Abstract

Expressions for radiation-induced forces are presented for the case of a Rayleigh particle near the focus of a Gaussian laser beam at near-resonant conditions. Classical electromagnetic theory was used to obtain the dependence of the scattering and gradient forces on the incident laser frequency, the beam convergence angle, and the spatial position of the particle with respect to the focus. Approximative numerical analysis performed for particles with a single resonant absorption peak demonstrates the occurrence of up to 50-fold enhanced trapping forces at near-resonant frequencies. The use of this technique of gradient force enhancement may provide optical tweezers with enhanced trapping strengths and a degree of specificity.

© 2002 Optical Society of America

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References

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  2. A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
    [CrossRef]
  3. K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [CrossRef] [PubMed]
  4. A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94, 4853–4860 (1997).
    [CrossRef] [PubMed]
  5. M. P. Sheetz, ed., Laser Tweezers in Cell Biology, Vol. 55 of Methods in Cell Biology Series (Academic, New York, 1998).
  6. 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]
  7. K. Sasaki, Z. Y. Shi, R. Kopelman, H. Masuhara, “Three-dimensional pH microprobing with an optically-manipulated fluorescent particle,” Chem. Lett. (2) 141–142 (1996).
  8. F. Gittes, C. F. Schmidt, “Thermal noise limitations on micromechanical experiments,” Eur. Biophys. J. Biophys. Lett. 27, 75–81 (1998).
    [CrossRef]
  9. A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
    [CrossRef]
  10. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
    [CrossRef]
  11. J. P. Gordon, A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
    [CrossRef]
  12. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  13. Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
    [CrossRef]
  14. A. Ashkin, J. M. Dziedzic, P. W. Smith, “Continuous-wave self-focusing and self-trapping of light in artificial Kerr media,” Opt. Lett. 7, 276–278 (1982).
    [CrossRef] [PubMed]
  15. 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]
  16. K. Svoboda, S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19, 930–932 (1994).
    [CrossRef] [PubMed]
  17. J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
    [CrossRef]
  18. S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
    [CrossRef] [PubMed]
  19. P. Meystre, M. Sargent, Elements of Quantum Optics (Springer, New York, 1999).
    [CrossRef]
  20. A. Ashkin, J. P. Gordon, “Stability of radiation-pressure particle traps: an optical Earnshaw theorem,” Opt. Lett. 8, 511–513 (1983).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  24. A. Yariv, Quantum Electronics (Wiley, New York, 1989).
  25. J. P. Barton, D. R. Alexander, “5th-order corrected electromagnetic-field components for a fundamental Gaussian-beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  26. P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988).
  27. A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).
  28. L. D. Landau, E. M. Lifshitz, “Course of theoretical physics,” in Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1960), Vol. 8, pp. 280–281.
  29. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, New York, 1976).
  30. R. Loudon, The Quantum Theory of Light (Oxford U. Press, New York, 1973).
  31. D. C. Cronemeyer, “Optical absorption characteristics of pink ruby,” J. Opt. Soc. Am. 56, 1703–1706 (1966).
    [CrossRef]
  32. C. D. Keefe, “Curvefitting imaginary components of optical properties: restrictions on the lineshape due to causality,”J. Mol. Spectrosc. 205, 261–268 (2001).
    [CrossRef] [PubMed]
  33. W. H. Press, S. A. Teulosky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
  34. E. J. G. Peterman, Division of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, Netherlands, F. Gittes, C. F. Schmidt are preparing a manuscript to be called “Laser-induced heating in optical traps.”
  35. Goodfellow Cambridge Limited, “Ruby,” (2001), http://www.goodfellow.com/static/e/aj60.html .
  36. G. M. Hale, M. R. Querry, “Optical constants of water in the 200 nm to 200 µm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]

2001 (1)

C. D. Keefe, “Curvefitting imaginary components of optical properties: restrictions on the lineshape due to causality,”J. Mol. Spectrosc. 205, 261–268 (2001).
[CrossRef] [PubMed]

2000 (1)

1998 (1)

F. Gittes, C. F. Schmidt, “Thermal noise limitations on micromechanical experiments,” Eur. Biophys. J. Biophys. Lett. 27, 75–81 (1998).
[CrossRef]

1997 (1)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94, 4853–4860 (1997).
[CrossRef] [PubMed]

1996 (2)

K. Sasaki, Z. Y. Shi, R. Kopelman, H. Masuhara, “Three-dimensional pH microprobing with an optically-manipulated fluorescent particle,” Chem. Lett. (2) 141–142 (1996).

Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
[CrossRef]

1994 (2)

K. Svoboda, S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19, 930–932 (1994).
[CrossRef] [PubMed]

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

1992 (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]

1989 (1)

J. P. Barton, D. R. Alexander, “5th-order corrected electromagnetic-field components for a fundamental Gaussian-beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

1986 (2)

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]

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

1983 (1)

1982 (1)

1980 (1)

J. P. Gordon, A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

1978 (2)

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
[CrossRef]

1973 (2)

1970 (2)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

1966 (1)

Alexander, D. R.

J. P. Barton, D. R. Alexander, “5th-order corrected electromagnetic-field components for a fundamental Gaussian-beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Asakura, T.

Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, New York, 1976).

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94, 4853–4860 (1997).
[CrossRef] [PubMed]

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]

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[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]

A. Ashkin, J. P. Gordon, “Stability of radiation-pressure particle traps: an optical Earnshaw theorem,” Opt. Lett. 8, 511–513 (1983).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, P. W. Smith, “Continuous-wave self-focusing and self-trapping of light in artificial Kerr media,” Opt. Lett. 7, 276–278 (1982).
[CrossRef] [PubMed]

J. P. Gordon, A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
[CrossRef]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, “5th-order corrected electromagnetic-field components for a fundamental Gaussian-beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Bjorkholm, J. E.

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]

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

Block, S. M.

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

K. Svoboda, S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19, 930–932 (1994).
[CrossRef] [PubMed]

Cable, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

Chaumet, P. C.

Chu, S.

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]

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

Cronemeyer, D. C.

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Dziedzic, J. M.

Eberly, J. H.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988).

Flannery, B. P.

W. H. Press, S. A. Teulosky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Freeman, R. R.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

Gittes, F.

F. Gittes, C. F. Schmidt, “Thermal noise limitations on micromechanical experiments,” Eur. Biophys. J. Biophys. Lett. 27, 75–81 (1998).
[CrossRef]

Gordon, J. P.

A. Ashkin, J. P. Gordon, “Stability of radiation-pressure particle traps: an optical Earnshaw theorem,” Opt. Lett. 8, 511–513 (1983).
[CrossRef] [PubMed]

J. P. Gordon, A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

Hale, G. M.

Harada, Y.

Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

Keefe, C. D.

C. D. Keefe, “Curvefitting imaginary components of optical properties: restrictions on the lineshape due to causality,”J. Mol. Spectrosc. 205, 261–268 (2001).
[CrossRef] [PubMed]

Kopelman, R.

K. Sasaki, Z. Y. Shi, R. Kopelman, H. Masuhara, “Three-dimensional pH microprobing with an optically-manipulated fluorescent particle,” Chem. Lett. (2) 141–142 (1996).

Landau, L. D.

L. D. Landau, E. M. Lifshitz, “Course of theoretical physics,” in Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1960), Vol. 8, pp. 280–281.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, “Course of theoretical physics,” in Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1960), Vol. 8, pp. 280–281.

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford U. Press, New York, 1973).

Masuhara, H.

K. Sasaki, Z. Y. Shi, R. Kopelman, H. Masuhara, “Three-dimensional pH microprobing with an optically-manipulated fluorescent particle,” Chem. Lett. (2) 141–142 (1996).

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, New York, 1976).

Meystre, P.

P. Meystre, M. Sargent, Elements of Quantum Optics (Springer, New York, 1999).
[CrossRef]

Milonni, P. W.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988).

Nieto-Vesperinas, M.

Pearson, D. B.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

Peterman, E. J. G.

E. J. G. Peterman, Division of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, Netherlands, F. Gittes, C. F. Schmidt are preparing a manuscript to be called “Laser-induced heating in optical traps.”

Press, W. H.

W. H. Press, S. A. Teulosky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Querry, M. R.

Sargent, M.

P. Meystre, M. Sargent, Elements of Quantum Optics (Springer, New York, 1999).
[CrossRef]

Sasaki, K.

K. Sasaki, Z. Y. Shi, R. Kopelman, H. Masuhara, “Three-dimensional pH microprobing with an optically-manipulated fluorescent particle,” Chem. Lett. (2) 141–142 (1996).

Schmidt, C. F.

F. Gittes, C. F. Schmidt, “Thermal noise limitations on micromechanical experiments,” Eur. Biophys. J. Biophys. Lett. 27, 75–81 (1998).
[CrossRef]

Shi, Z. Y.

K. Sasaki, Z. Y. Shi, R. Kopelman, H. Masuhara, “Three-dimensional pH microprobing with an optically-manipulated fluorescent particle,” Chem. Lett. (2) 141–142 (1996).

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).

Smith, P. W.

Svoboda, K.

K. Svoboda, S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19, 930–932 (1994).
[CrossRef] [PubMed]

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Teulosky, S. A.

W. H. Press, S. A. Teulosky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Vetterling, W. T.

W. H. Press, S. A. Teulosky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Appl. Opt. (1)

Astrophys. J. (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[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]

Chem. Lett. (1)

K. Sasaki, Z. Y. Shi, R. Kopelman, H. Masuhara, “Three-dimensional pH microprobing with an optically-manipulated fluorescent particle,” Chem. Lett. (2) 141–142 (1996).

Eur. Biophys. J. Biophys. Lett. (1)

F. Gittes, C. F. Schmidt, “Thermal noise limitations on micromechanical experiments,” Eur. Biophys. J. Biophys. Lett. 27, 75–81 (1998).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, “5th-order corrected electromagnetic-field components for a fundamental Gaussian-beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. Mol. Spectrosc. (1)

C. D. Keefe, “Curvefitting imaginary components of optical properties: restrictions on the lineshape due to causality,”J. Mol. Spectrosc. 205, 261–268 (2001).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (2)

J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

J. P. Gordon, A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Phys. Rev. Lett. (5)

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94, 4853–4860 (1997).
[CrossRef] [PubMed]

Other (13)

M. P. Sheetz, ed., Laser Tweezers in Cell Biology, Vol. 55 of Methods in Cell Biology Series (Academic, New York, 1998).

P. Meystre, M. Sargent, Elements of Quantum Optics (Springer, New York, 1999).
[CrossRef]

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

W. H. Press, S. A. Teulosky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

E. J. G. Peterman, Division of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, Netherlands, F. Gittes, C. F. Schmidt are preparing a manuscript to be called “Laser-induced heating in optical traps.”

Goodfellow Cambridge Limited, “Ruby,” (2001), http://www.goodfellow.com/static/e/aj60.html .

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988).

A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).

L. D. Landau, E. M. Lifshitz, “Course of theoretical physics,” in Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1960), Vol. 8, pp. 280–281.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, New York, 1976).

R. Loudon, The Quantum Theory of Light (Oxford U. Press, New York, 1973).

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Figures (7)

Fig. 1
Fig. 1

Focus geometry as discussed in text.

Fig. 2
Fig. 2

Absorption spectrum of dilute sample with particle number density = 2.7 ′ × 1025 m-3 and sample radius = 10 nm; a max = 745 m-1 at ω0 = 4.67 ′ × 1015 rad/s; HWHM = 0.274 ′ × 1015 rad/s. Datapoints from a single-absorption peak of ruby31 are fit with the CEO model of α″. Lorentzian and Gaussian forms of α″ with the same amplitude and width are determined, and their corresponding absorption spectra are plotted.

Fig. 3
Fig. 3

Plot of z dependence of the axial component of scattering force at resonance using the CEO fit for the polarizability. The decrease near focus for convergence angles ≥ 45° (NA ≥ 1.07) indicates a breakdown of the Gaussian beam approximation. Similar results occur for Gaussian and Lorentzian curve fits.

Fig. 4
Fig. 4

Plots of scaled-trap stiffness for CEO absorption fit. The stiffness κ is multiplied by λ2 to correct for the trivial (nonresonant) wavelength dependence. Radial trap stiffness κr is generally larger than the axial stiffness κz for a given convergence angle. At θ = 30° (NA = 0.76), the axial and radial stiffnesses increase by a factor of 3.0 and 4.3, respectively, compared to far off-resonant frequencies. For angles < 20° (NA < 0.52) no trapping occurs within the wavelength range shown.

Fig. 5
Fig. 5

Plots of scaled-trap stiffness for Lorentzian absorption fit. The stiffness κ is multiplied by λ2 to correct for the trivial (nonresonant) wavelength dependence. These results are similar to those for the CEO fit, since the resonant frequency is much larger than the resonance width (ω0/γ = 17). At θ = 30° (NA = 0.76), the axial stiffness increases by a factor of 2.5 compared to far off-resonant frequencies, whereas the radial stiffness increases by a factor of 3.8.

Fig. 6
Fig. 6

Plots of scaled-trap stiffness for Gaussian absorption fit. The stiffness κ is multiplied by λ2 to correct for the trivial (nonresonant) wavelength dependence. The overall stiffness values are similar to those for previous fits at far off-resonant frequencies. The total wavelength range over which a trap exists, however, is larger. Trapping enhancement is also possible for smaller θ. This results from the lack of long tails in the absorption spectrum that are present in the CEO and Lorentzian fits. At θ = 30° (NA = 0.76), the stiffness as one approaches resonance increases by a factor of 53 in the axial direction and by a factor of 56 in the radial direction as compared with far off-resonant frequencies. Convergence angle does not appear to affect strongly the rate of increase in trap stiffness; it only determines how close to resonance a trap can exist and the absolute value of the stiffness.

Fig. 7
Fig. 7

Plots of wavelengths corresponding to maximum trap stiffness for varying θ. Vertical lines have been added to the x axis to indicate where typical NAs (i.e., 0.5, 0.8, 1.1) occur. Generally, radial-trap stiffness is larger than axial, requiring a slightly smaller convergence angle for maximum stiffness at a given wavelength. For θ much smaller than 20° (NA = 0.52), no trap exists.

Tables (1)

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Table 1 Functional Form of Fitting Curves and Fit Parameters for Imaginary Polarizability

Equations (23)

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Fg=ε02RexˆjαEk* Ekxj=ε04xˆjxjEk*αEk,
Fs=ε02Re-ixˆjαEk* Ekxj=ε02ImxˆjEk*αEkxj,
Er=E02πw0wzexp-r2w2zexpi kmr22Rz×expikmz+iηz,
w2z=w021+zz02,
Rz=z1+z0z2,
ηz=tan-1zz0.
zˆ·Fg=-ε0π α |E0|2z w04z021w4z-2r2w6z×exp-2r2w2z,
rˆ·Fg=-2ε0π α|E0|2r w02w4zexp-2r2w2z,
zˆ·Fs=ε0π α|E0|2w02w2zkm1-r22z2-z02z2+z022-w02z0w2zexp-2r2w2z,
rˆ·Fs=ε0π α |E0|2w02w2zkmrRzexp-2r2w2z.
d2xdt2+2γ dxdt+ω02x=qEm.
αω=α+iα=q2mε0ω02-ω2+2iγωω02-ω22+4γ2ω2.
α+iα=q22mε0ω0γω0-ωγω0-ω2+γ2+i γ2ω0-ω2+γ2.
α=3Nεp/εm-1εp/εm+2,
a=Nαω/c.
αω=ALωω01ω0+ω2+γ2+1ω0-ω2+γ2,
αωALω0-ω2+γ2.
α ω=ALγω0γ2+ω0ω0+ωω0+ω2+γ2+γ2+ω0ω0-ωω0-ω2+γ2.
αω=AGωω0exp-ω-ω02γ2+exp-ω+ω02γ2,
αωAG exp-ω-ω02γ2
αω=2πAGγω01-ωγ Dω-ω0γ-ωγ Dω+ω0γ,
Dx=exp-x20xexpt2dt.
κj=-xjxˆj·Fg+Fsminimum,

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