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  1. G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. Paris 13, 97 (1982).
    [CrossRef]
  2. G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using a Bromwich Formalism,” J. Opt. Paris 16, 83 (1985).
    [CrossRef]
  3. 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, Paris 16, 239 (1985).
    [CrossRef]
  4. Our notations follow Kerker exactly The Scattering of Light and Other Electromagnetic RadiationAcademic, New York, 1969); H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), except for the spherical Bessel functions noted jn by Kerker and van de Hulst while we have chosen Ψn1 like L. Robin, Fonctions Sphériques de Legendre et Fonctions Sphéroidales (Gauthiers-Villars, Paris, 1959), Vol. 3.
  5. In Refs. 2 and 3, the beam is modeled using a series expansion of the potential vector. The L order (L for lowest) is the lowest order complying with Maxwell’s equations. The L− order is lower than the L order since only the first terms of the series are kept. For example, the basic radial function f is, respectively, f = Ψ0 at order L− and f = Ψ0(1 − 2Qrcosθ/l) at order L. Ψ0 being the well-known Fundamental mode of Gaussian beams: Ψ0=iQ exp(-iQr2 sin2θ/w02) where l is the so-called diffraction or spreading length of the beam, w0 is the beam radius at the waist, and Q = 1/(i+2r cosθ/l).
  6. G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of Laser Beams by Mie Scatter Centers: Numerical Results Using a Localized Approximation,” Appl. Opt. 25, 3539 (1986).
    [CrossRef] [PubMed]

1986

1985

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using a Bromwich Formalism,” J. Opt. Paris 16, 83 (1985).
[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, Paris 16, 239 (1985).
[CrossRef]

1982

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

Gouesbet, G.

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of Laser Beams by Mie Scatter Centers: Numerical Results Using a Localized Approximation,” Appl. Opt. 25, 3539 (1986).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using a Bromwich Formalism,” J. Opt. Paris 16, 83 (1985).
[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, Paris 16, 239 (1985).
[CrossRef]

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

Gréhan, G.

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of Laser Beams by Mie Scatter Centers: Numerical Results Using a Localized Approximation,” Appl. Opt. 25, 3539 (1986).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using a Bromwich Formalism,” J. Opt. Paris 16, 83 (1985).
[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, Paris 16, 239 (1985).
[CrossRef]

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

Maheu, B.

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of Laser Beams by Mie Scatter Centers: Numerical Results Using a Localized Approximation,” Appl. Opt. 25, 3539 (1986).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using a Bromwich Formalism,” J. Opt. Paris 16, 83 (1985).
[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, Paris 16, 239 (1985).
[CrossRef]

Appl. Opt.

J. Opt, Paris

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, Paris 16, 239 (1985).
[CrossRef]

J. Opt. Paris

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

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using a Bromwich Formalism,” J. Opt. Paris 16, 83 (1985).
[CrossRef]

Other

Our notations follow Kerker exactly The Scattering of Light and Other Electromagnetic RadiationAcademic, New York, 1969); H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), except for the spherical Bessel functions noted jn by Kerker and van de Hulst while we have chosen Ψn1 like L. Robin, Fonctions Sphériques de Legendre et Fonctions Sphéroidales (Gauthiers-Villars, Paris, 1959), Vol. 3.

In Refs. 2 and 3, the beam is modeled using a series expansion of the potential vector. The L order (L for lowest) is the lowest order complying with Maxwell’s equations. The L− order is lower than the L order since only the first terms of the series are kept. For example, the basic radial function f is, respectively, f = Ψ0 at order L− and f = Ψ0(1 − 2Qrcosθ/l) at order L. Ψ0 being the well-known Fundamental mode of Gaussian beams: Ψ0=iQ exp(-iQr2 sin2θ/w02) where l is the so-called diffraction or spreading length of the beam, w0 is the beam radius at the waist, and Q = 1/(i+2r cosθ/l).

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Figures (1)

Fig. 1
Fig. 1

Integration of Eq. (2) over the range 0.001 < kr < krmax order n = 60; beam waist parameter b0 = 20π value of g60 vs log(krmax).

Tables (2)

Tables Icon

Table I Comparison Between Approximate and Exact Coefficients gn

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Table II Example with Large Beam Waist

Equations (4)

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S 1 = n = 1 2 n + 1 n ( n + 1 ) g n [ a n π n ( cos θ ) + b n τ n ( cos θ ) ] , S 2 = n = 1 2 n + 1 n ( n + 1 ) g n [ a n π n ( cos θ ) + b n τ n ( cos θ ) ] ,
g n = 2 n + 1 π n ( n + 1 ) 1 ( - 1 ) n i n 0 π 0 i k r sin 2 θ f exp ( - i k r cos θ ) · Ψ n 1 ( k r ) P n 1 ( cos θ ) d θ d ( k r ) .
g n = exp { - [ ( n + 1 2 ) b 0 ] 2 } ,
f = exp [ - ( k r sin θ b 0 ) 2 ] .

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