Abstract

We prove an optical radiation Earnshaw theorem: A small dielectric particle cannot be trapped by using only the scattering force of optical radiation pressure. A corollary is that the gradient or dipole force is necessary to any successful optical trap. We discuss the implications of the theorem for recent proposals for the optical trapping of neutral atoms.

© 1983 Optical Society of America

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References

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  1. J. C. Maxwell, Treatise on Electricity and Magnetism (Clarendon, Oxford, 1904; Dover, New York, 1962); W. T. Scott, Am. J. Phys. 27, 418 (1959).
    [CrossRef] [PubMed]
  2. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
    [CrossRef]
  3. A. Ashkin, Science 210, 1081 (1980).
    [CrossRef] [PubMed]
  4. Absorption of light by the particles may occur and is included in the general theory outlined below.
  5. A. Ashkin, J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
    [CrossRef]
  6. G. Roosen, Can. J. Phys. 57, 1260 (1979).
    [CrossRef]
  7. A. Ashkin, Phys. Rev. Lett. 25, 1321 (1970).
    [CrossRef]
  8. G. A. Askar’yan, Zh. Eksp. Teor. Fiz. 42, 1567 (1962) [Sov. Phys. JETP 15, 1088 (1962)].
  9. A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 63, 1628 (1972) [Sov. Phys. JETP 36, 861 (1973)].
  10. V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Zh. Eksp. Teor. Fiz. 72, 1328 (1977) [Sov. Phys. JETP 45, 698 (1977)]; V. S. Letokhov, V. G. Minogin, Appl. Phys. 17, 99 (1978).
    [CrossRef]
  11. A. Ashkin, Phys. Rev. Lett. 40, 729 (1978).
    [CrossRef]
  12. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, London, 1960), p. 54.
  13. J. P. Gordon, Phys. Rev. A 8, 14 (1973).
    [CrossRef]
  14. A. Ashkin, unpublished experiments. See related work demonstrating gradient forces on submicrometer particles: P. W. Smith, A. Ashkin, W. J. Tomlinson, Opt. Lett. 6, 284 (1981); P. W. Smith, P. J. Maloney, A. Ashkin, Opt. Lett. 7, 347 (1982).
    [CrossRef] [PubMed]
  15. See, for example, J. E. Bjorkholm, R. R. Freeman, D. B. Pearson, Phys. Rev. A 23, 491 (1981); J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978); A. Ashkin, Science 210, 1081 (1980).
    [CrossRef] [PubMed]
  16. T. W. Hänsch, A. L. Schawlow, Opt. Commun. 13, 68 (1975).
    [CrossRef]
  17. V. G. Minogin, Kvantovaya Elektron. (Moscow) 9, 505 (1982) [Sov. J. Quantum Electron. 12, 299 (1982)].
  18. V. G. Minogin, J. Javainen, Opt. Commun. 43, 119 (1982).
    [CrossRef]
  19. A. Ashkin, J. P. Gordon, Opt. Lett. 4, 161 (1979).
    [CrossRef] [PubMed]
  20. J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
    [CrossRef]
  21. A. Boivin, J. Dow, E. Wolf, J. Opt. Soc. Am. 57, 1171 (1967).
    [CrossRef]
  22. D. J. Wineland, R. E. Drullinger, F. L. Walls, Phys. Rev. Lett. 40, 1639 (1978); W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 223 (1978).
    [CrossRef]
  23. W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
    [CrossRef]

1982 (3)

V. G. Minogin, Kvantovaya Elektron. (Moscow) 9, 505 (1982) [Sov. J. Quantum Electron. 12, 299 (1982)].

V. G. Minogin, J. Javainen, Opt. Commun. 43, 119 (1982).
[CrossRef]

W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

1981 (1)

See, for example, J. E. Bjorkholm, R. R. Freeman, D. B. Pearson, Phys. Rev. A 23, 491 (1981); J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978); A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

1980 (2)

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

1979 (2)

1978 (2)

D. J. Wineland, R. E. Drullinger, F. L. Walls, Phys. Rev. Lett. 40, 1639 (1978); W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 223 (1978).
[CrossRef]

A. Ashkin, Phys. Rev. Lett. 40, 729 (1978).
[CrossRef]

1977 (1)

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Zh. Eksp. Teor. Fiz. 72, 1328 (1977) [Sov. Phys. JETP 45, 698 (1977)]; V. S. Letokhov, V. G. Minogin, Appl. Phys. 17, 99 (1978).
[CrossRef]

1975 (1)

T. W. Hänsch, A. L. Schawlow, Opt. Commun. 13, 68 (1975).
[CrossRef]

1973 (1)

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

1972 (1)

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 63, 1628 (1972) [Sov. Phys. JETP 36, 861 (1973)].

1971 (1)

A. Ashkin, J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
[CrossRef]

1970 (2)

A. Ashkin, Phys. Rev. Lett. 25, 1321 (1970).
[CrossRef]

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

1967 (1)

1962 (1)

G. A. Askar’yan, Zh. Eksp. Teor. Fiz. 42, 1567 (1962) [Sov. Phys. JETP 15, 1088 (1962)].

Ashkin, A.

A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

A. Ashkin, J. P. Gordon, Opt. Lett. 4, 161 (1979).
[CrossRef] [PubMed]

A. Ashkin, Phys. Rev. Lett. 40, 729 (1978).
[CrossRef]

A. Ashkin, J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
[CrossRef]

A. Ashkin, Phys. Rev. Lett. 25, 1321 (1970).
[CrossRef]

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

A. Ashkin, unpublished experiments. See related work demonstrating gradient forces on submicrometer particles: P. W. Smith, A. Ashkin, W. J. Tomlinson, Opt. Lett. 6, 284 (1981); P. W. Smith, P. J. Maloney, A. Ashkin, Opt. Lett. 7, 347 (1982).
[CrossRef] [PubMed]

Askar’yan, G. A.

G. A. Askar’yan, Zh. Eksp. Teor. Fiz. 42, 1567 (1962) [Sov. Phys. JETP 15, 1088 (1962)].

Bjorkholm, J. E.

See, for example, J. E. Bjorkholm, R. R. Freeman, D. B. Pearson, Phys. Rev. A 23, 491 (1981); J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978); A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

Boivin, A.

Dow, J.

Drullinger, R. E.

D. J. Wineland, R. E. Drullinger, F. L. Walls, Phys. Rev. Lett. 40, 1639 (1978); W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 223 (1978).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
[CrossRef]

Freeman, R. R.

See, for example, J. E. Bjorkholm, R. R. Freeman, D. B. Pearson, Phys. Rev. A 23, 491 (1981); J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978); A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

Gordon, J. P.

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

A. Ashkin, J. P. Gordon, Opt. Lett. 4, 161 (1979).
[CrossRef] [PubMed]

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

Hänsch, T. W.

T. W. Hänsch, A. L. Schawlow, Opt. Commun. 13, 68 (1975).
[CrossRef]

Javainen, J.

V. G. Minogin, J. Javainen, Opt. Commun. 43, 119 (1982).
[CrossRef]

Kazantsev, A. P.

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 63, 1628 (1972) [Sov. Phys. JETP 36, 861 (1973)].

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, London, 1960), p. 54.

Letokhov, V. S.

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Zh. Eksp. Teor. Fiz. 72, 1328 (1977) [Sov. Phys. JETP 45, 698 (1977)]; V. S. Letokhov, V. G. Minogin, Appl. Phys. 17, 99 (1978).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, London, 1960), p. 54.

Maxwell, J. C.

J. C. Maxwell, Treatise on Electricity and Magnetism (Clarendon, Oxford, 1904; Dover, New York, 1962); W. T. Scott, Am. J. Phys. 27, 418 (1959).
[CrossRef] [PubMed]

Metcalf, H.

W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

Minogin, V. G.

V. G. Minogin, Kvantovaya Elektron. (Moscow) 9, 505 (1982) [Sov. J. Quantum Electron. 12, 299 (1982)].

V. G. Minogin, J. Javainen, Opt. Commun. 43, 119 (1982).
[CrossRef]

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Zh. Eksp. Teor. Fiz. 72, 1328 (1977) [Sov. Phys. JETP 45, 698 (1977)]; V. S. Letokhov, V. G. Minogin, Appl. Phys. 17, 99 (1978).
[CrossRef]

Pavlik, B. D.

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Zh. Eksp. Teor. Fiz. 72, 1328 (1977) [Sov. Phys. JETP 45, 698 (1977)]; V. S. Letokhov, V. G. Minogin, Appl. Phys. 17, 99 (1978).
[CrossRef]

Pearson, D. B.

See, for example, J. E. Bjorkholm, R. R. Freeman, D. B. Pearson, Phys. Rev. A 23, 491 (1981); J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978); A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

Phillips, W. D.

W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

Roosen, G.

G. Roosen, Can. J. Phys. 57, 1260 (1979).
[CrossRef]

Schawlow, A. L.

T. W. Hänsch, A. L. Schawlow, Opt. Commun. 13, 68 (1975).
[CrossRef]

Walls, F. L.

D. J. Wineland, R. E. Drullinger, F. L. Walls, Phys. Rev. Lett. 40, 1639 (1978); W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 223 (1978).
[CrossRef]

Wineland, D. J.

D. J. Wineland, R. E. Drullinger, F. L. Walls, Phys. Rev. Lett. 40, 1639 (1978); W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 223 (1978).
[CrossRef]

Wolf, E.

Appl. Phys. Lett. (1)

A. Ashkin, J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
[CrossRef]

Can. J. Phys. (1)

G. Roosen, Can. J. Phys. 57, 1260 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

Kvantovaya Elektron. (Moscow) (1)

V. G. Minogin, Kvantovaya Elektron. (Moscow) 9, 505 (1982) [Sov. J. Quantum Electron. 12, 299 (1982)].

Opt. Commun. (2)

V. G. Minogin, J. Javainen, Opt. Commun. 43, 119 (1982).
[CrossRef]

T. W. Hänsch, A. L. Schawlow, Opt. Commun. 13, 68 (1975).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (3)

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

See, for example, J. E. Bjorkholm, R. R. Freeman, D. B. Pearson, Phys. Rev. A 23, 491 (1981); J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978); A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

A. Ashkin, Phys. Rev. Lett. 25, 1321 (1970).
[CrossRef]

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

A. Ashkin, Phys. Rev. Lett. 40, 729 (1978).
[CrossRef]

D. J. Wineland, R. E. Drullinger, F. L. Walls, Phys. Rev. Lett. 40, 1639 (1978); W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 223 (1978).
[CrossRef]

W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

Science (1)

A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (3)

G. A. Askar’yan, Zh. Eksp. Teor. Fiz. 42, 1567 (1962) [Sov. Phys. JETP 15, 1088 (1962)].

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 63, 1628 (1972) [Sov. Phys. JETP 36, 861 (1973)].

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Zh. Eksp. Teor. Fiz. 72, 1328 (1977) [Sov. Phys. JETP 45, 698 (1977)]; V. S. Letokhov, V. G. Minogin, Appl. Phys. 17, 99 (1978).
[CrossRef]

Other (4)

Absorption of light by the particles may occur and is included in the general theory outlined below.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, London, 1960), p. 54.

J. C. Maxwell, Treatise on Electricity and Magnetism (Clarendon, Oxford, 1904; Dover, New York, 1962); W. T. Scott, Am. J. Phys. 27, 418 (1959).
[CrossRef] [PubMed]

A. Ashkin, unpublished experiments. See related work demonstrating gradient forces on submicrometer particles: P. W. Smith, A. Ashkin, W. J. Tomlinson, Opt. Lett. 6, 284 (1981); P. W. Smith, P. J. Maloney, A. Ashkin, Opt. Lett. 7, 347 (1982).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Geometry of the scattering force on a particle placed at Q in the far field of a Gaussian beam with waist w0 at z = 0.

Fig. 2
Fig. 2

Geometry of a proposed tetrahedral far-field scattering force atom trap, which we show to be unstable. The four beams waists are at A, B, C, and D.

Equations (4)

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F z = K w 2 exp ( 2 r 2 / w 2 ) ,
F r = F z ( r / z ) ,
F g = ( 1 / 4 ) grad ( E * · χ · E ) ,
F s = ( 1 / 2 ) Im { x ˆ j E * · χ · E / x j } .

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