Abstract

We present an improved formulation for low-frequency light scattering by an arbitrarily shaped particle, using a multiple-scattering development of a modified coupled dipole method. In this formulation the volume of a particle is discretized as an array of different types of dipolar subunit located on the sites of a cubic lattice. The main advantage of the formulation is to reduce the number of dipolar subunits and to obtain a better approximation of particle geometry than with the standard method that uses one type of dipole. Calculations performed for spherical, coated spherical, and cubic particles require less computing time and show good agreement with respect to a uniform discretization.

© 1992 Optical Society of America

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References

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  1. E. K. Purcell, C. R. Pennypacker, “Scattering and absorption by non spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [Crossref]
  2. B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988); P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete dipole approximation: a new algorithm exploiting the Block–Toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990); A. Lakhtakia, “Macroscopic theory of the coupled dipole approximation method,” Opt. Commun. 79, 1–5 (1990); V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Scattering by three dimensional anisotropic method,” IEEE Trans. Antennas Propag. 37, 800–802 (1989); C. E. Dungey, C. F. Bohren, “Light scattering by nonspherical particles: a refinement to the coupled-dipole method,” J. Opt. Soc. Am. A 8, 81–87 (1991); M. A. Taubenblatt, “Light scattering from cylindrical structures on surfaces,” Opt. Lett. 15, 255–257 (1990).
    [Crossref] [PubMed]
  3. S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986); M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
    [Crossref]
  4. Y. L. Yung, “Variational principle for scattering of light by dielectric particles,” Appl. Opt. 17, 3707–3709 (1978).
    [Crossref] [PubMed]
  5. P. Chiappetta, “Multiple scattering approach to light scattering by arbitrarily shaped particles,” J. Phys. A 13, 2101–2108 (1980).
    [Crossref]
  6. S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method,” J. Opt. Soc. Am. A 5, 1867–1872 (1988); “Hybrid method in light scattering by an arbitrary particle,” Appl. Opt. 28, 517–522 (1989).
    [Crossref] [PubMed]
  7. P. Chiappetta, J. M. Perrin, B. Torresani, “Low energy light scattering: a multiple scattering description,” Nuovo Cimento D 9, 717–725 (1987).
    [Crossref]
  8. P. Chiappetta, B. Torresani, “Electromagnetic scattering from a dielectric helix,” Appl. Opt. 27, 4856–4860 (1988).
    [Crossref] [PubMed]
  9. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 3.
  10. G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
    [Crossref] [PubMed]
  11. M. Reed, B. Simon, Methods of Modern Mathematical Physics. I—Functional Analysis (Academic, New York, 1972), p. 191.
  12. J. M. Perrin, J. P. Sivan, “Porosity and impurities within interstellar grains. Is the ultraviolet bump still explained by carbonaceous material?” Astron. Astrophys. 228, 238–245 (1990).

1990 (1)

J. M. Perrin, J. P. Sivan, “Porosity and impurities within interstellar grains. Is the ultraviolet bump still explained by carbonaceous material?” Astron. Astrophys. 228, 238–245 (1990).

1988 (4)

B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988); P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete dipole approximation: a new algorithm exploiting the Block–Toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990); A. Lakhtakia, “Macroscopic theory of the coupled dipole approximation method,” Opt. Commun. 79, 1–5 (1990); V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Scattering by three dimensional anisotropic method,” IEEE Trans. Antennas Propag. 37, 800–802 (1989); C. E. Dungey, C. F. Bohren, “Light scattering by nonspherical particles: a refinement to the coupled-dipole method,” J. Opt. Soc. Am. A 8, 81–87 (1991); M. A. Taubenblatt, “Light scattering from cylindrical structures on surfaces,” Opt. Lett. 15, 255–257 (1990).
[Crossref] [PubMed]

S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method,” J. Opt. Soc. Am. A 5, 1867–1872 (1988); “Hybrid method in light scattering by an arbitrary particle,” Appl. Opt. 28, 517–522 (1989).
[Crossref] [PubMed]

P. Chiappetta, B. Torresani, “Electromagnetic scattering from a dielectric helix,” Appl. Opt. 27, 4856–4860 (1988).
[Crossref] [PubMed]

G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
[Crossref] [PubMed]

1987 (1)

P. Chiappetta, J. M. Perrin, B. Torresani, “Low energy light scattering: a multiple scattering description,” Nuovo Cimento D 9, 717–725 (1987).
[Crossref]

1986 (1)

S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986); M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[Crossref]

1980 (1)

P. Chiappetta, “Multiple scattering approach to light scattering by arbitrarily shaped particles,” J. Phys. A 13, 2101–2108 (1980).
[Crossref]

1978 (1)

1973 (1)

E. K. Purcell, C. R. Pennypacker, “Scattering and absorption by non spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

Bohren, C. F.

Chiappetta, P.

P. Chiappetta, B. Torresani, “Electromagnetic scattering from a dielectric helix,” Appl. Opt. 27, 4856–4860 (1988).
[Crossref] [PubMed]

P. Chiappetta, J. M. Perrin, B. Torresani, “Low energy light scattering: a multiple scattering description,” Nuovo Cimento D 9, 717–725 (1987).
[Crossref]

P. Chiappetta, “Multiple scattering approach to light scattering by arbitrarily shaped particles,” J. Phys. A 13, 2101–2108 (1980).
[Crossref]

Draine, B. T.

B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988); P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete dipole approximation: a new algorithm exploiting the Block–Toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990); A. Lakhtakia, “Macroscopic theory of the coupled dipole approximation method,” Opt. Commun. 79, 1–5 (1990); V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Scattering by three dimensional anisotropic method,” IEEE Trans. Antennas Propag. 37, 800–802 (1989); C. E. Dungey, C. F. Bohren, “Light scattering by nonspherical particles: a refinement to the coupled-dipole method,” J. Opt. Soc. Am. A 8, 81–87 (1991); M. A. Taubenblatt, “Light scattering from cylindrical structures on surfaces,” Opt. Lett. 15, 255–257 (1990).
[Crossref] [PubMed]

Goedecke, G. H.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 3.

O’Brien, S. G.

Pennypacker, C. R.

E. K. Purcell, C. R. Pennypacker, “Scattering and absorption by non spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

Perrin, J. M.

J. M. Perrin, J. P. Sivan, “Porosity and impurities within interstellar grains. Is the ultraviolet bump still explained by carbonaceous material?” Astron. Astrophys. 228, 238–245 (1990).

P. Chiappetta, J. M. Perrin, B. Torresani, “Low energy light scattering: a multiple scattering description,” Nuovo Cimento D 9, 717–725 (1987).
[Crossref]

Purcell, E. K.

E. K. Purcell, C. R. Pennypacker, “Scattering and absorption by non spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

Reed, M.

M. Reed, B. Simon, Methods of Modern Mathematical Physics. I—Functional Analysis (Academic, New York, 1972), p. 191.

Salzman, G. C.

S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986); M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[Crossref]

Simon, B.

M. Reed, B. Simon, Methods of Modern Mathematical Physics. I—Functional Analysis (Academic, New York, 1972), p. 191.

Singham, S. B.

S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method,” J. Opt. Soc. Am. A 5, 1867–1872 (1988); “Hybrid method in light scattering by an arbitrary particle,” Appl. Opt. 28, 517–522 (1989).
[Crossref] [PubMed]

S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986); M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[Crossref]

Sivan, J. P.

J. M. Perrin, J. P. Sivan, “Porosity and impurities within interstellar grains. Is the ultraviolet bump still explained by carbonaceous material?” Astron. Astrophys. 228, 238–245 (1990).

Torresani, B.

P. Chiappetta, B. Torresani, “Electromagnetic scattering from a dielectric helix,” Appl. Opt. 27, 4856–4860 (1988).
[Crossref] [PubMed]

P. Chiappetta, J. M. Perrin, B. Torresani, “Low energy light scattering: a multiple scattering description,” Nuovo Cimento D 9, 717–725 (1987).
[Crossref]

Yung, Y. L.

Appl. Opt. (3)

Astron. Astrophys. (1)

J. M. Perrin, J. P. Sivan, “Porosity and impurities within interstellar grains. Is the ultraviolet bump still explained by carbonaceous material?” Astron. Astrophys. 228, 238–245 (1990).

Astrophys. J. (2)

E. K. Purcell, C. R. Pennypacker, “Scattering and absorption by non spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988); P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete dipole approximation: a new algorithm exploiting the Block–Toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990); A. Lakhtakia, “Macroscopic theory of the coupled dipole approximation method,” Opt. Commun. 79, 1–5 (1990); V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Scattering by three dimensional anisotropic method,” IEEE Trans. Antennas Propag. 37, 800–802 (1989); C. E. Dungey, C. F. Bohren, “Light scattering by nonspherical particles: a refinement to the coupled-dipole method,” J. Opt. Soc. Am. A 8, 81–87 (1991); M. A. Taubenblatt, “Light scattering from cylindrical structures on surfaces,” Opt. Lett. 15, 255–257 (1990).
[Crossref] [PubMed]

J. Chem. Phys. (1)

S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986); M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[Crossref]

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

J. Phys. A (1)

P. Chiappetta, “Multiple scattering approach to light scattering by arbitrarily shaped particles,” J. Phys. A 13, 2101–2108 (1980).
[Crossref]

Nuovo Cimento D (1)

P. Chiappetta, J. M. Perrin, B. Torresani, “Low energy light scattering: a multiple scattering description,” Nuovo Cimento D 9, 717–725 (1987).
[Crossref]

Other (2)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 3.

M. Reed, B. Simon, Methods of Modern Mathematical Physics. I—Functional Analysis (Academic, New York, 1972), p. 191.

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Figures (6)

Fig. 1
Fig. 1

a, Extinction and b, absorption cross sections versus size parameter for spheres of refractive index 1.33 + i0.1 in vacuum. Solid curves: Mie calculation; long-dashed curves: homogeneous partition (515) dipoles); short-dashed curves: bidipole model with 465 original dipoles and 22 new dipoles.

Fig. 2
Fig. 2

Angular distribution of a, scattering intensities i(θ) and i(θ) and b, polarization for a sphere of refractive index 1.33 + i0.1 in vacuum and size parameter 2.5. Solid curves: Mie calculation; long-dashed curves: homogeneous partition (515 dipoles); short-dashed curves: bidipole model with 465 original dipoles and 22 new dipoles.

Fig. 3
Fig. 3

Angular distribution of a, scattering intensities i(θ) and i(θ) and b, polarization for a coated sphere of internal-core-size parameter 1.6 and refractive index 1.55 + i0.1 and a spherical shell with size parameter 2.5 and index of refraction 1.33 + i0.05 in vacuum. Solid curves: continuum electromagnetic theory calculation; dashed curves: bidipole model with 487 dipoles including 22 new dipoles in the internal core.

Fig. 4
Fig. 4

a, Extinction and b, absorption cross sections versus the size parameter for cubes of refractive index 1.33 + i0.05 in vacuum. Solid curves: homogeneous partition (343 dipoles); long-dashed curves: homogeneous partition (125 dipoles); short-dashed curves: bidipole model with 231 original dipoles and 16 new dipoles.

Fig. 5
Fig. 5

Angular distribution of a, scattering intensities i(θ) and i(θ) and b, polarization for a cube of refractive index 1.57 + i0.006 in vacuum and size parameter 2. Solid curves: homogeneous partition (343 dipoles); dashed curves: bidipole model with 231 original dipoles and 16 new dipoles.

Fig. 6
Fig. 6

Angular distribution of a, scattering intensities i(θ) and i(θ) and b, polarization for a cube of refractive index 1.57 + i0.006 and size parameter 2, rotated by 45° with respect to the incident-wave vector. Solid curves: homogeneous partition (343 dipoles); dashed curves: bidipole model with 231 original dipoles and 16 new dipoles.

Equations (8)

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α = 3 4 π ρ m 2 - 1 m 2 + 2 ,
E ( r i ) = E inc ( r i ) + j = 1 j i N T i j · p j ,
p i = α E ( r i ) .
T ( r ) = exp ( i k r ) r 3 [ k 2 r 2 ( 1 - r r r 2 ) + ( 1 - i k r ) ( 3 r r r 2 - 1 ) ] .
p i = p 0 i + α j = 1 j i N T i j p o j + α 2 j = 1 j i N j = 1 l j T i j T j l p 0 l + ,
A = 7 α
p i = p 0 i + α j = 1 N 2 T i j p j + α j = 1 N 1 T i j p j +             ( i = 1 , N 2 ) ,
P i = P 0 i + A j = 1 N 2 T i j p j + A j = 1 N 1 T i j P j +             ( i = 1 , N 1 ) .

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