Abstract

Recently a so-called standard beam description of Gaussian beams was introduced [J. Opt. Soc. Am. A 11, 2503 (1994)]. However, it was afterward observed [Appl. Opt. 35, 2702 (1996)] that this description exhibits a finite radius of convergence, limiting its range of applicability. We introduce an improved standard beam description with an infinite radius of convergence. The utility of this improved description is illustrated by evaluation of radiation pressure forces under severe focusing conditions.

© 1998 Optical Society of America

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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, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–285 (1971).
    [CrossRef]
  3. G. Roosen, “La lévitation optique de sphères,” J. Can. Phys. 57(9), 1260–1279 (1979).
    [CrossRef]
  4. J. B. Snow, S. X. Qian, R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
    [CrossRef] [PubMed]
  5. R. E. Preston, T. R. Littieri, H. G. Semerjian, “Characterization of single levitated droplets by Raman spectroscopy,” Langmuir 1(3), 365–367 (1985).
    [CrossRef]
  6. B. J. Ackerson, A. H. Chowdhury, “Radiation pressure as a technique for manipulating the particle order in colloidal suspension,” Faraday Discuss. Chem. Soc. 83, 309–316 (1987).
    [CrossRef]
  7. N. Y. Misconi, J. P. Oliver, K. F. Ratcliff, E. T. Rusk, W. X. Wang, “Light scattering by laser levitated particles,” Appl. Opt. 29, 2276–2281 (1990).
    [CrossRef] [PubMed]
  8. N. Roth, K. Anders, A. Frohn, “Determination of size, evaporation rate, and freezing of water droplets using light scattering and radiation pressure,” Part. Part. Syst. Charact. 11(3), 207–211 (1994).
    [CrossRef]
  9. G. Gréhan, G. Gouesbet, “Optical levitation of a single particle to study the theory of quasi-elastic scattering of light,” Appl. Opt. 19, 2485–2487 (1980).
    [CrossRef]
  10. G. Gréhan, F. Guilloteau, G. Gouesbet, “Optical validation of the generalized Lorenz-Mie theory,” Part. Part. Syst. Charact. 7(4), 248–249 (1990).
    [CrossRef]
  11. F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the generalized Lorenz–Mie theory,” Appl. Opt. 31, 2942–2951 (1992).
    [CrossRef] [PubMed]
  12. 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]
  13. K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
    [CrossRef]
  14. S. C. Kuo, M. P. Scheetz, “Force of single kinesin molecule measured with optical tweezers,” Science 260, 232–234 (1993).
    [CrossRef] [PubMed]
  15. T. T. Perkins, S. R. Quake, D. E. Smith, S. Chut, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–826 (1994).
    [CrossRef] [PubMed]
  16. J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, “Single-molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, 298s–305s (1995).
    [PubMed]
  17. G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Optics (Paris) 8(3), 181–187 (1977).
    [CrossRef]
  18. 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]
  19. 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(10), 4594–4599 (1989).
    [CrossRef]
  20. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  21. G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Optics (Paris) 13(2), 97–103 (1982).
    [CrossRef]
  22. J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993).
    [CrossRef]
  23. W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping force on microphere with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
    [CrossRef]
  24. W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
    [CrossRef] [PubMed]
  25. K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
    [CrossRef]
  26. K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
    [CrossRef] [PubMed]
  27. G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
    [CrossRef]
  28. J. A. Lock, G. Gouesbet, “A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz–Mie theory. I: On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
    [CrossRef]
  29. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. 19, 1177–1179 (1979).
    [CrossRef]
  30. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66(7), 2800–2802 (1989).
    [CrossRef]
  31. G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
    [CrossRef] [PubMed]
  32. G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
    [CrossRef]
  33. G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
    [CrossRef] [PubMed]
  34. G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
    [CrossRef]
  35. B. Maheu, G. Gréhan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–26 (1987).
    [CrossRef] [PubMed]
  36. G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
    [CrossRef]
  37. G. Gouesbet, J. A. Lock, “A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz–Mie theory. II: Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
    [CrossRef]

1996 (2)

1995 (3)

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, “Single-molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, 298s–305s (1995).
[PubMed]

1994 (7)

N. Roth, K. Anders, A. Frohn, “Determination of size, evaporation rate, and freezing of water droplets using light scattering and radiation pressure,” Part. Part. Syst. Charact. 11(3), 207–211 (1994).
[CrossRef]

G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
[CrossRef]

T. T. Perkins, S. R. Quake, D. E. Smith, S. Chut, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–826 (1994).
[CrossRef] [PubMed]

J. A. Lock, G. Gouesbet, “A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz–Mie theory. I: On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
[CrossRef]

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

G. Gouesbet, J. A. Lock, “A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz–Mie theory. II: Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
[CrossRef]

1993 (4)

J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993).
[CrossRef]

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

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

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

1992 (2)

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the generalized Lorenz–Mie theory,” Appl. Opt. 31, 2942–2951 (1992).
[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]

1990 (3)

1989 (2)

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(10), 4594–4599 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66(7), 2800–2802 (1989).
[CrossRef]

1988 (1)

1987 (2)

B. J. Ackerson, A. H. Chowdhury, “Radiation pressure as a technique for manipulating the particle order in colloidal suspension,” Faraday Discuss. Chem. Soc. 83, 309–316 (1987).
[CrossRef]

B. Maheu, G. Gréhan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–26 (1987).
[CrossRef] [PubMed]

1986 (2)

1985 (2)

J. B. Snow, S. X. Qian, R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
[CrossRef] [PubMed]

R. E. Preston, T. R. Littieri, H. G. Semerjian, “Characterization of single levitated droplets by Raman spectroscopy,” Langmuir 1(3), 365–367 (1985).
[CrossRef]

1982 (1)

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Optics (Paris) 13(2), 97–103 (1982).
[CrossRef]

1980 (1)

1979 (2)

G. Roosen, “La lévitation optique de sphères,” J. Can. Phys. 57(9), 1260–1279 (1979).
[CrossRef]

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. 19, 1177–1179 (1979).
[CrossRef]

1977 (1)

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Optics (Paris) 8(3), 181–187 (1977).
[CrossRef]

1971 (1)

A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–285 (1971).
[CrossRef]

1970 (1)

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

Ackerson, B. J.

B. J. Ackerson, A. H. Chowdhury, “Radiation pressure as a technique for manipulating the particle order in colloidal suspension,” Faraday Discuss. Chem. Soc. 83, 309–316 (1987).
[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(10), 4594–4599 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66(7), 2800–2802 (1989).
[CrossRef]

Anders, K.

N. Roth, K. Anders, A. Frohn, “Determination of size, evaporation rate, and freezing of water droplets using light scattering and radiation pressure,” Part. Part. Syst. Charact. 11(3), 207–211 (1994).
[CrossRef]

Angelova, M. I.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

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]

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. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–285 (1971).
[CrossRef]

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

Barton, J. P.

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(10), 4594–4599 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66(7), 2800–2802 (1989).
[CrossRef]

Berns, M. W.

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

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

Bjorkholm, J. E.

Block, S. M.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Burns, J. E.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, “Single-molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, 298s–305s (1995).
[PubMed]

Chang, R. K.

Chowdhury, A. H.

B. J. Ackerson, A. H. Chowdhury, “Radiation pressure as a technique for manipulating the particle order in colloidal suspension,” Faraday Discuss. Chem. Soc. 83, 309–316 (1987).
[CrossRef]

Chu, S.

Chut, S.

T. T. Perkins, S. R. Quake, D. E. Smith, S. Chut, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–826 (1994).
[CrossRef] [PubMed]

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. 19, 1177–1179 (1979).
[CrossRef]

Delaunay, B.

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Optics (Paris) 8(3), 181–187 (1977).
[CrossRef]

Dziedzic, J. M.

Frohn, A.

N. Roth, K. Anders, A. Frohn, “Determination of size, evaporation rate, and freezing of water droplets using light scattering and radiation pressure,” Part. Part. Syst. Charact. 11(3), 207–211 (1994).
[CrossRef]

Gouesbet, G.

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

J. A. Lock, G. Gouesbet, “A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz–Mie theory. I: On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
[CrossRef]

G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
[CrossRef]

G. Gouesbet, J. A. Lock, “A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz–Mie theory. II: Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the generalized Lorenz–Mie theory,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

G. Gréhan, F. Guilloteau, G. Gouesbet, “Optical validation of the generalized Lorenz-Mie theory,” Part. Part. Syst. Charact. 7(4), 248–249 (1990).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

B. Maheu, G. Gréhan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–26 (1987).
[CrossRef] [PubMed]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Optics (Paris) 13(2), 97–103 (1982).
[CrossRef]

G. Gréhan, G. Gouesbet, “Optical levitation of a single particle to study the theory of quasi-elastic scattering of light,” Appl. Opt. 19, 2485–2487 (1980).
[CrossRef]

Gréhan, G.

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the generalized Lorenz–Mie theory,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

G. Gréhan, F. Guilloteau, G. Gouesbet, “Optical validation of the generalized Lorenz-Mie theory,” Part. Part. Syst. Charact. 7(4), 248–249 (1990).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

B. Maheu, G. Gréhan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–26 (1987).
[CrossRef] [PubMed]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Optics (Paris) 13(2), 97–103 (1982).
[CrossRef]

G. Gréhan, G. Gouesbet, “Optical levitation of a single particle to study the theory of quasi-elastic scattering of light,” Appl. Opt. 19, 2485–2487 (1980).
[CrossRef]

Guilloteau, F.

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the generalized Lorenz–Mie theory,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

G. Gréhan, F. Guilloteau, G. Gouesbet, “Optical validation of the generalized Lorenz-Mie theory,” Part. Part. Syst. Charact. 7(4), 248–249 (1990).
[CrossRef]

Imbert, C.

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Optics (Paris) 8(3), 181–187 (1977).
[CrossRef]

Kuo, S. C.

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

Littieri, T. R.

R. E. Preston, T. R. Littieri, H. G. Semerjian, “Characterization of single levitated droplets by Raman spectroscopy,” Langmuir 1(3), 365–367 (1985).
[CrossRef]

Lock, J. A.

Maheu, B.

Martinot-Lagarde, G.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Misconi, N. Y.

Molloy, J. E.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, “Single-molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, 298s–305s (1995).
[PubMed]

Oliver, J. P.

Perkins, T. T.

T. T. Perkins, S. R. Quake, D. E. Smith, S. Chut, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–826 (1994).
[CrossRef] [PubMed]

Pouligny, B.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Preston, R. E.

R. E. Preston, T. R. Littieri, H. G. Semerjian, “Characterization of single levitated droplets by Raman spectroscopy,” Langmuir 1(3), 365–367 (1985).
[CrossRef]

Qian, S. X.

Quake, S. R.

T. T. Perkins, S. R. Quake, D. E. Smith, S. Chut, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–826 (1994).
[CrossRef] [PubMed]

Ratcliff, K. F.

Ren, K. F.

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

Roosen, G.

G. Roosen, “La lévitation optique de sphères,” J. Can. Phys. 57(9), 1260–1279 (1979).
[CrossRef]

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Optics (Paris) 8(3), 181–187 (1977).
[CrossRef]

Roth, N.

N. Roth, K. Anders, A. Frohn, “Determination of size, evaporation rate, and freezing of water droplets using light scattering and radiation pressure,” Part. Part. Syst. Charact. 11(3), 207–211 (1994).
[CrossRef]

Rusk, E. T.

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(10), 4594–4599 (1989).
[CrossRef]

Scheetz, M. P.

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

Schmidt, C. F.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Semerjian, H. G.

R. E. Preston, T. R. Littieri, H. G. Semerjian, “Characterization of single levitated droplets by Raman spectroscopy,” Langmuir 1(3), 365–367 (1985).
[CrossRef]

Smith, D. E.

T. T. Perkins, S. R. Quake, D. E. Smith, S. Chut, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–826 (1994).
[CrossRef] [PubMed]

Snow, J. B.

Sonek, G. J.

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

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

Sparrow, J. C.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, “Single-molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, 298s–305s (1995).
[PubMed]

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Tregear, R. T.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, “Single-molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, 298s–305s (1995).
[PubMed]

Wang, W. X.

Wright, W. H.

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

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

Appl. Opt. (9)

N. Y. Misconi, J. P. Oliver, K. F. Ratcliff, E. T. Rusk, W. X. Wang, “Light scattering by laser levitated particles,” Appl. Opt. 29, 2276–2281 (1990).
[CrossRef] [PubMed]

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the generalized Lorenz–Mie theory,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef]

G. Gréhan, G. Gouesbet, “Optical levitation of a single particle to study the theory of quasi-elastic scattering of light,” Appl. Opt. 19, 2485–2487 (1980).
[CrossRef]

B. Maheu, G. Gréhan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–26 (1987).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–285 (1971).
[CrossRef]

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

Biophys. J. (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]

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, “Single-molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, 298s–305s (1995).
[PubMed]

Faraday Discuss. Chem. Soc. (1)

B. J. Ackerson, A. H. Chowdhury, “Radiation pressure as a technique for manipulating the particle order in colloidal suspension,” Faraday Discuss. Chem. Soc. 83, 309–316 (1987).
[CrossRef]

J. Appl. Phys. (2)

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(10), 4594–4599 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66(7), 2800–2802 (1989).
[CrossRef]

J. Can. Phys. (1)

G. Roosen, “La lévitation optique de sphères,” J. Can. Phys. 57(9), 1260–1279 (1979).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Optics (Paris) (2)

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Optics (Paris) 8(3), 181–187 (1977).
[CrossRef]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Optics (Paris) 13(2), 97–103 (1982).
[CrossRef]

Langmuir (1)

R. E. Preston, T. R. Littieri, H. G. Semerjian, “Characterization of single levitated droplets by Raman spectroscopy,” Langmuir 1(3), 365–367 (1985).
[CrossRef]

Nature (London) (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Opt. Commun. (1)

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

Opt. Lett. (2)

Part. Part. Syst. Charact. (3)

G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
[CrossRef]

G. Gréhan, F. Guilloteau, G. Gouesbet, “Optical validation of the generalized Lorenz-Mie theory,” Part. Part. Syst. Charact. 7(4), 248–249 (1990).
[CrossRef]

N. Roth, K. Anders, A. Frohn, “Determination of size, evaporation rate, and freezing of water droplets using light scattering and radiation pressure,” Part. Part. Syst. Charact. 11(3), 207–211 (1994).
[CrossRef]

Phys. Rev. (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. 19, 1177–1179 (1979).
[CrossRef]

Phys. Rev. Lett. (1)

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

Pure Appl. Opt. (1)

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Science (2)

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

T. T. Perkins, S. R. Quake, D. E. Smith, S. Chut, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–826 (1994).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Behavior of the BSC’s (standard and localized) versus n for the beam-waist center case (z 0 = 0).

Fig. 2
Fig. 2

Behavior of the real part of the BSC’s (improved standard, localized, and L5) versus n for z 0 = -5 μm.

Fig. 3
Fig. 3

Behavior of the imaginary part of the BSC’s (improved standard, localized, and L5) versus n for z 0 = -5 μm.

Fig. 4
Fig. 4

Radiation pressure forces and glass particles in air. The incident wavelength is 0.5 μm, and the beam-waist radius is 0.5 λ. The particle radius is a = 2 μm, and the relative refractive index is 1.5.

Equations (18)

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g n = exp ikz 0 p = 0 q = 0 - 2 isz 0 w 0 p × - s 2 q p + q ! p ! q ! 1 q ! n - 1 ! n - 1 - q ! n + 1 + q ! n + 1 ! ,
g n = p = 0 - s 2 p p ! n - 1 ! n - 1 - p ! n + 1 + p ! n + 1 ! .
g 1 = exp ikz 0 p = 0 - 2 isz 0 w 0 p .
g 1 = i = 1 4   S i ,
S 1 q = exp ikz 0 1 + A 4 + A 8 + A 4 q = exp ikz 0 1 - A 4 q + 1 1 - A 4 ,
g 1 = lim q exp ikz 0 1 1 - A 4 1 - A 4 q + 1 × 1 - i A - A 2 + i A 3 ,
g 1 = lim q exp ikz 0 1 1 + i A 1 - A 4 q + 1 .
f e R , θ = D 0 exp - s 2 R 2 D 0 sin 2 θ h e R , θ ,
f b R , θ = D 0 exp - s 2 R 2 D 0 sin 2 θ h b R , θ ,
h B 1 = D 0 ,
h B 3 = D 0 1 + 3 s 4 D 0 2 R 2 sin 2   θ - s 6 D 0 3 R 4 sin 4   θ ,
D 0 = 1 1 - 2 isz / w 0 .
0 sin 2   θ d θ   exp - iR   cos   θ P n 1 cos   θ = - 2 - i n - 1 n n + 1 j n R R
f = D   exp - s 2 R 2 D   sin 2   θ h Bi R , θ ,   i - 1 , 3 , 5 .
E = exp - s 2 R 2 1 + i 2 zs / w 0 ,
g n ¯ = exp ikz 0 1 + i A × p = 0 1 p ! - s 2 p 1 + i A p n + 1 + p ! n + 1 ! n - 1 ! n - 1 - p ! ,
n max 13 | z 0 | + 3 ,   l / 2 < | z 0 | < 5   μ m ,
n max 5 | z 0 | + 45 ,   5 < | z 0 | < 18   μ m ,

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