Abstract

The generalized Lorenz–Mie theory deals with the interaction between spheres and arbitrarily shaped illuminating beams. An efficient use of the theory requires efficient evaluation of the so-called beam-shape coefficients involved in the description of the illuminating beam. A less time-consuming method of evaluation relies on the localized approximation. However, it lacks flexibility when the description of the illuminating beam is modified. We present a new version of this method, called the integral localized approximation, that exhibits the desired property of flexibility.

© 1998 Optical Society of America

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  1. 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]
  2. G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
    [CrossRef]
  3. G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods to evaluate beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
    [CrossRef] [PubMed]
  4. G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
    [CrossRef]
  5. 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] [PubMed]
  6. G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
    [CrossRef]
  7. K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
    [CrossRef]
  8. 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]
  9. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
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    [CrossRef]
  11. 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]
  12. 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]
  13. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  14. 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]
  15. K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
    [CrossRef]
  16. G. Roosen, C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
    [CrossRef]
  17. G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
    [CrossRef] [PubMed]
  18. G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center, using a Bromwich formulation,” J. Opt. (Paris) 16, 83–83 (1985); republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 361–371.
  19. G. Gouesbet, G. Gréhan, B. Maheu, “The order of approximation in a theory of the scattering of a Gaussian beam by Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985), republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 352–360.

1996

1995

1994

1990

1989

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

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]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

1986

1985

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center, using a Bromwich formulation,” J. Opt. (Paris) 16, 83–83 (1985); republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 361–371.

G. Gouesbet, G. Gréhan, B. Maheu, “The order of approximation in a theory of the scattering of a Gaussian beam by Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985), republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 352–360.

1979

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

1978

G. Roosen, C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[CrossRef]

Alexander, D. R.

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

Barton, J. P.

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

Davis, L. W.

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

Gouesbet, G.

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

G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods to evaluate beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (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]

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[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]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (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]

G. Gouesbet, G. Gréhan, B. Maheu, “A 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]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

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] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center, using a Bromwich formulation,” J. Opt. (Paris) 16, 83–83 (1985); republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 361–371.

G. Gouesbet, G. Gréhan, B. Maheu, “The order of approximation in a theory of the scattering of a Gaussian beam by Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985), republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 352–360.

Gréhan, G.

G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods to evaluate beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (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]

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “A 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]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

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] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center, using a Bromwich formulation,” J. Opt. (Paris) 16, 83–83 (1985); republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 361–371.

G. Gouesbet, G. Gréhan, B. Maheu, “The order of approximation in a theory of the scattering of a Gaussian beam by Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985), republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 352–360.

Imbert, C.

G. Roosen, C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[CrossRef]

Letellier, C.

Lock, J. A.

Maheu, B.

G. Gouesbet, G. Gréhan, B. Maheu, “A 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]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

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] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center, using a Bromwich formulation,” J. Opt. (Paris) 16, 83–83 (1985); republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 361–371.

G. Gouesbet, G. Gréhan, B. Maheu, “The order of approximation in a theory of the scattering of a Gaussian beam by Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985), republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 352–360.

Ren, K. F.

Roosen, G.

G. Roosen, C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[CrossRef]

van de Hulst, H. C.

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

Appl. Opt.

J. Appl. Phys.

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. (Paris)

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center, using a Bromwich formulation,” J. Opt. (Paris) 16, 83–83 (1985); republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 361–371.

G. Gouesbet, G. Gréhan, B. Maheu, “The order of approximation in a theory of the scattering of a Gaussian beam by Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985), republished in Selected Papers on Light Scattering, M. Kerker, ed., Vol. 951 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Part I, pp. 352–360.

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

G. Roosen, C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[CrossRef]

Part. Part. Syst. Charact.

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

Phys. Rev. A

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

Other

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

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