Abstract

A generalization of the coupled-dipole method introduced by Purcell and Pennypacker [Astrophys. J. 186, 705 (1973)], a low-frequency method used to describe electromagnetic scattering by dielectric objects of arbitrary shape, is proposed. At each site of the cubic lattice, instead of a dipole moment there are an electric dipole, a magnetic dipole, and an electric quadrupole, leading to an improved description of the scattered fields.

© 1997 Optical Society of America

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References

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  1. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  2. H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 70.
  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).
    [CrossRef]
  4. M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
    [CrossRef]
  5. 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).
    [CrossRef]
  6. Y. L. Yung, “Variational principle for scattering of light by dielectric particles,” Appl. Opt. 17, 3707–3709 (1978).
    [CrossRef] [PubMed]
  7. P. Chiappetta, “Multiple scattering approach to light scattering by arbitrarily shaped particles,” J. Phys. A 13, 2101–2108 (1980).
    [CrossRef]
  8. 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).
    [CrossRef] [PubMed]
  9. B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  10. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  11. C. Bourrely, P. Chiappetta, T. Lemaire, B. Torrésani, “Multidipole formulation of the coupled dipole method for electromagnetic scattering by an arbitrary particle,” J. Opt. Soc. Am. A 9, 1336–1340 (1992).
    [CrossRef]
  12. 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]
  13. 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).
    [CrossRef]
  14. B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
    [CrossRef]

1994 (1)

1993 (1)

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

1992 (1)

1991 (1)

1990 (1)

1988 (3)

1986 (2)

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).
[CrossRef]

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. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Bohren, C. F.

Bourrely, C.

Chiappetta, P.

Draine, B. T.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

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).
[CrossRef]

B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Dungey, C. E.

Flatau, P. J.

Goedecke, G. H.

Goodman, J.

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

Lemaire, T.

O’Brien, S. G.

Pennypacker, C. R.

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

Purcell, E. M.

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

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).
[CrossRef]

M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

Singham, M. K.

M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

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).
[CrossRef] [PubMed]

M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

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).
[CrossRef]

Stephens, G. L.

Torrésani, B.

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 70.

Yung, Y. L.

Appl. Opt. (2)

Astrophys. J. (3)

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

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

J. Chem. Phys. (2)

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).
[CrossRef]

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 (5)

J. Phys. A (1)

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

Other (1)

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 70.

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Figures (5)

Fig. 1
Fig. 1

System of coordinates and notation.

Fig. 2
Fig. 2

Scattering intensities i1(θ) and i2(θ) for a sphere of size parameter kR=3.2 and of refractive index m=1.3. Solid curves, Mie theory; dotted curves, CMM with 1021 subunits; short-dashed curves, CDM with 1021 subunits; long-dashed curves, CDM with 2721 subunits.

Fig. 3
Fig. 3

Same as Fig. 2 but for a sphere of size parameter kR=4.5 and of refractive index m=1.2+0.1i. Solid curves, Mie theory; dotted curves, CMM with 515 subunits; dashed curves, CDM with 2109 subunits.

Fig. 4
Fig. 4

Same as Fig. 2 but for a sphere of size parameter kR=3 and of refractive index m=1.33+0.1i. Solid curves, Mie theory; dotted curves, CMM with 515 subunits; short-dashed curves, CDM with 515 subunits; long-dashed curves, CDM with 2109 subunits.

Fig. 5
Fig. 5

Scattering intensities i1(θ) and i2(θ) for an ellipsoid of size parameters ka=kc=2.9, kb=4.3 along the axes ox, oy, and oz, respectively, and of refractive index m=1.3. Solid curves, CDM with 4711 dipoles (regarded as the correct solution); dotted curves, CMM with 1853 subunits; dashed curves, CDM with 1853 dipoles.

Tables (2)

Tables Icon

Table 1 Error for Perpendicular Intensity

Tables Icon

Table 2 Error for Parallel Intensity

Equations (26)

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αe0=m2-1m2+2a3,
αe=αe01+(αe0/d3)[c1+m2c2-(2/3)ikd](kd)2,
αm=(ka)230(m2-1)a3,
α13q=ika m2-12m2+3a4einc,
α23q=ika m2-12m2+3a4einc,
αμμq=0,μ=1, . . ., 3,
pi=αeiE(ri),
mi=αmiB(ri),
Qi,μνRinc=αμνq·ERinc(ri),
Esca(r)=(r)p+Γ(r)m+F1(r)Q(n),
Bsca(r)=-Γ(r)p+(r)m+F2(r)Q(n),
(r)=exp(ikr)rk2(I-nn)+1-ikrr2(3nn-I),
Γr=ik expikrrik-1rn×,
F1r=expikr6r-ik3+3k2r+6ikr2-6r3×I-nn-1rk2+3ikr-3r2nn,
F2r=-ik6expikrrk2+3ikr-3r2n×,
pi=αeiE0(ri)+αeij=1,..,NjiEj(ri),
mi=αmiB0(ri)+αmij=1,..,Nji[-Γ(rij)pj+(rij)mj+F2(rij)Q(nij)],
Qi,μν=α,β=1,..,3αi,αβq·RμαRνβRTE0(ri)+j=1,,NjiRμαijRνβijRijTEj(ri),
Ej(ri)=(rij)pj+Γ(rij)mj+F1(rij)Q(nij),
Fsca(θ, ϕ)=i=1N exp(-ikn·ri)×pi-n×mi-ik6Qi(n).
σext=4πkE02i=1NImpi-n×mi-ik6Qi(n)·E0*(ri),
σsca=k4E020πdθ02πdϕFsca(θ, ϕ)2 sin θ,
σabs=σext-σsca,
i(θ)=k6πE0202πdϕFsca(θ, ϕ)·e2,=1, 2,
P(θ)=i1(θ)-i2(θ)i1(θ)+i2(θ),
e=0πdθiexact(θ)-imodel(θ)iexact(θ)21/2,=1, 2,

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