Abstract

Calculation of the radiation trapping force in laser tweezers by use of generalized Lorenz-Mie theory requires knowledge of the shape coefficients of the incident laser beam. The localized version of these coefficients has been developed and justified only for a moderately focused Gaussian beam polarized in the x direction and traveling in the positive z direction. Here the localized model is extended to a beam tightly focused and truncated by a high-numerical-aperture lens, aberrated by its transmission through the wall of the sample cell, and incident upon a spherical particle whose center is on the beam axis. We also consider polarization of the beam in the y direction and propagation in the negative z direction to be able to describe circularly polarized beams and reflected beams.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  29. K. F. Ren, G. Grehan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
    [CrossRef]
  30. G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, 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]
  31. K. F. Ren, G. Grehan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
    [CrossRef] [PubMed]
  32. H. Polaert, G. Grehan, G. Gouesbet, “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  41. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  42. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
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    [CrossRef]
  44. R. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  49. Ref. 48, p. 692, Eq. (6.574.2).

2004 (1)

2002 (1)

2001 (1)

2000 (2)

P. C. Chaumet, M. Nieto-Vesperinas, “Time-averaged total force on a polar sphere in an electromagnetic field,” Opt. Lett. 25, 1065–1067 (2000).
[CrossRef]

A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
[CrossRef]

1998 (3)

1997 (2)

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B 14, 3323–3333 (1997).
[CrossRef]

1996 (4)

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

T. Wohland, A. Rosin, E. H. K. Stelzer, “Theoretical determination of the influence of polarization on forces exerted by optical tweezers,” Optik (Stuttgart) 102, 181–190 (1996).

K. F. Ren, G. Grehan, 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 beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

1995 (7)

1994 (4)

1993 (2)

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

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]

1992 (2)

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

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1922–1930 (1992).
[CrossRef]

1990 (1)

1989 (4)

B. Maheu, G. Grehan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

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

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[CrossRef]

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

1988 (2)

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

G. Gouesbet, B. Maheu, G. Grehan, “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]

1987 (1)

1986 (2)

1985 (1)

1984 (1)

P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984).
[CrossRef]

1983 (1)

1979 (1)

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

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

R. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Alexander, D. R.

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

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[CrossRef]

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

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

Angelova, M. I.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, 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]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985), p. 668, Eqs. (12.81) and (12.81a) and footnote 2.

Asakura, T.

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

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, 4594–4602 (1989).
[CrossRef]

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[CrossRef]

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

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

Bar-Ziv, R.

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[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 forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Bjorkholm, J. E.

Booker, G. R.

Brevik, I.

Chang, S.

Chaumet, P. C.

Chu, S.

Crichton, J. H.

P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984).
[CrossRef]

Davis, L. W.

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

Dogariu, A. C.

A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
[CrossRef]

Dziedzic, J. M.

Felgner, H.

Gan, X. S.

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Gauthier, R. C.

Gouesbet, G.

H. Polaert, G. Grehan, G. Gouesbet, “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

K. F. Ren, G. Grehan, 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 beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

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

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

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

G. Gouesbet, G. Grehan, 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]

B. Maheu, G. Grehan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

G. Gouesbet, B. Maheu, G. Grehan, “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. Grehan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–25 (1987).
[CrossRef] [PubMed]

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

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 634, Eq. (5.52.1).

Grehan, G.

H. Polaert, G. Grehan, G. Gouesbet, “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

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

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, 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. Grehan, “Partial-wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

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

G. Gouesbet, G. Grehan, 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]

B. Maheu, G. Grehan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

G. Gouesbet, B. Maheu, G. Grehan, “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. Grehan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–25 (1987).
[CrossRef] [PubMed]

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

Gu, M.

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Gussgard, R.

Harada, Y.

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

Ke, P. C.

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Kim, J. S.

Laczik, Z.

Lee, S. S.

Lindmo, T.

Lock, J. A.

Maheu, B.

Marston, P. L.

P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984).
[CrossRef]

Martinot-Lagarde, G.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, 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]

Meller, A.

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Muller, O.

Nemoto, S.

Nieto-Vesperinas, M.

Polaert, H.

Pouligny, B.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, 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]

Rajagopalan, R.

A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
[CrossRef]

Ren, K. F.

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

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

Richards, R.

R. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Rohrbach, A.

Rosin, A.

T. Wohland, A. Rosin, E. H. K. Stelzer, “Theoretical determination of the influence of polarization on forces exerted by optical tweezers,” Optik (Stuttgart) 102, 181–190 (1996).

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 634, Eq. (5.52.1).

Schaub, S. A.

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[CrossRef]

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

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

Schliwa, M.

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 forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Stelzer, E. H. K.

Tlusty, T.

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Togo, H.

Torok, P.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 208–209.

Varga, P.

Wohland, T.

T. Wohland, A. Rosin, E. H. K. Stelzer, “Theoretical determination of the influence of polarization on forces exerted by optical tweezers,” Optik (Stuttgart) 102, 181–190 (1996).

Wolf, E.

R. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

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 forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Appl. Opt. (12)

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]

S. Nemoto, H. Togo, “Axial force acting on a dielectric sphere in a focused laser beam,” Appl. Opt. 37, 6386–6394 (1998).
[CrossRef]

J. A. Lock, “Improved Gaussian beam scattering algorithm,” Appl. Opt. 34, 559–570 (1995).
[CrossRef] [PubMed]

H. Felgner, O. Muller, M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34, 977–982 (1995).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Grehan, “Partial-wave representations 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 beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

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

H. Polaert, G. Grehan, G. Gouesbet, “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

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

A. Rohrbach, E. H. K. Stelzer, “Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494–2507 (2002).
[CrossRef] [PubMed]

J. A. Lock, “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. II. On-axis trapping force,” Appl. Opt. 43, 2545–2554 (2004).
[CrossRef] [PubMed]

B. Maheu, G. Grehan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–25 (1987).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

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

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[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]

J. Appl. Phys. (3)

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

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

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (9)

G. Gouesbet, B. Maheu, G. Grehan, “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]

G. Gouesbet, G. Grehan, 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]

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

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

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]

P. Torok, P. Varga, Z. Laczik, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
[CrossRef]

P. Torok, P. Varga, Z. Laczik, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation (errata),” J. Opt. Soc. Am. A 12, 1605 (1995).
[CrossRef]

P. Torok, P. Varga, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995).
[CrossRef]

A. Rohrbach, E. H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2001).
[CrossRef]

J. Opt. Soc. Am. B (3)

Langmuir (1)

A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
[CrossRef]

Opt. Commun. (3)

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

B. Maheu, G. Grehan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

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

Opt. Lett. (2)

Optik (Stuttgart) (1)

T. Wohland, A. Rosin, E. H. K. Stelzer, “Theoretical determination of the influence of polarization on forces exerted by optical tweezers,” Optik (Stuttgart) 102, 181–190 (1996).

Phys. Rev. A (2)

P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984).
[CrossRef]

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

Phys. Rev. Lett. (1)

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Proc. R. Soc. London Ser. A (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

R. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Pure Appl. Opt. (1)

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, 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]

Rev. Sci. Instrum. (1)

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Other (4)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 208–209.

G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985), p. 668, Eqs. (12.81) and (12.81a) and footnote 2.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 634, Eq. (5.52.1).

Ref. 48, p. 692, Eq. (6.574.2).

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Tables (3)

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Table 1 Actual 1/e2 Intensity Transverse Half-Width wa of a Davis-Barton Fifth-Order Focused Gaussian Beam (D5) and a Localized Focused Gaussian Beam (L) at the Center of the Focal Waist As a Function of Intended Half-Width wi for λ = 1.06 μm and n1 = 1.50

Tables Icon

Table 2 Focal Plane Airy Disk Radius ρAiry in Medium n1 of the Original and Localized Versions of a Plane Wave Focused by a Lens As a Function of Maximum Convergence Angle α of the Lens for λ = 1.06 μm and n1 = 1.50

Tables Icon

Table 3 Focal Plane Airy Disk Radius ρAiry Along the x and y Axes of the Original and Localized Versions of a Plane Wave Focused by a Lens and Reflected by a Flat Interface As a Function of Maximum Convergence Angle α of the Lens for λ = 1.06 μm, n1 = 1.50, and n2 = 1.33

Equations (110)

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E=E0erur+eθuθ+eϕuϕ,
B=nE0/cbrur+bθuθ+bϕuϕ,
err, θ, ϕ=-i l=1m=-ll ll+1Al,mjlnkr/nkr×πl|m|θsinθexpimϕ,
eθr, θ, ϕ=i l=1m=-llmBl,mjlnkrπl|m|θ-Al,mLlnkrτl|m|θexpimϕ,
eϕr, θ, ϕ=-l=1m=-llBl,mjlnkrτl|m|θ-mAl,mLlnkrπl|m|θexpimϕ,
brr, θ, ϕ=-i l=1m=-ll ll+1Bl,mjlnkr/nkr×πl|m|θsinθexpimϕ,
bθr, θ, ϕ=-i l=1m=-llmAl,mjlnkrπl|m|θ+Bl,mLlnkrτl|m|θexpimϕ,
bϕr, θ, ϕ=l=1m=-llAl,mjlnkrτl|m|θ+mBl,mLlnkrπl|m|θexpimϕ.
Llnkrjlnkr/nkr+jlnkr,
πl|m|θPl|m|cosθ/sinθ,
τl|m|θd/dθPl|m|cosθ,
Al,m=i/2π2l+1/2ll+1l-|m|!/l+|m|!nkr/jlnkr0πsinθdθ×02πdϕerr, θ, ϕPl|m|cosθexp-imϕ,
Bl,m=i/2π2l+1/2ll+1l-|m|!/l+|m|!nkr/jlnkr0πsinθdθ×02πdϕbrr, θ, ϕPl|m|cosθexp-imϕ.
Al,±1=il2l+1gl/2ll+1,
Bl,±1=±iil2l+1hl/2ll+1.
E=E0G1e cosϕur+G2e cosϕuθ-G3e sinϕuϕ,
B=nE0/cG1b sinϕur+G2b sinϕuθ+G3b cosϕuϕ,
G1er, θ=-i l=1 il2l+1×gljlnkr/nkrπlθsinθ,
G2er, θ=l=1il2l+1/ll+1hljlnkrπlθ-iglLlnkrτlθ,
G3er, θ=l=1il2l+1/ll+1hljlnkrτlθ-iglLlnkrπlθ,
G1br, θ=-i l=1 il2l+1×hljlnkr/nkrπlθsinθ,
G2br, θ=l=1il2l+1/ll+1gljlnkrπlθ-ihlLlnkrτlθ,
G3br, θ=l=1il2l+1/ll+1gljlnkrτlθ-ihlLlnkrπlθ;
πlθπl1θ,
τlθτl1θ.
F1uG1u sinθ+G2u cosθ,
F2uG1u sinθ+G2u cosθ-G3u,
F3uG1u cosθ-G2u sinθ
E=E0F1e-F2e sin2ϕux+F2e sinϕcosϕuy+F3e cosϕuz,
B=nE0/cF2b sinϕcosϕux+F1b-F2b cos2ϕuy+F3b sinϕuz.
Al,±1=±iil2l+1gl/2ll+1,
Bl,±1=-il2l+1hl/2ll+1.
E=E0G1e sinϕur+G2e sinϕuθ+G3e cosϕuϕ =E0F2e sinϕcosϕux+F1e-F2e cos2ϕuy+F3e sinϕuz,
B=nE0/c-G1b cosϕur-G2b cosϕuθ+G3b sinϕuϕ =nE0/c{-F1b-F2b sin2ϕux-F2b sinϕcosϕuy-F3b cosϕuz.
Al,±1=--il2l+1gl/2ll+1,
Bl±1=±i-il2l+1hl/2ll+1.
Al,±1=±i-il2l+1gl/2ll+1,
Bl,±1=--il2l+1hl/2ll+1.
I±z=E*×B · ±uz/μ0,
I±z=nE02/μ0cF1e*F1b-F2e*F1b+F1e*F2b/2+cos2ϕF2e*F1b-F1e*F2b/2,
E* · E=E02F1e*F1e+F3e*F3e+F1e*-F2e*×F1e-F2e/2+cos2ϕF3e*F3e-F2e*F2e+F1e*F2e+F2e*F1e/2,
E=E0 exp-ρ2/w2ux,
B=nE0/cexp-ρ2/w2uy,
ρr sinθ
F1e=F1b=D expinkz-z0exp-Dρ2/w2,
F2e=F2b=F3e=F3b=0,
D1+2isz-z0/w-1,
s1/nkw,
F1e=F1b=D1+s23ρ2D2/w2-ρ4D3/w4+s410ρ4D4/w4-5ρ6D5/w6+ρ8D6/2w8expinkz-z0exp-Dρ2/w2,
F2e=F2b=2ρ2D3/w2s2+s44ρ2D2/w2-ρ4D3/w4expinkz-z0exp-Dρ2/w2,
F3e=F3b=-2isρD/wF1e.
NA=n1 sinα,
Fie=Fib=-in1kF 0αsinθ1dθ1cosθ11/2×expin1kz-z0cosθ1pi,
p1=1/21+cosθ1J0n1kρ sinθ1+1-cosθ1J2n1kρ sinθ1,
p2=1-cosθ1J2n1kρ sinθ1,
p3=-i sinθ1J1n1kρ sinθ1.
Fiu=-in1kF 0αsinθ1dθ1cosθ11/2×expin2k cosθ2z-d-n1k×cosθ1z0-dpiu
p1e=1/2tTE+tTM cosθ2J0n1kρ sinθ1+tTE-tTM cosθ2J2n1kρ sinθ1,
p2e=tTE-tTM cosθ2J2n1kρ sinθ1,
p3e=-itTM sinθ2J1n1kρ sinθ1,
p1b=1/2tTM+tTE cosθ2J0n1kρ sinθ1+tTM-tTE cosθ2J2n1kρ sinθ1,
p2b=tTM-tTE cosθ2J2n1kρ sinθ1,
p3b=-itTE sinθ2J1n1kρ sinθ1;
n1 sinθ1=n2 sinθ2.
tTE=2 cosθ1/cosθ1+n2/n1cosθ2,
tTM=2 cosθ1/n2/n1cosθ1+cosθ2.
zfocus=z0-n1-n2z0-d/n1.
ρ2=8n13v3/27n2n12-n22z0-d,
v=zfocus-z.
Fiu=-in1kF 0αsinθ1dθ1cosθ11/2×expi-n1k cosθ1z0-d+n1k×cosθ1d-zpiu
p1e=1/2rTE-rTM cosθ1J0n1kρ sinθ1+rTE+rTM cosθ1J2n1kρ sinθ1,
p2e=rTE+rTM cosθ1J2n1kρ sinθ1,
p3e=-irTM sinθ1J1n1kρ sinθ1,
p1b=-1/2rTM-rTE cosθ1J0n1kρ sinθ1+rTM+rTE cosθ1J2n1kρ sinθ1,
p2b=-rTM+rTE cosθ2J2n1kρ sinθ1,
p3b=irTE sinθ1J1n1kρ sinθ1.
rTE=cosθ1-n2/n1cosθ2/cosθ1+n2/n1cosθ2,
rTM=n2/n1cosθ1-cosθ2/n2/n1cosθ1+cosθ2.
Fiufiuexpinkz
fref1e+f3e cosθ/sinθ,
frbf1b+f3b cosθ/sinθ
er=expinkzfre sinθcosϕ,
br=expinkzfrb sinθsinϕ.
gl=frenkr=l+1/2, θ=π/2=f1enkr=l+1/2, θ=π/2,
hl=frbnkr=l+1/2, θ=π/2=f1bnkr=l+1/2, θ=π/2.
er=expinkzfre sinθsinϕ,
br=-expinkzfrb sinθcosϕ,
er=exp-inkzfre sinθcosϕ,
br=-exp-inkzfrb sinθsinϕ,
Fiufiuexp-inkz.
er=exp-inkzfre sinθsinϕ,
br=exp-inkzfrb sinθcosϕ.
gl=hl=D exp-inkz0exp-Ds2l+1/22,
gl=hl=D exp-inkz0exp-Ds2l+2l-1.
F1e=F1b=exp-inkz0/1-2isz0/w,
F2e=F2b=F3e=F3b=0.
F1e=g1,
F1b=h1,
F2e=F2b=F3e=F3b=0,
F1e=F1b=exp-inkz0exp-9s2/41-2isz0/w/1-2isz0/w,
F2e=F2b=F3e=F3b=0,
gl=hl=-in1kF 0αsinθ1dθ1cosθ11/2×expin1kz-z0cosθ11/21+cosθ1J0l+1/2sinθ1+1-cosθ1J2l+1/2sinθ1.
Iz=nE02/μ0cF1F1-F2
E* · E=E02F12+|F3|2+F1-F22/2+cos2ϕ×|F3|2-F22+2F1F2/2,
Iz=nE02/μ0cexp-2ρ2/w21+s24ρ2/w2-2ρ4/w4+s415ρ4/w4+4ρ6/w6+2ρ8/w8+Os6.
E* · E=E02exp-2ρ2/w21+s26ρ2/w2-2ρ4/w4+4s2 cos2ϕρ2/w2+Os4.
wxactual=20 x2E*ϕ=0 · Eϕ=0dx0E*ϕ=0 · Eϕ=0dx1/2 =w1+7s2/4+Os4,
wyactual=20 y2E*ϕ=π/2 · Eϕ=π/2dy0E*ϕ=π/2 · Eϕ=π/2dy1/2 =w1-s2/4+Os4.
ρAiry=0.617λ/NA.
P=E02/μ0cπF2 sin2α+Osin10α

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