Abstract

The beam-shape coefficients of arbitrary off-axis Gaussian beams in spheroidal coordinates are evaluated with a generalized Lorenz–Mie theory. The light-scattering properties of absorbing and nonabsorbing homogeneous spheroidal particles, such as the angular distribution of scattered intensity for a wide range of particles sizes and different complex refractive indices versus the magnitude and location of the beam waist, are investigated.

© 2003 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, “Interaction between infinite cylinders and an arbitrarily shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
    [CrossRef] [PubMed]
  3. L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
    [CrossRef]
  4. G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Description of arbitrarily shaped beams in elliptical cylinder coordinates, by using a plane-wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
    [CrossRef]
  5. 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]
  6. S. Nag, B. P. Sinha, “Electromagnetic plane wave scattering by a system of two uniformly lossy dielectric prolate spheroids in arbitrary orientation,” IEEE Trans. Antennas Propag. 43, 322–327 (1995).
    [CrossRef]
  7. T. G. Tsuei, P. W. Barber, “Information content of the scattering matrix for spheroidal particles,” Appl. Opt. 24, 2391–2396 (1985).
    [CrossRef] [PubMed]
  8. J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
    [CrossRef]
  9. B. P. Sinha, R. H. Hacphie, “Electromagnetic scattering by prolate spheroids for a plane wave with arbitrary polarization and angle of incidence,” Radio Sci. 12, 171–184 (1997).
    [CrossRef]
  10. J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995).
    [CrossRef] [PubMed]
  11. 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, 239–245 (1985).
    [CrossRef]
  12. G. Gouesbet, “Validity of the localized approximation for arbitrarily shaped beams in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
    [CrossRef]
  13. Y. Han, Z. S. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001).
    [CrossRef]
  14. Y. Han, Z. S. Wu, “Absorption and scattering by an oblate particle,” J. Opt. A: Pure Appl. 4, 74–77 (2002).
    [CrossRef]
  15. C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).
  16. M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
    [CrossRef]
  17. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
    [CrossRef] [PubMed]
  18. D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing, and weakly absorbing nonspherical particles and comparison with geometrical optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
    [CrossRef] [PubMed]
  19. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), pp. 3–27.
  20. C. F. Bohren, D. R. Huffman, Absortion and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 397–399.
  21. J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. I. On-axis beam,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
    [CrossRef]
  22. G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beam,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
    [CrossRef]
  23. G. Gouesbet, G. Grehan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
    [CrossRef] [PubMed]
  24. G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theory for assemblies of spheres and aggregates,” J. Opt. A: Pure Appl. Opt. 1, 706–712 (1999).
    [CrossRef]
  25. G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 3–5, 277–333 (2000).
  26. J. P. Barton, “Internal and near-surface electromagnetic fields for an absorbing spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 6471–8473 (1995).
  27. J. P. Barton, “Internal and near-surface electromagnetic fields for a layered spheroid with arbitrary illumination,” Appl. Opt. 40, 3598–3607 (2001).
    [CrossRef]
  28. J. P. Barton, “Electromagnetic field calculations for an irregularly shaped, near-spheroidal particle with arbitrary illumination,” J. Opt. Soc. Am. A 19, 2429–2435 (2002).
    [CrossRef]
  29. Y. Han, Z. S. Wu, “The expansion coefficients of a spheroidal particle illuminated by a Gaussian beam,” IEEE Trans. Antennas Trans. 49, 615–620 (2001).
    [CrossRef]
  30. K. F. Ren, G. Grehan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory: faster algorithm for computation of beam shape coefficient gnm,” Part. Part. Charact. 9, 144–150 (1992).
    [CrossRef]
  31. A. Doicu, T. Wriedt, “Computation of the beam-shape coefficients in the generalized Lorenz–Mie theory by using the translational addition theorem for spherical vector wave functions,” Appl. Opt. 36, 2971–2978 (1997).
    [CrossRef] [PubMed]
  32. S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
    [CrossRef] [PubMed]
  33. S. Asano, “Light scattering properties of spheroidal particles,” Appl. Opt. 18, 712–723 (1979).
    [CrossRef] [PubMed]
  34. S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
    [CrossRef] [PubMed]
  35. Y. Han, Z. S. Wu, “Discussion of the boundary condition forelectromagnetic scattering by spheroidal particles,” Acta Phys. Sin. 49, 57–60 (2000).
  36. Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
    [CrossRef]
  37. R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
    [CrossRef] [PubMed]
  38. S. Zhang, J. Jin, Computation of Special Functions (Wiley, New York, 1996).
  39. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

2002 (3)

Y. Han, Z. S. Wu, “Absorption and scattering by an oblate particle,” J. Opt. A: Pure Appl. 4, 74–77 (2002).
[CrossRef]

Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

J. P. Barton, “Electromagnetic field calculations for an irregularly shaped, near-spheroidal particle with arbitrary illumination,” J. Opt. Soc. Am. A 19, 2429–2435 (2002).
[CrossRef]

2001 (3)

2000 (2)

G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 3–5, 277–333 (2000).

Y. Han, Z. S. Wu, “Discussion of the boundary condition forelectromagnetic scattering by spheroidal particles,” Acta Phys. Sin. 49, 57–60 (2000).

1999 (4)

G. Gouesbet, “Validity of the localized approximation for arbitrarily shaped beams in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
[CrossRef]

G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theory for assemblies of spheres and aggregates,” J. Opt. A: Pure Appl. Opt. 1, 706–712 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Description of arbitrarily shaped beams in elliptical cylinder coordinates, by using a plane-wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

1997 (4)

1996 (1)

1995 (4)

1994 (3)

1992 (1)

K. F. Ren, G. Grehan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory: faster algorithm for computation of beam shape coefficient gnm,” Part. Part. Charact. 9, 144–150 (1992).
[CrossRef]

1991 (2)

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[CrossRef]

R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
[CrossRef] [PubMed]

1988 (2)

1985 (2)

T. G. Tsuei, P. W. Barber, “Information content of the scattering matrix for spheroidal particles,” Appl. Opt. 24, 2391–2396 (1985).
[CrossRef] [PubMed]

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, 239–245 (1985).
[CrossRef]

1980 (1)

1979 (1)

1975 (1)

Alexander, D. R.

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[CrossRef]

Asano, S.

Barber, P. W.

Barton, J. P.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absortion and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 397–399.

Carlson, B. E.

Doicu, A.

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).

Gouesbet, G.

Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 3–5, 277–333 (2000).

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Description of arbitrarily shaped beams in elliptical cylinder coordinates, by using a plane-wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

G. Gouesbet, “Validity of the localized approximation for arbitrarily shaped beams in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theory for assemblies of spheres and aggregates,” J. Opt. A: Pure Appl. Opt. 1, 706–712 (1999).
[CrossRef]

G. Gouesbet, “Interaction between infinite cylinders and an arbitrarily shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
[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, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beam,” J. Opt. Soc. Am. A 11, 2516–2525 (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 beam,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
[CrossRef]

K. F. Ren, G. Grehan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory: faster algorithm for computation of beam shape coefficient gnm,” Part. Part. Charact. 9, 144–150 (1992).
[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. Grehan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

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, 239–245 (1985).
[CrossRef]

Grehan, G.

G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 3–5, 277–333 (2000).

G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theory for assemblies of spheres and aggregates,” J. Opt. A: Pure Appl. Opt. 1, 706–712 (1999).
[CrossRef]

K. F. Ren, G. Grehan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory: faster algorithm for computation of beam shape coefficient gnm,” Part. Part. Charact. 9, 144–150 (1992).
[CrossRef]

G. Gouesbet, G. Grehan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

Gréhan, G.

Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Description of arbitrarily shaped beams in elliptical cylinder coordinates, by using a plane-wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

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, 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, 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, 239–245 (1985).
[CrossRef]

Hacphie, R. H.

B. P. Sinha, R. H. Hacphie, “Electromagnetic scattering by prolate spheroids for a plane wave with arbitrary polarization and angle of incidence,” Radio Sci. 12, 171–184 (1997).
[CrossRef]

Han, Y.

Y. Han, Z. S. Wu, “Absorption and scattering by an oblate particle,” J. Opt. A: Pure Appl. 4, 74–77 (2002).
[CrossRef]

Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Y. Han, Z. S. Wu, “The expansion coefficients of a spheroidal particle illuminated by a Gaussian beam,” IEEE Trans. Antennas Trans. 49, 615–620 (2001).
[CrossRef]

Y. Han, Z. S. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001).
[CrossRef]

Y. Han, Z. S. Wu, “Discussion of the boundary condition forelectromagnetic scattering by spheroidal particles,” Acta Phys. Sin. 49, 57–60 (2000).

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), pp. 3–27.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absortion and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 397–399.

Jin, J.

S. Zhang, J. Jin, Computation of Special Functions (Wiley, New York, 1996).

Lock, J. A.

Macke, A.

Maheu, B.

Mees, L.

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Description of arbitrarily shaped beams in elliptical cylinder coordinates, by using a plane-wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

Méès, L.

Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Mishchenko, M. I.

D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing, and weakly absorbing nonspherical particles and comparison with geometrical optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), pp. 3–27.

Nag, S.

S. Nag, B. P. Sinha, “Electromagnetic plane wave scattering by a system of two uniformly lossy dielectric prolate spheroids in arbitrary orientation,” IEEE Trans. Antennas Propag. 43, 322–327 (1995).
[CrossRef]

Onofri, F.

Ren, K. F.

Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Description of arbitrarily shaped beams in elliptical cylinder coordinates, by using a plane-wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

K. F. Ren, G. Grehan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory: faster algorithm for computation of beam shape coefficient gnm,” Part. Part. Charact. 9, 144–150 (1992).
[CrossRef]

Sato, M.

Sinha, B. P.

B. P. Sinha, R. H. Hacphie, “Electromagnetic scattering by prolate spheroids for a plane wave with arbitrary polarization and angle of incidence,” Radio Sci. 12, 171–184 (1997).
[CrossRef]

S. Nag, B. P. Sinha, “Electromagnetic plane wave scattering by a system of two uniformly lossy dielectric prolate spheroids in arbitrary orientation,” IEEE Trans. Antennas Propag. 43, 322–327 (1995).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Travis, L. D.

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), pp. 3–27.

Tsuei, T. G.

van de Hulst, H. C.

Wang, R. T.

Wielaard, D. J.

Wriedt, T.

Wu, S. Z.

Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Wu, Z. S.

Y. Han, Z. S. Wu, “Absorption and scattering by an oblate particle,” J. Opt. A: Pure Appl. 4, 74–77 (2002).
[CrossRef]

Y. Han, Z. S. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001).
[CrossRef]

Y. Han, Z. S. Wu, “The expansion coefficients of a spheroidal particle illuminated by a Gaussian beam,” IEEE Trans. Antennas Trans. 49, 615–620 (2001).
[CrossRef]

Y. Han, Z. S. Wu, “Discussion of the boundary condition forelectromagnetic scattering by spheroidal particles,” Acta Phys. Sin. 49, 57–60 (2000).

Yamamoto, G.

Zhang, S.

S. Zhang, J. Jin, Computation of Special Functions (Wiley, New York, 1996).

Acta Phys. Sin. (1)

Y. Han, Z. S. Wu, “Discussion of the boundary condition forelectromagnetic scattering by spheroidal particles,” Acta Phys. Sin. 49, 57–60 (2000).

Appl. Opt. (16)

R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
[CrossRef] [PubMed]

A. Doicu, T. Wriedt, “Computation of the beam-shape coefficients in the generalized Lorenz–Mie theory by using the translational addition theorem for spherical vector wave functions,” Appl. Opt. 36, 2971–2978 (1997).
[CrossRef] [PubMed]

S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
[CrossRef] [PubMed]

S. Asano, “Light scattering properties of spheroidal particles,” Appl. Opt. 18, 712–723 (1979).
[CrossRef] [PubMed]

S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
[CrossRef] [PubMed]

G. Gouesbet, G. Grehan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

J. P. Barton, “Internal and near-surface electromagnetic fields for an absorbing spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 6471–8473 (1995).

J. P. Barton, “Internal and near-surface electromagnetic fields for a layered spheroid with arbitrary illumination,” Appl. Opt. 40, 3598–3607 (2001).
[CrossRef]

G. Gouesbet, “Interaction between infinite cylinders and an arbitrarily shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
[CrossRef] [PubMed]

L. Mees, K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

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]

T. G. Tsuei, P. W. Barber, “Information content of the scattering matrix for spheroidal particles,” Appl. Opt. 24, 2391–2396 (1985).
[CrossRef] [PubMed]

J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995).
[CrossRef] [PubMed]

Y. Han, Z. S. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing, and weakly absorbing nonspherical particles and comparison with geometrical optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
[CrossRef] [PubMed]

Atomization Sprays (1)

G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 3–5, 277–333 (2000).

IEEE Trans. Antennas Propag. (1)

S. Nag, B. P. Sinha, “Electromagnetic plane wave scattering by a system of two uniformly lossy dielectric prolate spheroids in arbitrary orientation,” IEEE Trans. Antennas Propag. 43, 322–327 (1995).
[CrossRef]

IEEE Trans. Antennas Trans. (1)

Y. Han, Z. S. Wu, “The expansion coefficients of a spheroidal particle illuminated by a Gaussian beam,” IEEE Trans. Antennas Trans. 49, 615–620 (2001).
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J. Opt. Soc. Am. A (5)

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Y. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field,” Opt. Commun. 210, 1–9 (2002).
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Figures (5)

Fig. 1
Fig. 1

Angular distribution of the intensity functions for prolate spheroids illuminated by a Gaussian beam (TM mode) with w 0 = 2 μm, a/ b = 2, α = 30, (x 0′, y 0′, z 0′) = (0, 0, 0), (1, 0, 0), and (1, 1, 1), respectively.

Fig. 2
Fig. 2

Angular distribution of the intensity functions for unpolarized Gaussian-beam illumination of prolate spheroids with w 0 = 2 μm, a/ b = 4, 2, and 1.000001 (sphere), α = 30 ñ = 1.33, (x 0′, y 0′, z 0′) = (1, 1, 1).

Fig. 3
Fig. 3

Intensity functions for prolate and oblate spheroids with α = 30, w 0 = 2 μm, ñ = 1.33, (x 0′, y 0′, z 0′) = (1, 1, 1), and a/ b = 2 for both prolate and oblate spheroids.

Fig. 4
Fig. 4

Comparison of the angular distribution of the intensity functions for Gaussian-beam scattering (w 0 = 3λ) at (x 0′, y 0′, z 0′) = (1, 0, 0) by a nonabsorbing (n = 1.33 + 0.0i) and absorbing (n = 1.33 + 0.05i) prolate spheroid for a TM mode with α = 10, a/ b = 2.

Fig. 5
Fig. 5

Forward-scattering and backscattering intensity functions of a prolate spheroid with a/ b = 1.2, ñ = 1.33 for unpolarized Gaussian-beam illumination with w 0 = 3λ and (x 0′, y 0′, z 0′) = (0, 0, 0), (x 0′, y 0′, z 0′) = (1, 0, 0), (x 0′, y 0′, z 0′) = (1, 1, 1).

Equations (58)

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Ei=E0m=0n=mgn,TEmcmemnr1r, θ, ϕ+ign,TMmcnomnr1r, θ, ϕ,
Pnmcos θjnkr=2n+m!2n+1n-m!l=m,m+1×il-nNml dn-mmlSmlc, ηRml1c, ζ,
moemnr1r, θ, ϕ=l=m,m+1 2n+m!2n+1n-m!il-nNml×dn-mmlMoemlζr1c, ζ, η, ϕaζ+Moemlηr1c, ζ, η, ϕaη+Moemlϕr1c, ζ, η, ϕaϕ=l=m,m+1 2n+m!2n+1n-m!il-nNml×dn-mmlMoemlr1c, ζ, η, ϕ,
noemnr1r, θ, ϕ=l=m,m+1 2n+m!2n+1n-m!il-nNml×dn-mmlNoemlζr1c, ζ, η, ϕaζ+Noemlηr1c, ζ, η, ϕaη+Noemlϕr1c, ζ, η, ϕaϕ=l=m,m+1 2n+m!2n+1n-m!il-nNml×dn-mmlNoemlr1c, ζ, η, ϕ.
Ei=E0m=0n=m inGn,TEmcMemnr1c, ζ, η, ϕ+iGn,TMmcNomnr1c, ζ, η, ϕTE mode.
Gn,TEm=i-mNmn-1r=0,1 2r+2m!2r+2m+1r!×i-rdrmngr+m,TEm,
Gn,TMm=i-mNmn-1r=0,1 2r+2m!2r+2m+1r!×i-rdrmngr+m,TMm,
Nmn=r=0,1 2r+2m!2r+2m+1r!drmn2,
Ei=E0n=1m=-nn Cnig˜n,TEmcmmnr1r, θ, ϕ+g˜n,TMmcnmnr1r, θ, ϕ,
Cn=in2n+1nn+1,
g˜n,TMm=expikz0iQ¯exp-iQ¯ρnw02×exp-iQ¯x02+y02w0212j+=mjp Ψjp+j-=mjp Ψjp,
g˜n,TEm=expikz0iQ¯exp-iQ¯ρnw02×exp-iQ¯x02+y02w0212ij+=mjp Ψjp-j-=mjp Ψjp,
ρn=n+1/22π λ,
Q¯=1i-2z0l,
Ψ=iQ¯ρnw02jx0-iy0j-px0+iy0pj-p!p!,
jp=j=0p=0j,
j+=j+1-2p,
j-=j-1-2p,
Ei=E0m=-n=|m| Cnig˜n,TEmcmmnr1r, θ, ϕ+g˜n,TMmcnmnr1r, θ, ϕ.
g˜n,TE-m=-1mm+n!m-n! g˜n,TEm,
g˜n,TM-m=-1m+1m+n!m-n! g˜n,TMm,
Ei=E0m=0n=m Cni2-δ0mg˜n,TEmcmemnr1r, θ, ϕ+2ig˜n,TMmcnomnr1r, θ, ϕ.
gn,TEm=iCng˜n,TEm2-δ0m,
gn,TMm=2Cng˜n,TMm,
Gn,TEm=i-mNmnr=0,1 2r+2m!2r+2m+1r!×i-rdrmngr+m,TEmc=i2-δ0mNmnr=0,1 2r+2m!r+mr+m+1r! ×drmng˜r+m,TEmc,
Gn,TMm=i-mNmnr=0,1 2r+2m!2r+2m+1r!×i-rdrmngr+m,TMmc=2Nmnr=0,1 2r+2m!r+mr+m+1r!×drmng˜r+m,TMmc,
Gn,TE=i-1N1nr=0,1 2r+2!2r+3r! i-rdr1ngr+1,TEc=4iN1nr=0,1 dr1ng˜r+1,TEc,
Gn,TM=i-1N1nr=0,1 2r+2!2r+3r! i-rdr1ngr+m,TMc=4N1nr=0,1 dr1ng˜r+m,TMc.
c-ic, ζiζ.
ETEi=m=0n=m inGn,TEmMemnr1cI, ζ, η, ϕ+iGn,TMmNomnr1cI, ζ, η, ϕ,
HTEi=k1ωμ1m=0n=m inGn,TMmMomnr1cI, ζ, η, ϕ-iGn,TEmNemnr1cI, ζ, η, ϕ,
ETEw=m=0n=m inδn,TEmMemnr1cII, ζ, η, ϕ+iγn,TEmNomnr1cII, ζ, η, ϕ,
HTEw=k2ωμ2m=0n=m inγn,TEmMomnr1cII, ζ, η, ϕ-iδn,TEmNemnr1cII, ζ, η, ϕ;
ETEs=m=0n=m inβn,TEmMemnr3cI, ζ, η, ϕ+iαn,TEmNomnr3cI, ζ, η, ϕ,
HTEs=k1ωμ1m=0n=m inαn,TEmMomnr3cI, ζ, η, ϕ-iβn,TEmNemnr3cI, ζ, η, ϕ.
ETMi=m=0n=m inGn,TMmMomnr1cI, ζ, η, ϕ-iGn,TEmNemnr1cI, ζ, η, ϕ,
HTMi=-k1ωμ1m=0n=m inGn,TEmMemnr1cI, ζ, η, ϕ+iGn,TMmNomnr1cI, ζ, η, ϕ;
ETMw=m=0n=m inγn,TMmMomnr1cII, ζ, η, ϕ-iδn,TMmNemnr1cII, ζ, η, ϕ,
HTMw=-k2ωμ2m=0n=m inδn,TMmMemnr1cII, ζ, η, ϕ+iγn,TMmNomnr1[cII, ζ, η, ϕ};
ETMs=m=0n=m inαn,TMmMomnr3cI, ζ, η, ϕ-iβn,TMmNemnr3cI, ζ, η, ϕ,
HTMs=-k1ωμ1m=0n=m inβn,TMmMemnr3cI, ζ, η, ϕ+iαn,TMmNomnr3cI, ζ, η, ϕ.
Eηi+Eηs=Eηw Eϕi+Eϕs=Eϕw Hηi+Hηs=Hηw  at ζ=ζ0. Hϕi+Hϕs=Hϕw
ETEs=iλI2πrexpi 2πrλI×-m=0n=mαn,TEmdSmncos θdθ+βn,TEmm Smncos θsin θsin mϕaη+m=0n=mαn,TEmm Smncos θsin θ+βn,TEmdSmncos θdθcos mϕaϕ.
ETMs=iλI2πrexpi 2πrλIm=0n=mβn,TMmdSmncos θdθ+αn,TMmm Smncos θsin θcos mϕaη+m=0n=mβn,TMmm Smncos θsin θ+αn,TMmdSmncos θdθsin mϕaϕ.
α=2πaλ,
nmax>α+4α1/3+2.
x0=x0w0, y0=y0w0, z0=z0l,
Moemnri=Moemnηriaη+Moemnζriaζ+Moemnϕriaϕ=mζζ2-η21/21-η21/2 Smnc, ηRmni×c, ζ-1cossinmϕaη-mηζ2-η21/2ζ2-11/2 Smnc, ηRmni×c, ζ-1cossinmϕaζ+1-η21/2ζ2-11/2ζ2-η2×ζ ddη Smnc, ηRmnic, ζ-ηSmnc, ηddζ Rmnic, ζsincosmϕaϕ,
Noemnri=Noemnηriaη+Noemnζriaζ+Noemnϕriaϕ =1-η21/2kfζ2-η21/2ddη Smnζζζ2-1ζ2-η2 Rmni-ηSmnζζ2-1ζ2-η2ddζ Rmni+m2η1-η2ζ2-1 SmnRmnisincosmϕaη-ζ2-11/2kfζ2-η21/2×-ηη1-η2ζ2-η2 Smnddζ Rmni+ζ η1-η2ζ2-η2ddη SmnRmni-m2ζ1-η2ζ2-1 SmnRmnisincosmϕaζ+m1-η21/2ζ2-11/2kfζ2-η21/2×-1ζ2-1ddηηSmnRmni-11-η2 SmnddζζRmni-cossinmϕaϕ.
moemnrir, θ, ϕ=msin θ znkrPnmcos θcos mϕsin mϕeθ-znkrPnmcos θθsin mϕcos mϕeϕ,
noemnrir, θ, ϕ=nn+1kr znkrPnmcos θcos mϕsin mϕer+1krrrznkrPnmcos θθsin mϕcos mϕeθmkr sin θr×rznkrPnmcos θcos mϕsin mϕeϕ,
Pn-mcos θ=-1mn-m!n+m! Pnmcos θ,
me-mnr1=-1mn-m!n+m!memnr1,
mo-mnr1=-1m+1n-m!n+m!momnr1,
ne-mnr1=-1mn-m!n+m!nemnr1,
no-mnr1=-1m+1n-m!n+m!nomnr1,
mmnr1=memnr1+imomnr1,
nmnr1=nemnr1+inomnr1.

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