO) model for optical trapping (after Ashkin13). The scattering force Fs points in the direction of the incident ray, while the gradient force Fg is perpendicular to the direction of the incident ray. The intensities of the reflected and refracted rays are determined by the Fresnel transmission T and reflection R coefficients at a dielectric boundary, and by the power P of the incident ray. The angle of incidence is θ1 and the angle of refraction is θ2.

Fig. 2
Fig. 2

Predicted axial trapping efficiency Q as a function of axial position for several laser spot sizes representative of optical traps. A 1-μm-diameter amorphous silica (n = 1.45) microsphere suspended in water and trapped at a wavelength of 1.06 μm was assumed.

Fig. 3
Fig. 3

Predicted axial trapping efficiency Q as a function of axial position for several microsphere radii. An amorphous silica microsphere suspended in water and trapped at a wavelength of 1.06 μm with a spot size of 0.4 μm was assumed.

Fig. 4
Fig. 4

Calculated axial force as a function of refractive index with the EM model. The sphere diameter was assumed to be 1 μm, and the wavelength was 1.06 μm.

Fig. 5
Fig. 5

Schematic diagram of the optical trap.

Fig. 6
Fig. 6

Transverse, or viscous, drag force as a function of power for polystyrene microspheres suspended in water of varying diameter and motion parallel ║ and perpendicular ┴ to the laser beam polarization. Data for the 1-μm-diameter microsphere is shown in the inset. A, 1 μm (┴); B, 1 μm (║); C, 5 μm (┴); D, 5 μm (║); E, 10 μm (┴); F, 10 μm (║); G, 20 μm (┴); H, 20 μm (║).

Fig. 7
Fig. 7

Transverse, or viscous, drag force as a function of power and cone angle for 20-μm-diameter polystyrene microspheres suspended in water. Cone angles are A: 60°, B: 56°, C: 41°, and D: 32°.

Tables (5)

Tables Icon

Table 1 Measured Spot Size for Various High Numerical Aperture Microscope Objectives and the Corresponding Maximum Backward Axial Trapping Q

Tables Icon

Table 2 Maximum Backward Axial Trapping Q in Water as a Function of Sphere Diametera

Tables Icon

Table 3 Maximum Backward Axial Trapping Q as a Function of the Numerical Aperture and the Distance Below the Cover Glassa

Tables Icon

Table 4 Maximum Transverse Trapping Q as a Function of Sphere Diametera

Tables Icon

Table 5 Maximum Transverse Trapping Q as a Function of Maximum Convergence Anglea

Equations (19)

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

p s = { 1 + R cos 2 θ 1 T 2 [ cos 2 ( θ 1 θ 2 ) + R cos 2 θ 1 ] 1 + R 2 + 2 R cos θ 2 } p i , = Q s p i ,
p g = { R sin 2 θ 1 T 2 [ sin 2 ( θ 1 θ 2 ) + R sin 2 θ 1 ] 1 + R 2 + 2 R cos θ 2 } p i , = Q g p i ,
F s = n 1 Q s P / c ,
F g = n 1 Q g P / c .
n = a + b / λ 0 2 ,
P ( x ) = P 0 ω 2 π x exp ( 2 x 2 ω 2 ) d x ,
P ( x ) = ( P 0 / 2 ) erfc ( 2 1 / 2 x / ω ) .
ω = 0.7830 ( x 10 % x 90 % ) .
F = 6 π r υ μ 1 9 16 ( r h ) + 1 8 ( r h ) 3 45 256 ( r h ) 4 1 16 ( r h ) 5 ,
F = 1 4 π 0 2 π 0 π { ɛ ( I ) E r E + B r B 1 2 ( ɛ ( I ) E 2 + B 2 ) r ̂ } × r 2 sin θ d θ d ϕ | r > a ,
F z = a 2 E 0 2 α 2 8 π l = 1 m = l l I m [ l ( l + 2 ) × ( l m + 1 ) ( l + m + 1 ) ( 2 l + 3 ) ( 2 l + 1 ) ( 2 ɛ ( I ) c l + 1 , m c l m * + ɛ ( I ) c l + 1 , m C l m * + ɛ ( I ) C l + 1 , m c l , m * + 2 d l + 1 , m d l m * + d l + 1 , m D l m * + D l + 1 , m d l , m * ) + ɛ ( I ) m ( 2 c l , m d l m * + c l , m D l m * + C l , m d l , m * ) ] ,
E 0 2 = 16 P ɛ ( I ) c ω 0 2 ( 1 + s 2 + 1.5 s 4 ) ,
C l m = a 2 l ( l + 1 ) ψ l ( k ( I ) a ) 0 2 π 0 π sin θ E r ( i ) ( a , θ , ϕ ) × Y l m * ( θ , ϕ ) d θ d ϕ ,
D l m = a 2 l ( l + 1 ) ψ l ( k ( I ) a ) 0 2 π 0 π sin θ B r ( i ) ( a , θ , ϕ ) × Y l m * ( θ , ϕ ) d θ d ϕ ,
x l x N f ( x ) d x = h [ 1 2 f 1 + f 2 + f 3 + + f N 1 + 1 2 f N ] + O [ ( b a ) 3 f N 2 ] ,
c l m = ψ l ( k ( I I ) a ) ψ l ( k ( I ) a ) ñ ψ l ( k ( I I ) a ) ψ l ( k ( I ) a ) ñ ψ l ( k ( I I ) a ) ξ l ( 1 ) ( k ( I ) a ) ψ l ( k ( I I ) a ) ξ l ( 1 ) ( k ( I ) a ) C l m ,
d l m = ñ ψ l ( k ( I I ) a ) ψ l ( k ( I ) a ) ψ l ( k ( I I ) a ) ψ l ( k ( I ) a ) ψ l ( k ( I I ) a ) ξ l ( 1 ) ( k ( I ) a ) ñ ψ l ( k ( I I ) a ) ξ l ( 1 ) ( k ( I ) a ) D l m ,
ψ n + 1 ( X ) = 2 n + 1 X ψ n ( X ) ψ n 1 ( X )
l max = X + 4 X 1 / 3 + 2 ,

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