Abstract

Based on the expansion of a Gaussian beam in terms of spheroidal vector wave functions given by us and the generalized Lorenz–Mie theory that provides the general framework, a theoretical procedure to determine the scattered fields of a spheroidal particle for incidence of a Gaussian beam described by a localized beam model is presented. As a result, for a dielectric and conducting spheroidal particle, numerical results of the normalized differential scattering cross section are evaluated, and the scattering characteristics are discussed concisely.

© 2010 Optical Society of America

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References

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  1. S. Asano and G. Yamamoto, “Light scattering by a spheroid particle,” Appl. Opt. 14, 29-49 (1975).
    [PubMed]
  2. S. Asano, “Light scattering properties of spheroidal particles,” Appl. Opt. 18, 712-723 (1979).
    [CrossRef] [PubMed]
  3. A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268-273 (1992).
    [CrossRef]
  4. D. S. Wang and P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190-1197 (1979).
    [CrossRef] [PubMed]
  5. J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542-5551 (1995).
    [CrossRef] [PubMed]
  6. J. P. Barton, “Internal, near-surface, and scattered electromagnetic fields for a layered spheroid with arbitrary illumination,” Appl. Opt. 40, 3596-3607 (2001).
    [CrossRef]
  7. G. Gouesbet, B. Maheu, and 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]
  8. B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 56-67 (1988).
    [CrossRef]
  9. G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998-1003 (1990).
    [CrossRef]
  10. G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beam in the generalized Lorenz-Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641-1650 (1999).
    [CrossRef]
  11. G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: a perspective,” J. Quant. Spectrosc. Radiat. Transf. 110, 1223-1238 (2009).
    [CrossRef]
  12. Y. P. Han and Z. S. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501-2509 (2001).
    [CrossRef]
  13. Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, and G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1-9 (2002).
    [CrossRef]
  14. Y. P. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621-6629 (2003).
    [CrossRef] [PubMed]
  15. Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
    [CrossRef]
  16. F. Xu, K. F. Ren, and X. Cai, “Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates,” J. Opt. Soc. Am. A 24, 109-118 (2007).
    [CrossRef]
  17. F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119-131 (2007).
    [CrossRef]
  18. F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
    [CrossRef]
  19. F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: analytical solution,” Phys. Rev. A 78, 013843 (2008).
    [CrossRef]
  20. A. Doicu and T. Wriedt, “Formulations of the extended boundary condition method for incident Gaussian beams using multiple-multipole expansions,” J. Mod. Opt. 44, 785-801 (1997).
    [CrossRef]
  21. B. T. Drain and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499 (1994).
    [CrossRef]
  22. Y. P. Han, H. Y. Zhang, and G. X. Han, “The expansion coefficients of arbitrarily shaped beam in oblique illumination,” Opt. Express 15, 735-746 (2007).
    [CrossRef] [PubMed]
  23. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton Univ. Press, 1957), Chapt. 4.
  24. C. Flammer, Spheroidal Wave Functions (Stanford Univ. Press, 1957).
  25. H. Y. Zhang and Y. P. Han, “Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients,” J. Opt. Soc. Am. B 11, 255-260 (2008).
    [CrossRef]
  26. L. W. Davis, “Theory of electromagnetic beam,” Phys. Rev. A 19, 1177-1179 (1979).
    [CrossRef]

2009 (1)

G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: a perspective,” J. Quant. Spectrosc. Radiat. Transf. 110, 1223-1238 (2009).
[CrossRef]

2008 (2)

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: analytical solution,” Phys. Rev. A 78, 013843 (2008).
[CrossRef]

H. Y. Zhang and Y. P. Han, “Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients,” J. Opt. Soc. Am. B 11, 255-260 (2008).
[CrossRef]

2007 (4)

2004 (1)

Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
[CrossRef]

2003 (1)

2002 (1)

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

2001 (2)

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

J. P. Barton, “Internal, near-surface, and scattered electromagnetic fields for a layered spheroid with arbitrary illumination,” Appl. Opt. 40, 3596-3607 (2001).
[CrossRef]

1999 (1)

1997 (1)

A. Doicu and T. Wriedt, “Formulations of the extended boundary condition method for incident Gaussian beams using multiple-multipole expansions,” J. Mod. Opt. 44, 785-801 (1997).
[CrossRef]

1995 (1)

1994 (1)

1992 (1)

A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268-273 (1992).
[CrossRef]

1990 (1)

1988 (2)

G. Gouesbet, B. Maheu, and 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, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 56-67 (1988).
[CrossRef]

1979 (3)

1975 (1)

Asano, S.

Barber, P. W.

Barton, J. P.

J. P. Barton, “Internal, near-surface, and scattered electromagnetic fields for a layered spheroid with arbitrary illumination,” Appl. Opt. 40, 3596-3607 (2001).
[CrossRef]

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

Cai, X.

Davis, L. W.

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

Doicu, A.

A. Doicu and T. Wriedt, “Formulations of the extended boundary condition method for incident Gaussian beams using multiple-multipole expansions,” J. Mod. Opt. 44, 785-801 (1997).
[CrossRef]

Drain, B. T.

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton Univ. Press, 1957), Chapt. 4.

Flammer, C.

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

Flatau, P. J.

Gouesbet, G.

G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: a perspective,” J. Quant. Spectrosc. Radiat. Transf. 110, 1223-1238 (2009).
[CrossRef]

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: analytical solution,” Phys. Rev. A 78, 013843 (2008).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119-131 (2007).
[CrossRef]

Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
[CrossRef]

Y. P. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621-6629 (2003).
[CrossRef] [PubMed]

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

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

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998-1003 (1990).
[CrossRef]

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 56-67 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, and 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]

Gréhan, G.

F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119-131 (2007).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[CrossRef]

Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
[CrossRef]

Y. P. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621-6629 (2003).
[CrossRef] [PubMed]

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

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998-1003 (1990).
[CrossRef]

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 56-67 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, and 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]

Han, G. X.

Han, Y. P.

H. Y. Zhang and Y. P. Han, “Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients,” J. Opt. Soc. Am. B 11, 255-260 (2008).
[CrossRef]

Y. P. Han, H. Y. Zhang, and G. X. Han, “The expansion coefficients of arbitrarily shaped beam in oblique illumination,” Opt. Express 15, 735-746 (2007).
[CrossRef] [PubMed]

Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
[CrossRef]

Y. P. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621-6629 (2003).
[CrossRef] [PubMed]

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

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

Lock, J. A.

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: analytical solution,” Phys. Rev. A 78, 013843 (2008).
[CrossRef]

Maheu, B.

Méès, L.

Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
[CrossRef]

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

Ren, K. F.

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[CrossRef]

F. Xu, K. F. Ren, and X. Cai, “Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates,” J. Opt. Soc. Am. A 24, 109-118 (2007).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119-131 (2007).
[CrossRef]

Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
[CrossRef]

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

Sebak, A. R.

A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268-273 (1992).
[CrossRef]

Sinha, B. P.

A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268-273 (1992).
[CrossRef]

Tropea, C.

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: analytical solution,” Phys. Rev. A 78, 013843 (2008).
[CrossRef]

Wang, D. S.

Wriedt, T.

A. Doicu and T. Wriedt, “Formulations of the extended boundary condition method for incident Gaussian beams using multiple-multipole expansions,” J. Mod. Opt. 44, 785-801 (1997).
[CrossRef]

Wu, S. Z.

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

Wu, Z. S.

Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
[CrossRef]

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

Xu, F.

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: analytical solution,” Phys. Rev. A 78, 013843 (2008).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[CrossRef]

F. Xu, K. F. Ren, and X. Cai, “Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates,” J. Opt. Soc. Am. A 24, 109-118 (2007).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119-131 (2007).
[CrossRef]

Yamamoto, G.

Zhang, H. Y.

H. Y. Zhang and Y. P. Han, “Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients,” J. Opt. Soc. Am. B 11, 255-260 (2008).
[CrossRef]

Y. P. Han, H. Y. Zhang, and G. X. Han, “The expansion coefficients of arbitrarily shaped beam in oblique illumination,” Opt. Express 15, 735-746 (2007).
[CrossRef] [PubMed]

Appl. Opt. (7)

IEEE Trans. Antennas Propag. (1)

A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268-273 (1992).
[CrossRef]

J. Mod. Opt. (1)

A. Doicu and T. Wriedt, “Formulations of the extended boundary condition method for incident Gaussian beams using multiple-multipole expansions,” J. Mod. Opt. 44, 785-801 (1997).
[CrossRef]

J. Opt. (Paris) (1)

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 56-67 (1988).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Opt. Soc. Am. B (1)

H. Y. Zhang and Y. P. Han, “Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients,” J. Opt. Soc. Am. B 11, 255-260 (2008).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf. (1)

G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: a perspective,” J. Quant. Spectrosc. Radiat. Transf. 110, 1223-1238 (2009).
[CrossRef]

Opt. Commun. (2)

Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71-77 (2004).
[CrossRef]

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

Opt. Express (1)

Phys. Rev. A (2)

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

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: analytical solution,” Phys. Rev. A 78, 013843 (2008).
[CrossRef]

Phys. Rev. E (1)

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[CrossRef]

Other (2)

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton Univ. Press, 1957), Chapt. 4.

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

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Figures (4)

Fig. 1
Fig. 1

Cartesian coordinate system O x y z is parallel to the Gaussian beam coordinate system O x y z , and the Cartesian coordinates of O in O x y z are ( x 0 , y 0 = 0 , z 0 ) . O x y z is obtained by a rigid-body rotation of O x y z through a single Euler angle β. A spheroidal particle is natural to O x y z .

Fig. 2
Fig. 2

Normalized differential scattering cross sections π σ ( θ , 0 ) λ 2 , π σ ( θ , π 4 ) λ 2 , and π σ ( θ , π 2 ) λ 2 for a dielectric spheroid ( k a = 5 , n ̃ = 1.33 , a b = 2 , β = π 3 ) illuminated by a Gaussian beam of w 0 = 2 λ .

Fig. 3
Fig. 3

Normalized differential scattering cross sections π σ ( θ , 0 ) λ 2 , and π σ ( θ , π 4 ) λ 2 , and π σ ( θ , π 2 ) λ 2 for a conducting spheroid ( k a = 6 , a b = 2 , β = π 4 ) for incidence of a Gaussian beam with w 0 = 2 λ .

Fig. 4
Fig. 4

Comparison between the normalized differential scattering cross section π σ ( θ , 0 ) λ 2 for a dielectric spheroid ( k a = 10 , n ̃ = 1.33 , a b = 2 ) (solid curve) and that for a conducting spheroid ( k a = 10 , a b = 2 ) (dotted curve), all with β = π 4 and illuminated by a Gaussian beam of w 0 = 2 λ .

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

E i = E 0 m = 0 n = m i n [ G n , TE m M e m n r ( 1 ) ( c , ζ , η , ϕ ) + i G n , TM m N o m n r ( 1 ) ( c , ζ , η , ϕ ) ] ,
H i = E 0 k ω μ m = 0 n = m i n [ G n , TM m M o m n r ( 1 ) ( c , ζ , η , ϕ ) i G n , TE m N e m n r ( 1 ) ( c , ζ , η , ϕ ) ] ,
[ G n , TE m G n , TM m ] = r = 0 , 1 s = 0 r + m 2 ( r + 2 m ) ! ( 2 r + 2 m + 1 ) r ! i r m N m n d r m n ( c ) [ g r + m , TE s m g r + m , TM s m ] ,
N m n = 2 r = 0 , 1 ( r + 2 m ) ! [ d r m n ( c ) ] 2 ( 2 r + 2 m + 1 ) r ! ,
[ g n , TE s m g n , TM m s ] = 2 ( 1 + δ s 0 ) ( 1 + δ m 0 ) i n 2 n + 1 n ( n + 1 ) ( 1 ) s + m [ ( n + s ) ! ( n m ) ! ( n s ) ! ( n + m ) ! ] 1 2 [ g n , TE s i g n , TM s ] [ ( 1 ) n u m s ( n ) ( π + β ) ± u m s ( n ) ( β ) ] ,
u m s ( n ) ( β ) = [ ( n + m ) ! ( n m ) ! ( n + s ) ! ( n s ) ! ] 1 2 σ ( n + s n m σ ) ( n s σ ) ( 1 ) n m σ ( cos β 2 ) 2 σ + s + m ( sin β 2 ) 2 n 2 σ s m .
g n , TE 1 = 1 2 g n , g n , TM 1 = i 2 g n ,
[ G n , TE m G n , TM m ] = 2 N m n ( 1 ) m 1 r = 0 , 1 d r m n ( c ) ( r + m ) ( r + m + 1 ) g r + m [ ( 2 δ 0 m ) d P r + m m ( cos β ) d β 2 m P r + m m ( cos β ) sin β ] .
g n = 1 1 + 2 i s z 0 w 0 exp ( i k z 0 ) exp [ s 2 ( n + 1 2 ) 2 1 + 2 i s z 0 w 0 ] ,
E s = E 0 m = 0 n = m i n [ β m n M e m n r ( 3 ) ( c , ζ , η , ϕ ) + i α m n N o m n r ( 3 ) ( c , ζ , η , ϕ ) ] ,
H s = E 0 k ω μ m = 0 n = m i n [ α m n M o m n r ( 3 ) ( c , ζ , η , ϕ ) i β m n N e m n r ( 3 ) ( c , ζ , η , ϕ ) ] ,
E w = E 0 m = 0 n = m i n [ δ m n M e m n r ( 1 ) ( c 1 , ζ , η , ϕ ) + i γ m n N o m n r ( 1 ) ( c 1 , ζ , η , ϕ ) ] ,
H w = E 0 k 1 ω μ m = 0 n = m i n [ γ m n M o m n r ( 1 ) ( c 1 , ζ , η , ϕ ) i δ m n N e m n r ( 1 ) ( c 1 , ζ , η , ϕ ) ] ,
{ E η i + E η s = E η w , E ϕ i + E ϕ s = E ϕ w H η i + H η s = H η w , H ϕ i + H ϕ s = H ϕ w } at ζ = ζ 0 ,
E η i + E η s = 0 , E ϕ i + E ϕ s = 0 at ζ = ζ 0 ,
n = m i n [ Γ ] [ α m n β m n δ m n γ m n ] = n = m i n [ G ] [ U m n ( 1 ) , t ( c ) V m n ( 1 ) , t ( c ) X m n ( 1 ) , t ( c ) Y m n ( 1 ) , t ( c ) ] ,
n = m i n [ Γ ] [ α m n β m n ] = n = m i n [ G ] [ U m n ( 1 ) , t ( c ) V m n ( 1 ) , t ( c ) X m n ( 1 ) , t ( c ) Y m n ( 1 ) , t ( c ) ] .
[ G ] = [ G n , TE m G n , TM m 0 0 G n , TM m G n , TE m 0 0 0 0 G n , TE m G n , TM m 0 0 G n , TM m G n , TE m ] ,
[ Γ ] = [ V m n ( 3 ) , t ( c ) U m n ( 3 ) , t ( c ) U m n ( 1 ) , t ( c 1 ) V m n ( 1 ) , t ( c 1 ) U m n ( 3 ) , t ( c ) V m n ( 3 ) , t ( c ) k 1 k V m n ( 1 ) , t ( c 1 ) k 1 k U m n ( 1 ) , t ( c 1 ) Y m n ( 3 ) , t ( c ) X m n ( 3 ) , t ( c ) X m n ( 1 ) , t ( c 1 ) Y m n ( 1 ) , t ( c 1 ) X m n ( 3 ) , t ( c ) Y m n ( 3 ) , t ( c ) k 1 k Y m n ( 1 ) , t ( c 1 ) k 1 k X m n ( 1 ) , t ( c 1 ) ] ,
[ G ] = [ G n , TE m G n , TM m 0 0 0 0 G n , TE m G n , TM m ] ,
[ Γ ] = [ V m n ( 3 ) , t ( c ) U m n ( 3 ) , t ( c ) Y m n ( 3 ) , t ( c ) X m n ( 3 ) , t ( c ) ] .
E η s = E 0 i λ 2 π r exp ( i 2 π r λ ) m = 0 n = m [ α m n d S m n ( c , cos θ ) d θ + m β m n S m n ( c , cos θ ) sin θ ] sin m ϕ ,
E ϕ s = E 0 i λ 2 π r exp ( i 2 π r λ ) m = 0 n = m [ m α m n S m n ( c , cos θ ) sin θ + β m n d S m n ( c , cos θ ) d θ ] cos m ϕ .
σ ( θ , ϕ ) = 4 π r 2 | E s E 0 | 2 = λ 2 π ( | T 1 ( θ , ϕ ) | 2 + | T 2 ( θ , ϕ ) | 2 ) ,
T 1 ( θ , ϕ ) = m = 0 n = m [ m β m n S m n ( c , cos θ ) sin θ + α m n d S m n ( c , cos θ ) d θ ] sin m ϕ ,
T 2 ( θ , ϕ ) = m = 0 n = m [ m α m n S m n ( c , cos θ ) sin θ + β m n d S m n ( c , cos θ ) d θ ] cos m ϕ .

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