Abstract

We present what is, to the best of our knowledge, the first detailed calculation of the reverse trapping force acting on a dielectric sphere when it is illuminated by a strongly focused laser beam. The calculation is carried out within the geometrical optics approximation. The phenomenon of laser trapping was discovered experimentally by Ashkin et al. [ Opt. Lett. 11, 288 ( 1986)] and is of great practical interest in view of the possibility it offers for freely manipulating biological particles, such as viruses and bacteria, in a nondestructive manner. We support our calculations by a qualitative experiment that clearly shows the accessibility of the trapping effect in practice. We use, as an experimental improvement, an objective with a central field stop producing a conical dark field. This enhances the relative contribution from high-N.A. illumination and makes it easier to achieve optical trapping.

© 1992 Optical Society of America

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970);“The pressure of laser light,” Sci. Am. 226, 63 (1972);A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283 (1971);“Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586 (1974).
    [CrossRef]
  2. A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081 (1980);see also V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1 (1981).
    [CrossRef] [PubMed]
  3. A. Ashkin, J. P. Gordon, “Stability of radiation-pressure particle traps: an optical Earnshaw theorem,” Opt. Lett. 8, 511 (1983).
    [CrossRef] [PubMed]
  4. A. Ashkin, J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by attenuating light beams,” Phys. Rev. Lett. 54, 1245 (1985).
    [CrossRef] [PubMed]
  5. G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6 (1976).
  6. G. Roosen, B. Delaunay, C. Imbert, “Étude de la pression de radiation exercée par un faisceau lumineux sur une sphére refringente,” J. Opt. (Paris) 8, 181 (1977).
    [CrossRef]
  7. G. Roosen, “Effets mécaniques de la lumière: étude théorique, experimentale et applications,” thèse d’état (Université Paris XI, Orsay, France, 1978).
  8. G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260 (1979).
    [CrossRef]
  9. G. Roosen, S. Slansky, “Influence of the beam divergence on the exerted force on a sphere by a laser beam and required conditions for a stable optical levitation,” Opt. Commun. 29, 341 (1979).
    [CrossRef]
  10. 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 (1986).
    [CrossRef] [PubMed]
  11. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).
  12. I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133 (1979).
    [CrossRef]
  13. A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254 (1989).
    [CrossRef]
  14. H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Laser trapping, spectroscopy, and ablation of a single latex particle in water,” Chem. Lett. (Jpn) 8, 1479 (1990);“Spatial pattern formation, size selection, and directional flow of polymer latex particles by laser trapping technique,” Chem. Lett. (Jpn) 3, 469 (1991).
    [CrossRef]
  15. S. Sato, M. Ohyumi, H. Shibata, H. Inaba, “Optical trapping of small particles using a 1.3-μm compact InGaAsP diode laser,” Opt. Lett. 16, 282 (1991).
    [CrossRef] [PubMed]
  16. A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517 (1987).
    [CrossRef] [PubMed]
  17. T. N. Buican, M. J. Smyth, 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 (1987).
    [CrossRef] [PubMed]
  18. S. M. Block, D. F. Blair, H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514 (1989).
    [CrossRef]
  19. M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
    [CrossRef]
  20. A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. (USA) 86, 7914 (1989).
    [CrossRef]
  21. A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346 (1990).
    [CrossRef]
  22. S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature (London) 348, 348 (1990).
    [CrossRef]
  23. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965).
  24. 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 (1988);“Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900 (1989).
    [CrossRef]
  25. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800 (1989).
    [CrossRef]
  26. 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 (1989);“Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709 (1989).
    [CrossRef]
  27. P. Mulser, “Radiation pressure on macroscopic bodies,” J. Opt. Soc. Am. B 2, 1814 (1985).
    [CrossRef]
  28. C. Møller, The Theory of Relativity, 2nd ed. (Clarendon, Oxford, 1972).
  29. See, for instance, M. Kerker, The Scattering of Light (Academic, New York, 1969).
  30. A. Drobnik, K. Łukaszewski, “Direct calculations of radiation pressure for spherical particles,” J. Opt. Soc. Am. A 7, 943 (1990).
    [CrossRef]
  31. A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart & Winston, New York, 1971), Chap. 3.
  32. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177 (1979).
    [CrossRef]
  33. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  34. H. M. Lai, P. T. Leung, K. L. Poon, K. Young, “Electrostrictive distortion of a micrometer-sized droplet by a laser pulse,” J. Opt. Soc. Am. B 6, 2430 (1989).
    [CrossRef]
  35. I. Brevik, “Fluids in electric and magnetic fields: pressure variation and stability,” Can. J. Phys. 60, 449 (1982).
    [CrossRef]
  36. H. Minkowski, “Die Grundgleichungen für die electromagnetischen Vorgänge in bewegten Körpern,” Nachr. Kgl. Ges. Wiss. Göttingen, p. 53 (1908).
  37. M. Abraham, “Zur Elektrodynamik bewegter Körper,” Rend. Cir. Mat. Palermo 28, 1 (1990);Rend. Cir. Mat. Palermo 30, 33 (1910).
    [CrossRef]
  38. I. Brevik, “Electromagnetic energy-momentum tensor within material media,” Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. 37(11), 1 (1970);Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. 37(13), 1 (1970);“Photon drag experiment and the electromagnetic momentum in matter,” Phys. Rev. B 33, 1058 (1986).

1991 (1)

1990 (5)

M. Abraham, “Zur Elektrodynamik bewegter Körper,” Rend. Cir. Mat. Palermo 28, 1 (1990);Rend. Cir. Mat. Palermo 30, 33 (1910).
[CrossRef]

A. Drobnik, K. Łukaszewski, “Direct calculations of radiation pressure for spherical particles,” J. Opt. Soc. Am. A 7, 943 (1990).
[CrossRef]

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Laser trapping, spectroscopy, and ablation of a single latex particle in water,” Chem. Lett. (Jpn) 8, 1479 (1990);“Spatial pattern formation, size selection, and directional flow of polymer latex particles by laser trapping technique,” Chem. Lett. (Jpn) 3, 469 (1991).
[CrossRef]

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

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature (London) 348, 348 (1990).
[CrossRef]

1989 (7)

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800 (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 (1989);“Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709 (1989).
[CrossRef]

S. M. Block, D. F. Blair, H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514 (1989).
[CrossRef]

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. (USA) 86, 7914 (1989).
[CrossRef]

H. M. Lai, P. T. Leung, K. L. Poon, K. Young, “Electrostrictive distortion of a micrometer-sized droplet by a laser pulse,” J. Opt. Soc. Am. B 6, 2430 (1989).
[CrossRef]

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 (1988);“Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900 (1989).
[CrossRef]

1987 (2)

1986 (1)

1985 (2)

P. Mulser, “Radiation pressure on macroscopic bodies,” J. Opt. Soc. Am. B 2, 1814 (1985).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by attenuating light beams,” Phys. Rev. Lett. 54, 1245 (1985).
[CrossRef] [PubMed]

1983 (1)

1982 (1)

I. Brevik, “Fluids in electric and magnetic fields: pressure variation and stability,” Can. J. Phys. 60, 449 (1982).
[CrossRef]

1980 (1)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081 (1980);see also V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1 (1981).
[CrossRef] [PubMed]

1979 (4)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177 (1979).
[CrossRef]

G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260 (1979).
[CrossRef]

G. Roosen, S. Slansky, “Influence of the beam divergence on the exerted force on a sphere by a laser beam and required conditions for a stable optical levitation,” Opt. Commun. 29, 341 (1979).
[CrossRef]

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133 (1979).
[CrossRef]

1977 (1)

G. Roosen, B. Delaunay, C. Imbert, “Étude de la pression de radiation exercée par un faisceau lumineux sur une sphére refringente,” J. Opt. (Paris) 8, 181 (1977).
[CrossRef]

1976 (1)

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6 (1976).

1970 (2)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970);“The pressure of laser light,” Sci. Am. 226, 63 (1972);A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283 (1971);“Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586 (1974).
[CrossRef]

I. Brevik, “Electromagnetic energy-momentum tensor within material media,” Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. 37(11), 1 (1970);Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. 37(13), 1 (1970);“Photon drag experiment and the electromagnetic momentum in matter,” Phys. Rev. B 33, 1058 (1986).

1908 (1)

H. Minkowski, “Die Grundgleichungen für die electromagnetischen Vorgänge in bewegten Körpern,” Nachr. Kgl. Ges. Wiss. Göttingen, p. 53 (1908).

Abraham, M.

M. Abraham, “Zur Elektrodynamik bewegter Körper,” Rend. Cir. Mat. Palermo 28, 1 (1990);Rend. Cir. Mat. Palermo 30, 33 (1910).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800 (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 (1989);“Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709 (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 (1988);“Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900 (1989).
[CrossRef]

Andrews, J. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
[CrossRef]

Ashkin, A.

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

A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. (USA) 86, 7914 (1989).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254 (1989).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517 (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 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by attenuating light beams,” Phys. Rev. Lett. 54, 1245 (1985).
[CrossRef] [PubMed]

A. Ashkin, J. P. Gordon, “Stability of radiation-pressure particle traps: an optical Earnshaw theorem,” Opt. Lett. 8, 511 (1983).
[CrossRef] [PubMed]

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081 (1980);see also V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1 (1981).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970);“The pressure of laser light,” Sci. Am. 226, 63 (1972);A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283 (1971);“Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586 (1974).
[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 (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 (1989);“Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709 (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 (1988);“Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900 (1989).
[CrossRef]

Berg, H. C.

S. M. Block, D. F. Blair, H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514 (1989).
[CrossRef]

Berns, M. W.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
[CrossRef]

Bjorkholm, J. E.

Blair, D. F.

S. M. Block, D. F. Blair, H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514 (1989).
[CrossRef]

Block, S. M.

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature (London) 348, 348 (1990).
[CrossRef]

S. M. Block, D. F. Blair, H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514 (1989).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965).

Brevik, I.

I. Brevik, “Fluids in electric and magnetic fields: pressure variation and stability,” Can. J. Phys. 60, 449 (1982).
[CrossRef]

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133 (1979).
[CrossRef]

I. Brevik, “Electromagnetic energy-momentum tensor within material media,” Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. 37(11), 1 (1970);Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. 37(13), 1 (1970);“Photon drag experiment and the electromagnetic momentum in matter,” Phys. Rev. B 33, 1058 (1986).

Buican, T. N.

Chu, S.

Crissman, H. A.

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177 (1979).
[CrossRef]

Delaunay, B.

G. Roosen, B. Delaunay, C. Imbert, “Étude de la pression de radiation exercée par un faisceau lumineux sur une sphére refringente,” J. Opt. (Paris) 8, 181 (1977).
[CrossRef]

Drobnik, A.

Dziedzic, J. M.

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

A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. (USA) 86, 7914 (1989).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254 (1989).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517 (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 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by attenuating light beams,” Phys. Rev. Lett. 54, 1245 (1985).
[CrossRef] [PubMed]

Euteneuer, U.

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

Goldstein, L. S. B.

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature (London) 348, 348 (1990).
[CrossRef]

Gordon, J. P.

Imbert, C.

G. Roosen, B. Delaunay, C. Imbert, “Étude de la pression de radiation exercée par un faisceau lumineux sur une sphére refringente,” J. Opt. (Paris) 8, 181 (1977).
[CrossRef]

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6 (1976).

Inaba, H.

Kerker, M.

See, for instance, M. Kerker, The Scattering of Light (Academic, New York, 1969).

Kitamura, N.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Laser trapping, spectroscopy, and ablation of a single latex particle in water,” Chem. Lett. (Jpn) 8, 1479 (1990);“Spatial pattern formation, size selection, and directional flow of polymer latex particles by laser trapping technique,” Chem. Lett. (Jpn) 3, 469 (1991).
[CrossRef]

Koshioka, M.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Laser trapping, spectroscopy, and ablation of a single latex particle in water,” Chem. Lett. (Jpn) 8, 1479 (1990);“Spatial pattern formation, size selection, and directional flow of polymer latex particles by laser trapping technique,” Chem. Lett. (Jpn) 3, 469 (1991).
[CrossRef]

Lai, H. M.

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).

Leung, P. T.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).

Lukaszewski, K.

Martin, J. C.

Masuhara, H.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Laser trapping, spectroscopy, and ablation of a single latex particle in water,” Chem. Lett. (Jpn) 8, 1479 (1990);“Spatial pattern formation, size selection, and directional flow of polymer latex particles by laser trapping technique,” Chem. Lett. (Jpn) 3, 469 (1991).
[CrossRef]

Minkowski, H.

H. Minkowski, “Die Grundgleichungen für die electromagnetischen Vorgänge in bewegten Körpern,” Nachr. Kgl. Ges. Wiss. Göttingen, p. 53 (1908).

Misawa, H.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Laser trapping, spectroscopy, and ablation of a single latex particle in water,” Chem. Lett. (Jpn) 8, 1479 (1990);“Spatial pattern formation, size selection, and directional flow of polymer latex particles by laser trapping technique,” Chem. Lett. (Jpn) 3, 469 (1991).
[CrossRef]

Møller, C.

C. Møller, The Theory of Relativity, 2nd ed. (Clarendon, Oxford, 1972).

Mulser, P.

Ohyumi, M.

Poon, K. L.

Profeta, G. A.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
[CrossRef]

Roosen, G.

G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260 (1979).
[CrossRef]

G. Roosen, S. Slansky, “Influence of the beam divergence on the exerted force on a sphere by a laser beam and required conditions for a stable optical levitation,” Opt. Commun. 29, 341 (1979).
[CrossRef]

G. Roosen, B. Delaunay, C. Imbert, “Étude de la pression de radiation exercée par un faisceau lumineux sur une sphére refringente,” J. Opt. (Paris) 8, 181 (1977).
[CrossRef]

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6 (1976).

G. Roosen, “Effets mécaniques de la lumière: étude théorique, experimentale et applications,” thèse d’état (Université Paris XI, Orsay, France, 1978).

Salzman, G. C.

Sasaki, K.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Laser trapping, spectroscopy, and ablation of a single latex particle in water,” Chem. Lett. (Jpn) 8, 1479 (1990);“Spatial pattern formation, size selection, and directional flow of polymer latex particles by laser trapping technique,” Chem. Lett. (Jpn) 3, 469 (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 (1989);“Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709 (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 (1988);“Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900 (1989).
[CrossRef]

Schliwa, M.

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

Schnapp, B. J.

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature (London) 348, 348 (1990).
[CrossRef]

Schütze, K.

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

Shibata, H.

Slansky, S.

G. Roosen, S. Slansky, “Influence of the beam divergence on the exerted force on a sphere by a laser beam and required conditions for a stable optical levitation,” Opt. Commun. 29, 341 (1979).
[CrossRef]

Smyth, M. J.

Stewart, C. C.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Tromberg, B. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
[CrossRef]

Walter, R. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965).

Wright, W. H.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
[CrossRef]

Yariv, A.

A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart & Winston, New York, 1971), Chap. 3.

Young, K.

Appl. Opt. (1)

Ber. Bunsenges. Phys. Chem. (1)

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254 (1989).
[CrossRef]

Can. J. Phys. (2)

G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260 (1979).
[CrossRef]

I. Brevik, “Fluids in electric and magnetic fields: pressure variation and stability,” Can. J. Phys. 60, 449 (1982).
[CrossRef]

Chem. Lett. (Jpn) (1)

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Laser trapping, spectroscopy, and ablation of a single latex particle in water,” Chem. Lett. (Jpn) 8, 1479 (1990);“Spatial pattern formation, size selection, and directional flow of polymer latex particles by laser trapping technique,” Chem. Lett. (Jpn) 3, 469 (1991).
[CrossRef]

J. Appl. Phys. (3)

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 (1988);“Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800 (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 (1989);“Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709 (1989).
[CrossRef]

J. Opt. (Paris) (1)

G. Roosen, B. Delaunay, C. Imbert, “Étude de la pression de radiation exercée par un faisceau lumineux sur une sphére refringente,” J. Opt. (Paris) 8, 181 (1977).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

Nachr. Kgl. Ges. Wiss. Göttingen (1)

H. Minkowski, “Die Grundgleichungen für die electromagnetischen Vorgänge in bewegten Körpern,” Nachr. Kgl. Ges. Wiss. Göttingen, p. 53 (1908).

Nature (London) (3)

S. M. Block, D. F. Blair, H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514 (1989).
[CrossRef]

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

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature (London) 348, 348 (1990).
[CrossRef]

Opt. Commun. (1)

G. Roosen, S. Slansky, “Influence of the beam divergence on the exerted force on a sphere by a laser beam and required conditions for a stable optical levitation,” Opt. Commun. 29, 341 (1979).
[CrossRef]

Opt. Lett. (3)

Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. (1)

I. Brevik, “Electromagnetic energy-momentum tensor within material media,” Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. 37(11), 1 (1970);Parts 1 and 2, Mat. Fys. Medd. Dan. Vid. Selsk. 37(13), 1 (1970);“Photon drag experiment and the electromagnetic momentum in matter,” Phys. Rev. B 33, 1058 (1986).

Phys. Lett. (1)

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6 (1976).

Phys. Rep. (1)

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133 (1979).
[CrossRef]

Phys. Rev. A (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177 (1979).
[CrossRef]

Phys. Rev. Lett. (2)

A. Ashkin, J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by attenuating light beams,” Phys. Rev. Lett. 54, 1245 (1985).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970);“The pressure of laser light,” Sci. Am. 226, 63 (1972);A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283 (1971);“Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586 (1974).
[CrossRef]

Proc. Natl. Acad. Sci. (USA) (2)

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. (USA) 86, 4539 (1989).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. (USA) 86, 7914 (1989).
[CrossRef]

Rend. Cir. Mat. Palermo (1)

M. Abraham, “Zur Elektrodynamik bewegter Körper,” Rend. Cir. Mat. Palermo 28, 1 (1990);Rend. Cir. Mat. Palermo 30, 33 (1910).
[CrossRef]

Science (2)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081 (1980);see also V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1 (1981).
[CrossRef] [PubMed]

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

Other (7)

A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart & Winston, New York, 1971), Chap. 3.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965).

G. Roosen, “Effets mécaniques de la lumière: étude théorique, experimentale et applications,” thèse d’état (Université Paris XI, Orsay, France, 1978).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

C. Møller, The Theory of Relativity, 2nd ed. (Clarendon, Oxford, 1972).

See, for instance, M. Kerker, The Scattering of Light (Academic, New York, 1969).

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Figures (8)

Fig. 1
Fig. 1

Geometry for the calculation of the trapping force on a sphere in a strongly focused laser beam.

Fig. 2
Fig. 2

Axial force Fz versus longitudinal displacement z0. Wavelength in water λ = 0.488/1.33 μm, radius ρ = 5 μm, relative refractive index n = 1.2, next = 1.33. a, w0 = 0.4 μm; b, w0 = 0.3 μm; c, w0 = 0.2 μm.

Fig. 3
Fig. 3

Same as Fig. 1 but with a conical dark field whose numerical aperture is 0.4. Parameters w0 for curves a, b, and c are the same as in Fig. 2.

Fig. 4
Fig. 4

Infrared laser: λ = 1.06/1.33 μm, ρ = 15 μm, n = 1.05, next = 1.33. a, w0 = 1.5 μm; b, w0 = 1 μm; c, w0 = 0.8 μm; d, w0 = 0.6 μm; e, w0 = 0.4 μm.

Fig. 5
Fig. 5

Variation of Fz with n, when λ = 0.488/1.33 μm, ρ = 5 μm, next = 1.33. a, w0 = 0.4 μm, z0 = 10 μm; b, w0 = 0.3 μm, z0 = 8.8 μm; c, w0 = 0.2 μm, z0 = 7.6 μm; see text for explanation.

Fig. 6
Fig. 6

Same as Fig. 5 but with an infrared laser: λ = 1.06/1.33 μm, ρ = 15 μm, next = 1.33. a, w0 = 1.5 μm, z0 = 40 μm; b, w0 = 0.8 μm, z0 = 35 μm; c, w0 = 0.6 μm, z0 = 30 μm; d, w0 = 0.4 μm, z0 = 25 μm; see text.

Fig. 7
Fig. 7

Apparatus for the optical trapping of polysterene spheres.

Fig. 8
Fig. 8

Sketch of the momentum transfer between ingoing and transmitted photons, assuming that |pin| = |pout|. (a) z component of momentum transfer positive. (b) z component of momentum transfer negative, implying a reverse force on the sphere.

Equations (29)

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f = ½ E 2 .
2 π ρ / λ 100 .
F i = f i d V = S ik n k d A d d t g i d V .
S ik = E i D k H i B k + ½ δ ik ( E D + H B ) ,
F i = S ik n k d A .
E 2 ( x , y , z ) = 2 P π n ext 0 c w 2 ( z ) exp [ 2 ( x 2 + y 2 ) w 2 ( z ) ] ,
w ( z ) = w 0 [ 1 + ( λ z π w 0 2 ) 2 ] 1 / 2
s = λ / ( 2 π w 0 ) .
R C = z [ 1 + ( π w 0 2 / λ z ) 2 ] .
R C = ( z 0 + Z ) + ( π w 0 2 / λ ) 2 z 0 + Z .
X = ρ sin Θ cos Φ , Y = ρ sin Θ sin Φ , Z = ρ cos Θ .
CM = ( ρ 2 + R z 2 Z 2 + ρ 0 2 + 2 Y ρ 0 ) 1 / 2 ,
cos i = Z 2 ρ 2 R z Z ρ 0 Y ρ ( ρ 2 + R z 2 Z 2 + ρ 0 2 + 2 Y ρ 0 ) 1 / 2 ,
cos θ 1 = Z 2 R z Z ρ 0 Y ρ [ ( Z R z ) 2 + ρ 0 2 ] 1 / 2 ,
R z = ( R C 2 ρ 2 + Z 2 ρ 0 2 2 Y ρ 0 ) 1 / 2 .
dF = ext E I 2 d A cos i ( û I R û R k = 0 T 2 R k û T k ) .
d F Z 1 = ext E I 2 d A cos i [ cos ( i θ 1 ) + R cos ( i + θ 1 ) T 2 cos ( 2 r i θ 1 ) + R cos ( i + θ 1 ) 1 + R 2 + 2 R cos 2 r ] ,
d F Y 1 = ext E I 2 d A cos i [ sin ( i θ 1 ) R sin ( i + θ 1 ) T 2 sin ( 2 r i θ 1 ) R sin ( i + θ 1 ) 1 + R 2 + 2 R cos 2 r ] ,
F z = 2 π ρ 2 ext 0 θ max E I 2 sin θ × cos i [ cos ( i θ ) + R cos ( i + θ ) T 2 cos ( 2 r i θ ) + R cos ( i + θ ) 1 + R 2 + 2 R cos 2 r ] d θ .
E I 2 = 2 P π n ext 0 c w 2 ( z ) exp [ 2 ρ 2 sin 2 θ w 2 ( z ) ] ,
cos i = ρ sin 2 θ + R z cos θ ( ρ 2 sin 2 θ + R z 2 ) 1 / 2 ,
ρ sin θ max tan θ max = R z = ( R C 2 ρ 2 sin 2 θ max ) 1 / 2 ,
ρ sin θ min = R C sin γ ,
n = ( int / ext ) 1 / 2 .
σ z ( + ) = 0 E I 2 cos θ ( 1 + R cos 2 θ ) .
σ z AM = 0 E I 2 cos θ [ 1 + R cos 2 θ n T cos ( θ r ) ] .
σ AM = 2 0 E I 2 [ ( n 1 ) / ( n + 1 ) ] .
f H = 1 2 E 2 + 1 2 ( E 2 τ d d τ ) .
σ H = σ AM + T 2 n E I 2 τ d d τ = 2 3 0 E I 2 ( n 1 ) 2 .

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