Abstract

This paper applies two different techniques to the problem of scattering by two spheres in contact:modal analysis, which is an exact method, and the discrete-dipole approximation (DDA). Good agreement is obtained, which further demonstrates the utility of the DDA to scattering problems for irregular particles. The choice of the DDA polarizability scheme is discussed in detail. We show that the lattice dispersion relation provides excellent improvement over the Clausius–Mossoti polarizability parameterization.

© 1993 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 nonspherical dielectric grains,” Astrophys. J. 186, 705–714(1973).
    [CrossRef]
  2. 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]
  3. J. J. Goodman, B. T. Draine, P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. 16, 1198–1200 (1991).
    [CrossRef] [PubMed]
  4. B. T. Draine, J. J. Goodman, “Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. (to be published).
    [PubMed]
  5. K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
    [CrossRef] [PubMed]
  6. D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
    [CrossRef]
  7. W. J. Wiscombe, A. Mugnai, Single Scattering from Nonspherical Chebyshev Particles: A Compendium of Calculations, NASA Ref. Pub. 1157 (Goddard Space Flight Center, NASA, Greenbelt, Maryland, 1986).
  8. G. H. Goedecke, A. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
    [CrossRef] [PubMed]
  9. J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251 (1990).
    [CrossRef]
  10. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  11. The fortran program DDSCAT.4b is available from P. J. Flatau on request. Direct queries to Internet address pflatau@macao.ucsd.edu or drain@astro.princeton.edu.
  12. P. J. Flatau, “Scattering by irregular particles in anomalous diffraction and discrete dipole approximations,” Tech. Rep. 517 (Colorado State University, Fort Collins, Colo.1992).

1991 (3)

1990 (2)

1988 (2)

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

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

1973 (1)

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

Draine, B. T.

J. J. Goodman, B. T. Draine, P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. 16, 1198–1200 (1991).
[CrossRef] [PubMed]

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]

B. T. Draine, J. J. Goodman, “Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. (to be published).
[PubMed]

Flatau, P. J.

Fuller, K. A.

Goedecke, G. H.

Goodman, J. J.

J. J. Goodman, B. T. Draine, P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. 16, 1198–1200 (1991).
[CrossRef] [PubMed]

B. T. Draine, J. J. Goodman, “Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. (to be published).
[PubMed]

Greenberg, J. M.

J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251 (1990).
[CrossRef]

Hage, J. I.

J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251 (1990).
[CrossRef]

Mackowski, D. W.

D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
[CrossRef]

Mugnai, A.

W. J. Wiscombe, A. Mugnai, Single Scattering from Nonspherical Chebyshev Particles: A Compendium of Calculations, NASA Ref. Pub. 1157 (Goddard Space Flight Center, NASA, Greenbelt, Maryland, 1986).

O’Brien, A. G.

Pennypacker, C. R.

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

Purcell, E. M.

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

Stephens, G. L.

Wiscombe, W. J.

W. J. Wiscombe, A. Mugnai, Single Scattering from Nonspherical Chebyshev Particles: A Compendium of Calculations, NASA Ref. Pub. 1157 (Goddard Space Flight Center, NASA, Greenbelt, Maryland, 1986).

Appl. Opt. (2)

Astrophys. J. (3)

J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251 (1990).
[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 nonspherical dielectric grains,” Astrophys. J. 186, 705–714(1973).
[CrossRef]

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

Opt. Lett. (1)

Proc. R. Soc. London Ser. A (1)

D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
[CrossRef]

Other (4)

W. J. Wiscombe, A. Mugnai, Single Scattering from Nonspherical Chebyshev Particles: A Compendium of Calculations, NASA Ref. Pub. 1157 (Goddard Space Flight Center, NASA, Greenbelt, Maryland, 1986).

B. T. Draine, J. J. Goodman, “Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. (to be published).
[PubMed]

The fortran program DDSCAT.4b is available from P. J. Flatau on request. Direct queries to Internet address pflatau@macao.ucsd.edu or drain@astro.princeton.edu.

P. J. Flatau, “Scattering by irregular particles in anomalous diffraction and discrete dipole approximations,” Tech. Rep. 517 (Colorado State University, Fort Collins, Colo.1992).

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Figures (4)

Fig. 1
Fig. 1

Two pseudospheres composed of 2 × 32 × 32 × 32 point dipoles. Light is travelling along the x axis. Spheres are rotated (α = 30).

Fig. 2
Fig. 2

Scattering by a sphere with refractive index m = 1.33 + 0.001i for x = ka = 10 and α = 0. Exact results for S11 and S22 are compared with S11 and S22 results that were computed by the DDA for x = 10.

Fig. 3
Fig. 3

(a) Qsca and Qabs for two spheres of refractive index m = 1.33 + 0.01i in contact, (b) fractional error in computed value of Qsca, (c) Qabs for the N = 2 × 34,512 two pseudospheres of Fig. 1. Results are shown for three different prescriptions for the dipole polarizabilities: CMRR, VIEF, and LDR as functions of x = k0aeff, α = 30.

Fig. 4
Fig. 4

(a) Dependence of Qsca on orientation for the two spheres of Fig. 3 with x = 5, (b) fractional error in computed value of Qsca as a function of α for the two pseudospheres of Fig. 1.

Equations (7)

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a i + j = 1 , j i N 3 T i j a j = p i ,
α = α ( n r ) 1 - ( 2 / 3 ) i [ α ( n r ) / d 3 ] ( k 0 d ) 3 ,
α ( n r ) α ( 0 ) 1 + [ α ( 0 ) / d 3 ] ( b 1 + m 2 b 2 + m 2 b 3 S ) ( k 0 d ) 2 ,
b 1 = c 1 / π = - 1.8915316 ,
b 2 = c 2 / π = 0.1648469 ,
b 3 = - ( 3 c 2 + c 3 ) / π = - 1.7700004 ,
α i ( 0 ) 3 d 3 4 π ( m i 2 - 1 m i 2 + 2 ) .

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