Abstract

A previously developed theoretical procedure for determination of electromagnetic fields associated with the interaction of a higher-order Gaussian beam with a homogeneous spherical particle is used to investigate the effects of incident beam type on far-field scattering. Far-field scattering patterns are calculated for (0,0), (0,1), and (1,1) mode Hermite–Gaussian beams and for the helix doughnut mode beam. The effects of incident beam type on the angular distribution of far-field scattering, for both on-sphere-center and off-sphere-center focusing, are examined.

© 1998 Optical Society of America

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References

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  1. J. P. Barton, “Electromagnetic-field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects,” Appl. Opt. 36, 1303–1311 (1997).
    [CrossRef]
  2. W.-C. Tsai, R. J. Pogorzelski, “Eigenfunction solution of the scattering of beam radiation fields by spherical objects,” J. Opt. Soc. Am. 65, 1457–1463 (1975).
    [CrossRef]
  3. R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
    [CrossRef]
  4. H. Chew, M. Kerker, D. D. Cooke, “Light scattering in converging beams,” Opt. Lett. 1, 138–140 (1977).
    [CrossRef]
  5. C. Yeh, S. Colak, P. Barber, “Scattering of sharply focused beams by arbitrarily shaped dielectric particles: an exact solution,” Appl. Opt. 21, 4426–4433 (1982).
    [CrossRef] [PubMed]
  6. G. Grehan, 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]
  7. J.-P. Chevaillier, J. Fabre, P. Hamelin, “Forward scattered light intensities by a sphere located anywhere in a Gaussian beam,” Appl. Opt. 25, 1222–1225 (1986).
    [CrossRef] [PubMed]
  8. S. O. Park, S. S. Lee, “Forward far-field pattern of a laser beam scattered by a water-suspended homogeneous sphere trapped by a focused laser beam,” J. Opt. Soc. Am. A 4, 417–422 (1987).
    [CrossRef]
  9. B. Maheu, G. Grehan, G. Gouesbet, “Laser beam scattering by individual spherical particles: numerical results and application to optical sizing,” Part. Charact. 4, 141–146 (1987).
    [CrossRef]
  10. J. A. Lock, “Contributions 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]
  11. J. T. Hodges, G. Grehan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
    [CrossRef]
  12. J. A. Lock, J. T. Hodges, “Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle,” Appl. Opt. 35, 4283–4290 (1996).
    [CrossRef]
  13. J. A. Lock, J. T. Hodges, “Far-field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle,” Appl. Opt. 35, 6605–6616 (1996).
    [CrossRef]

1997 (1)

1996 (2)

1995 (1)

1993 (1)

1987 (2)

B. Maheu, G. Grehan, G. Gouesbet, “Laser beam scattering by individual spherical particles: numerical results and application to optical sizing,” Part. Charact. 4, 141–146 (1987).
[CrossRef]

S. O. Park, S. S. Lee, “Forward far-field pattern of a laser beam scattered by a water-suspended homogeneous sphere trapped by a focused laser beam,” J. Opt. Soc. Am. A 4, 417–422 (1987).
[CrossRef]

1986 (2)

1982 (1)

1977 (1)

1976 (1)

R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

1975 (1)

Barber, P.

Barton, J. P.

Chevaillier, J.-P.

Chew, H.

Colak, S.

Cooke, D. D.

Fabre, J.

Gouesbet, G.

Grehan, G.

Hamelin, P.

Hodges, J. T.

Kerker, M.

Lee, S. S.

Lock, J. A.

Lun, E.

R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

Maheu, B.

B. Maheu, G. Grehan, G. Gouesbet, “Laser beam scattering by individual spherical particles: numerical results and application to optical sizing,” Part. Charact. 4, 141–146 (1987).
[CrossRef]

G. Grehan, 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]

Park, S. O.

Pogorzelski, R. J.

R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

W.-C. Tsai, R. J. Pogorzelski, “Eigenfunction solution of the scattering of beam radiation fields by spherical objects,” J. Opt. Soc. Am. 65, 1457–1463 (1975).
[CrossRef]

Presser, C.

Tsai, W.-C.

Yeh, C.

Appl. Opt. (7)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Part. Charact. (1)

B. Maheu, G. Grehan, G. Gouesbet, “Laser beam scattering by individual spherical particles: numerical results and application to optical sizing,” Part. Charact. 4, 141–146 (1987).
[CrossRef]

Radio Sci. (1)

R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Geometric arrangement for the higher-order Gaussian beam incident on a homogeneous spherical particle problem.

Fig. 2
Fig. 2

Gray-level visualization (white ⇒ high, black ⇒ low) of calculated far-field forward-scattering intensity projected onto a flat surface extending from 0° to +45° in the y-axis (vertical) direction and from -45° to +45° in the x-axis (horizontal) direction. On-sphere-center focusing ( 0= 0 = 0 = 0). From top to bottom: TEM00 (x) mode, TEM01 (x) mode, TEM11 (x) mode, and TEM dn (lhel) mode. For forward scattering, the 0° to 10° region has been intentionally blacked out. Relative index of refraction = (1.3, 0.0), particle size parameter α = 38.31549 (nonresonance), and beam waist radius 0 = 1.414.

Fig. 3
Fig. 3

Gray-level visualization of calculated backward scattering for on-sphere-center focusing ( 0= 0 = 0 = 0).

Fig. 4
Fig. 4

Gray-level visualization of calculated forward scattering for on-sphere-edge focusing ( 0 = 1.0, 0 = 0 = 0). For forward scattering, the 0° to 10° region has been intentionally blacked out.

Fig. 5
Fig. 5

Gray-level visualization of calculated backward scattering for on-sphere-edge focusing ( 0 = 1.0, 0 = 0 = 0).

Fig. 6
Fig. 6

Polar-angle-integrated, azimuthal-angle-dependent, far-field scattering intensity S r (ϕ) for the TEM00 (x) mode beam as a function of on-x-axis focal point positioning. Relative index of refraction = (1.3, 0.0), particle size parameter α = 38.31549 (nonresonance), beam waist radius 0 = 1.414, and polar angle lower integration limit θ0 = 10° = π/18.

Fig. 7
Fig. 7

Azimuthal far-field scattering intensity S r (ϕ) for the TEM01 (x) mode beam as a function of on-x-axis focal point positioning.

Fig. 8
Fig. 8

Azimuthal far-field scattering intensity S r (ϕ) for the TEM11 (x) mode beam as a function of on-x-axis focal point positioning.

Fig. 9
Fig. 9

Azimuthal far-field scattering intensity S r (ϕ) for the TEM dn (lhel) mode left-handed helix doughnut beam as a function of on-x-axis focal point positioning.

Equations (4)

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ξ l 1 α r ˜ = ψ l α r ˜ - i χ l α r ˜     - i l + 1 exp i α r ˜ ,
ξ l 1 α r ˜ = ψ l α r ˜ - i χ l α r ˜     - i l exp i α r ˜ ,
S r θ ,   ϕ = lim r r 2 S r c 8 π   E 0 2 π a 2 = lim r ˜ r ˜ 2 π   Real E θ s H ϕ s * - E ϕ s H θ s * .
S r ϕ = θ 0 π   S r θ ,   ϕ sin θ d θ ,

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