Abstract

Scattering of electromagnetic arbitrary-shaped beams by particles is a topic of growing theoretical (and practical) interest. This topic, however, has suffered from a lack of description of shaped beams that exactly satisfies Maxwell’s equations. As a remedy, this paper presents an exact description of arbitrary-shaped beams for use in light-scattering theories. This general description is illustrated by consideration of Gaussian beams in the so-called modified localized approximation.

© 1996 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. B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
    [CrossRef]
  3. G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
    [CrossRef]
  4. F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
    [CrossRef] [PubMed]
  5. G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
    [CrossRef]
  6. G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Char. 12, 242–256 (1995).
    [CrossRef]
  7. G. Gouesbet, “Interaction between an infinite cylinder and arbitrary-shaped beams,” submitted to Appl. Opt.
  8. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  9. J. F. Rice, The Approximation of Functions (Addison-Wesley, Reading Mass., 1964, Vol. 1; 1969, Vol. 2).
  10. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  11. G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
    [CrossRef] [PubMed]
  12. G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. 13, 97–103 (1982).
    [CrossRef]
  13. G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center, using a Bromwich formulation,” J. Opt. (Paris) 16, 83–93 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 361–371.
    [CrossRef]
  14. 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]
  15. 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]
  16. 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]
  17. G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gnin the generalized Lorenz–Mie theory using three difference methods,” Appl. Opt. 27, 4874–4883 (1998).
    [CrossRef]
  18. 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]
  19. J. P. Barton, D. R. Alexander, “Fifth order corrected electromagnetic field components for fundamental Gaussian beams,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  20. 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]
  21. 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]
  22. G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
    [CrossRef] [PubMed]
  23. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  24. G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase-Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Char. 11, 133–145 (1994).
    [CrossRef]
  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. G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
    [CrossRef]
  27. G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. 16, 239–247 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 352–360.
    [CrossRef]
  28. L. Robin, Fonctions Sphériques de Legendre et Fonctions Sphéroïdales (Gauthier-Villars, Paris, 1957–1959), Vols. 1–3.
  29. P. Poincelot, Précis d’Électromagnétisme Théorique (Masson, Paris, 1963).
  30. 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]
  31. 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]

1998 (1)

1996 (3)

1995 (4)

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

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
[CrossRef]

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Char. 12, 242–256 (1995).
[CrossRef]

1994 (7)

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

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase-Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Char. 11, 133–145 (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]

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]

1990 (1)

1989 (1)

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

1988 (3)

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. 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. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

1986 (1)

1985 (2)

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center, using a Bromwich formulation,” J. Opt. (Paris) 16, 83–93 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 361–371.
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. 16, 239–247 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 352–360.
[CrossRef]

1982 (1)

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

1979 (1)

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

Alexander, D. R.

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

Barton, J. P.

J. P. Barton, D. R. Alexander, “Fifth order corrected electromagnetic field components for fundamental Gaussian beams,” 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]

Durst, F.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase-Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Char. 11, 133–145 (1994).
[CrossRef]

Gouesbet, G.

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gnin the generalized Lorenz–Mie theory using three difference methods,” Appl. Opt. 27, 4874–4883 (1998).
[CrossRef]

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, “Higher-order descriptions of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
[CrossRef]

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

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
[CrossRef]

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Char. 12, 242–256 (1995).
[CrossRef]

G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
[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. 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. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase-Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Char. 11, 133–145 (1994).
[CrossRef]

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, 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]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[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. 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, 83–93 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 361–371.
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. 16, 239–247 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 352–360.
[CrossRef]

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

G. Gouesbet, “Interaction between an infinite cylinder and arbitrary-shaped beams,” submitted to Appl. Opt.

Gréhan, G.

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gnin the generalized Lorenz–Mie theory using three difference methods,” Appl. Opt. 27, 4874–4883 (1998).
[CrossRef]

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]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

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

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase-Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Char. 11, 133–145 (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]

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, 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. 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. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (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, 83–93 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 361–371.
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. 16, 239–247 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 352–360.
[CrossRef]

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

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Letellier, C.

Lock, J. A.

Maheu, B.

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gnin the generalized Lorenz–Mie theory using three difference methods,” Appl. Opt. 27, 4874–4883 (1998).
[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, 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]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[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. 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, 83–93 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 361–371.
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. 16, 239–247 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 352–360.
[CrossRef]

Naqwi, A.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase-Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Char. 11, 133–145 (1994).
[CrossRef]

Onofri, F.

Poincelot, P.

P. Poincelot, Précis d’Électromagnétisme Théorique (Masson, Paris, 1963).

Ren, K. F.

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]

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]

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]

Rice, J. F.

J. F. Rice, The Approximation of Functions (Addison-Wesley, Reading Mass., 1964, Vol. 1; 1969, Vol. 2).

Robin, L.

L. Robin, Fonctions Sphériques de Legendre et Fonctions Sphéroïdales (Gauthier-Villars, Paris, 1957–1959), Vols. 1–3.

van de Hulst, H. C.

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

Appl. Opt. (6)

J. Appl. Phys. (1)

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

J. Opt. (3)

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

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. 16, 239–247 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 352–360.
[CrossRef]

J. Opt. (Paris) (5)

G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
[CrossRef]

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, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
[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, 83–93 (1985).Republished in Selected Papers on Light Scattering, M. Kerker, ed., SPIE Milestone Series (SPIE, Bellingham, Wash., 1988), Vol. 951, Part 1, pp. 361–371.
[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]

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

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]

Part. Part. Syst. Char. (2)

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase-Doppler systems: study of a near-forward and a near-backward geometry,” Part. Part. Syst. Char. 11, 133–145 (1994).
[CrossRef]

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Char. 12, 242–256 (1995).
[CrossRef]

Part. Part. Syst. Charact. (1)

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

Phys. Rev. A (1)

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

Other (6)

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M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

G. Gouesbet, “Interaction between an infinite cylinder and arbitrary-shaped beams,” submitted to Appl. Opt.

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

L. Robin, Fonctions Sphériques de Legendre et Fonctions Sphéroïdales (Gauthier-Villars, Paris, 1957–1959), Vols. 1–3.

P. Poincelot, Précis d’Électromagnétisme Théorique (Masson, Paris, 1963).

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Equations (80)

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( U , V , W ) = ( k u , k υ , k w ) ,
( E u , E υ , E w ) = E 0 exp ( i W ) p = 0 q = 0 l = 0 × ( E pql u , E pql υ , E pql w ) U p V q W l ,
( H u , H υ , H w ) = H 0 exp ( i W ) p = 0 q = 0 l = 0 × ( H pql u , H pql υ , H pql w ) U p V q W l ,
E u = E 0 exp ( i W ) ,
H υ = H 0 exp ( i W ) ,
E 000 u = H 000 υ = 1 .
curl E = i μ ω H ,
div H = 0 ,
curl H = + i ω E ,
div H = 0 ,
ω = k H 0 E 0 , ω μ = k E 0 H 0 .
E w V E υ W + i E 0 H 0 H u = 0 ,
E u W E w U + i E 0 H 0 H υ = 0 ,
E υ U E u V + i E 0 H 0 H w = 0 ,
H u U + H υ V + H w W = 0 ,
H w V H υ W i H 0 E 0 E u = 0 ,
H u W H w U i H 0 E 0 E υ = 0 ,
H υ U H u V i H 0 E 0 E w = 0 ,
E u U + E υ V + E w W = 0.
( q + 1 ) E p q + 1 l w ( l + 1 ) E pql + 1 υ + i ( E pql υ + H pql u ) = 0 ,
( l + 1 ) E p q + 1 l u ( p + 1 ) E p + 1 q l w + i ( H pql υ E pql u ) = 0 ,
( p + 1 ) E p + 1 q l υ ( q + 1 ) E p q + 1 l u + i H pql w = 0 ,
( p + 1 ) H p + 1 q l u + ( q + 1 ) H p q + 1 l υ + ( l + 1 ) × H pql + 1 w i H pql w = 0 ,
( q + 1 ) H p q + 1 l w ( l + 1 ) H pql + 1 υ + i ( H pql υ E pql u ) = 0 ,
( l + 1 ) H pql + 1 u ( p + 1 ) H p + 1 q l w i ( H pql u + E pql υ ) = 0 ,
( p + 1 ) H p + 1 q l υ ( q + 1 ) H p q + 1 l u i E pql w = 0 ,
( p + 1 ) E p + 1 q l u + ( q + 1 ) E p q + 1 l υ + ( l + 1 ) E pql + 1 w i E pql w = 0 .
s = 1 k w 0 ,
g n l = j = 0 l ( 1 ) j j ! n j s 2 j ,
n 0 = 1 ,
n j = ( n j ) ( n j + 1 ) , . . . , ( n 1 ) ( n + 2 ) × ( n + 3 ) , . . . , ( n + j + 1 ) , j > 0 .
g n = j = 0 ( 1 ) j j ! n j s 2 j ,
g n = exp [ ( n + 1 2 ) 2 s 2 ] = l = 0 ( 1 ) l l ! ( n + 1 2 ) 2 l s 2 l .
g n = exp [ s 2 ( n 1 ) ( n + 2 ) ] = l = 0 ( 1 ) l l ! [ ( n 1 ) ( n + 2 ) ] l s 2 l .
E θ = E 0 r cos ϕ n = 1 c n p w g n ( d r Ψ n 1 d r τ n ikr Ψ n 1 π n ) ,
E ϕ = E 0 r cos ϕ n = 1 c n p w g n ( d r Ψ n 1 d r π n ikr Ψ n 1 τ n ) ,
E r = E 0 r cos ϕ n = 1 c n p w g n n ( n + 1 ) Ψ n 1 P n 1 ,
H θ = H 0 r sin ϕ n = 1 c n p w g n ( d r Ψ n 1 d r τ n ikr Ψ n 1 π n ) ,
H ϕ = H 0 r cos ϕ n = 1 c n p w g n ( d r Ψ n 1 d r π n ikr Ψ n 1 τ n ) ,
H r = H 0 r sin ϕ n = 1 c n p w g n n ( n + 1 ) Ψ n 1 P n 1 .
c n p w = 1 i k ( i ) n 2 n + 1 n ( n + 1 ) .
τ n = d P n 1 d θ ,
π n = P n 1 sin θ .
E u = E 0 r n = 1 c n p w g n [ cos θ cos 2 ϕ ( d r Ψ n 1 d r τ n ikr Ψ n 1 π n ) + sin 2 ϕ ( d r Ψ n 1 d r π n ikr Ψ n 1 τ n ) + sin θ cos 2 ϕ n ( n + 1 ) Ψ n 1 P n 1 ] .
g n = l = 0 G 2 l s 2 l ,
G 2 l = k = 0 l α l k N k ,
N = n ( n + 1 ) ,
α l k = ( 1 ) 2 l k k ! ( l k ) ! 2 l k .
E u = E 0 ikr l = 0 s 2 l p = 0 l α l p ( E u 1 p cos θ cos 2 ϕ + E u 2 p sin 2 ϕ + E u 3 p sin θ cos 2 ϕ ) ,
E u 1 p = n = 1 ( i ) n 2 n + 1 n ( n + 1 ) N p ( d r Ψ n 1 d r τ n ikr Ψ n 1 π n ) ,
E u 2 p = n = 1 ( i ) n 2 n + 1 n ( n + 1 ) N p ( d r Ψ n 1 d r π n ikr Ψ n 1 τ n ) ,
E u 3 p = n = 1 ( i ) n ( 2 n + 1 ) N p Ψ n 1 P n 1 .
n = 1 ( i ) n 2 n + 1 n ( n + 1 ) ( d r Ψ n 1 d r τ n ikr Ψ n 1 π n ) = ikr cos θ exp ( ikr cos θ ) ,
P n 1 = d P n d θ ,
n = 0 ( i ) n ( 2 n + 1 ) Ψ n 1 P n = exp ( ikr cos θ ) ,
n ( n + 1 ) Ψ n 1 = r ( d 2 d r 2 + k 2 ) ( r Ψ n 1 ) .
E u 10 = ikr cos θ exp ( ikr cos θ )
E u 1 p = ( r 2 θ 2 i k sin θ θ ) [ r 2 ( 2 r 2 + k 2 ) ] p 1 × r exp ( ikr cos θ ) , p > 0 .
n = 1 ( i ) n 2 n + 1 n ( n + 1 ) ( d r Ψ n 1 d r π n ikr Ψ n 1 τ n ) = ikr exp ( ikr cos θ )
E u 20 = ikr exp ( ikr cos θ ) .
E u 2 p = ( 1 sin θ 2 r θ i k 2 θ 2 ) [ r 2 ( 2 r 2 + k 2 ) ] p 1 × r exp ( ikr cos θ ) , p > 0 .
E u 30 = ikr sin θ exp ( ikr cos θ ) ,
E u 3 p = i k sin θ r [ r 2 ( 2 r 2 + k 2 ) ] p r 2 exp ( ikr cos θ ) , p > 0 .
E u = E 0 exp ( ikr cos θ ) + E 0 ikr l = 1 s 2 l p = 0 l α l p ( E u 1 p cos θ cos 2 ϕ + E u 2 p sin 2 ϕ + E u 3 p sin θ cos 2 ϕ ) ,
E u = j = 0 3 E u 2 j s 2 j ,
E u 0 = E 0 exp ( iKC ) ,
E u 2 = K E u , 0 ( K S 2 2 i C ) ,
E u 4 = E u , 0 K 2 [ 8 K 8 i C + K S 2 ( K 2 S 2 + 4 C ϕ 2 8 iKC + 14 ) ] ,
E u 6 = E u , 0 K 6 { 32 i C 48 i K 2 C + 112 K K S 2 [ 56 C ϕ 2 196 iKC + 156 72 iKC C ϕ 2 72 K 2 + K 2 S 2 ( K 2 S 2 18 iKC + 98 + 12 C ϕ 2 ) ] } ,
K = k r ,
C = cos θ , S = sin θ ,
C ϕ = cos ϕ , S ϕ = sin ϕ .
E u = E 0 exp ( i W ) ( 1 + s 2 [ 2 i W ( U 2 + V 2 ) ] + s 4 × [ 4 W 2 4 i W ( 1 + U 2 + V 2 ) + 1 2 ( U 4 + V 4 ) + U 2 V 2 + 5 U 2 + 3 V 2 ] + s 6 { 8 i W 3 + 4 W 2 ( 14 3 + 3 U 2 + 3 V 2 ) + 1 3 i W [ 9 ( U 2 + V 2 ) 2 + 110 U 2 + 74 V 2 + 16 ] 1 6 ( U 2 + V 2 ) 3 19 3 U 4 13 3 V 4 32 3 U 2 V 2 50 3 U 2 22 3 V 2 } ) .
E υ = 2 E 0 U V exp ( i W ) × { s 4 + s 6 [ 6 i W ( U 2 + V 2 ) 14 3 ] } ,
E w = E 0 U exp ( i W ) × { 2 i s 2 + 2 s 4 [ 4 W i ( U 2 + V 2 ) 2 i ] + s 6 [ 24 i W 2 + 4 W ( 3 U 2 + 3 V 2 + 28 3 ) + i ( U 2 + V 2 ) 2 + 46 3 i ( U 2 + V 2 ) + 16 3 i ] } ,
H u = 2 H 0 U V exp ( i W ) × { s 4 + s 6 [ 6 i W ( U 2 + V 2 ) 14 3 ] } ,
H υ = H 0 exp ( i W ) { 1 + s 2 [ 2 i W ( U 2 + V 2 ) ] + s 4 [ 4 W 2 4 i W ( 1 + U 2 + V 2 ) + 1 2 ( U 4 + V 4 ) + U 2 V 2 + 3 U 2 + 5 V 2 ] + s 6 [ 8 i W 3 + 4 W 2 ( 14 3 + 3 U 2 + 3 V 2 ) + 1 3 i W [ 9 ( U 2 + V 2 ) 2 + 74 U 2 + 110 V 2 + 16 ] 1 6 ( U 2 + V 2 ) 3 13 3 U 4 19 3 V 4 32 3 U 2 V 2 22 3 U 2 50 3 V 2 ] } ,
H w = H 0 V exp ( i W ) × { 2 i s 2 + 2 s 4 [ 4 W i ( U 2 + V 2 ) 2 i ] + s 6 [ 24 i W 2 + 4 W ( 3 U 2 + 3 V 2 + 28 3 ) + i ( U 2 + V 2 ) 2 + 46 3 i ( U 2 + V 2 ) + 16 3 i ] } .
H u = H 0 E 0 E υ ,
H w = H 0 E 0 V U E w ,

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