Abstract

The discrete-dipole approximation (DDA) for scattering calculations, including the relationship between the DDA and other methods, is reviewed. Computational considerations, i.e., the use of complex-conjugate gradient algorithms and fast-Fourier-transform methods, are discussed. We test the accuracy of the DDA by using the DDA to compute scattering and absorption by isolated, homogeneous spheres as well as by targets consisting of two contiguous spheres. It is shown that, for dielectric materials (|m| ≲ 2), the DDA permits calculations of scattering and absorption that are accurate to within a few percent.

© 1994 Optical Society of America

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  1. C. F. Bohren, S. B. Singham, “Backscattering by non- spherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
    [CrossRef]
  2. The fortranprogram ddscat.4b is available from the authors. Direct queries to the Internet address draine@astro.princeton.edu or pflatau@macao.ucsd.edu.
  3. H. DeVoe, “Optical properties of molecular aggregates. I. Classical model of electronic absorption and refraction,” J. Chem. Phys. 41, 393–400 (1964).
    [CrossRef]
  4. H. DeVoe, “Optical properties of molecular aggregates. II. Classical theory of the refraction, absorption, and optical activity of solutions and crystals,” J. Chem. Phys. 43, 3199–3208 (1965).
    [CrossRef]
  5. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  6. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  7. 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]
  8. S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: a physical reformulation of the coupled-dipoles method,” Opt. Lett. 12, 10–12 (1987).
    [CrossRef] [PubMed]
  9. H. A. Lorentz, Theory of Electrons (Teubner, Leipzig, 1909).
  10. E. L. Wright, “The ultraviolet extinction from interstellar graphitic onions,” Nature (London) 366, 227–228 (1988).
    [CrossRef]
  11. A. Lakhtakia, “General theory of the Purcell-Pennypacker scattering approach and its extension to bianisotropic scatterers,” Astrophys. J. 394, 494–499 (1992).
    [CrossRef]
  12. A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields,” Int. J. Mod. Phys. C3, 583–603 (1992).
  13. J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross-section shape,” IEEE Trans. Antennas Propag. AP-13, 334–343 (1965).
    [CrossRef]
  14. R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
  15. R. Harrington, “Origin and development of the method of moments for field computation,” IEEE Antennas Propag. Mag. 32(3), 31–35 (1990).
    [CrossRef]
  16. 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]
  17. D. E. Livesay, K. Chen, “Electromagnetic fields induced inside arbitrarily shaped biological bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
    [CrossRef]
  18. A. W. Glison, “Recent advances in frequency domain techniques for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 25, 2867–2871 (1989).
  19. E. K. Miller, “A selective survey of computational electromagnetics,” IEEE Trans. Antennas Propag. 36, 1281–1305 (1988).
    [CrossRef]
  20. M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aerosols,” Appl. Opt. 28, 3083–3091 (1989).
    [CrossRef] [PubMed]
  21. J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251–259 (1990).
    [CrossRef]
  22. E. H. Newman, K. Kingsley, “An introduction to the method of moments,” J. Comput. Phys. 68, 1–18 (1991).
    [CrossRef]
  23. 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]
  24. J. M. Perrin, J. P. Sivan, “Light scattering by dust grains: effects of the state of the surface on the validity of the discrete dipole approximation,” C. R. Acad. Sci. Paris Ser. II 316, 47–53 (1993).
  25. J. D. Jackson, Classical Electromagnetism (Wiley, New York, 1975).
  26. 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]
  27. 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]
  28. P. J. Flatau, K. A. Fuller, D. W. Mackowski, “Scattering by two spheres in contact: comparisons between discrete dipole approximation and modal analysis,” Appl. Opt. 32, 3302–3305 (1993).
    [CrossRef] [PubMed]
  29. F. Rouleau, P. G. Martin, “A new method to calculate the extinction properties of irregularly shaped particles,” Astrophys. J. 414, 803–814 (1993).
    [CrossRef]
  30. W. Hager, Applied Numerical Linear Algebra (Prentice-Hall, Englewood Cliffs, N.J., 1988).
  31. 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]
  32. 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]
  33. T. K. Sarkar, X. Yang, E. Arvas, “A limited survey of various conjugate gradient methods for complex matrix equations arising in electromagnetic wave interactions,” Wave Motion 10, 527–546 (1988).
    [CrossRef]
  34. A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, “Numerical implementation of the conjugate gradient method and the CG-FFT for electromagnetic scattering,” in Application of Conjugate Gradient Method to Electromagnetics and Signal Processing, T. K. Sarkar, ed. (Elsevier, New York, 1991), Chap. 5.
  35. R. W. Freund, N. M. Nachtigal, “QMR: a quasi-minimal residual method for non-Hermitian linear systems,” Numer. Math. 60, 315–339 (1991).
    [CrossRef]
  36. 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]
  37. L. Knockaert, “A note on the relationship between the conjugate gradient method and polynomials orthogonal over the spectrum of a linear operator,” IEEE Trans. Antennas Propag. AP-35, 1089–1091 (1987).
    [CrossRef]
  38. A. F. Peterson, C. F. Smith, R. Mittra, “Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propag. 36, 1177–1179 (1988).
    [CrossRef]
  39. C. F. Smith, A. F. Peterson, R. Mittra, “A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields,” IEEE Trans. Antennas Propag. 37, 1490–1493 (1989).
    [CrossRef]
  40. P. Joly, “Résolution de systèmes linéaires avec plusieurs members par la méthode du gradient conjugué,” Tech. Rep. R-91012 (Publications du Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Paris, 1991).
  41. V. Simoncini, E. Gallopoulos, “An iterative method for nonsymmetric systems with multiple right-hand sides,” Tech. Rep. 1242 (Center for Supercomputing Research and Development, University of Illinois at Urbana–Champaign, Champaign, III., 1992).
  42. P. J. Flatau, T. Schneider, F. Evans, ccg-pak—fortran. Conjugate gradient package for solving complex matrix equations (1993).Available from pflatau@ucsd.edu.
  43. D. T. Borup, O. P. Gandhi, “Calculation of high- resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
    [CrossRef]
  44. T. K. Sarkar, E. Arvas, S. M. Rao, “Application of the fast Fourier transform and the conjugate gradient method for efficient solution of electromagnetic scattering from both electrically large and small conducting bodies,” Electromagnetics 5, 99–122 (1985).
    [CrossRef]
  45. P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  46. D.-S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
    [CrossRef] [PubMed]
  47. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
    [CrossRef]
  48. W. C. Chew, C.-C. Lu, “NEPAL—an algorithm for solving the volume integral equation,” Microwave Opt. Tech. Lett. 6, 185–188 (1993).
    [CrossRef]
  49. W. C. Chew, Y. M. Wang, L. Gurel, “Recursive algorithm for wave-scattering using windowed addition theorem,” J. Electromagn. Waves Appl. 6, 1537–1560 (1992).
    [CrossRef]
  50. J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily- shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
    [CrossRef]
  51. J. C. Ku, “Comparisons of coupled-dipole solutions and dipole refractive indices for light scattering and absorption by arbitrarily shaped or agglomerated particles,” J. Opt. Soc. Am. A 10, 336–342 (1993).
    [CrossRef]
  52. K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
    [CrossRef] [PubMed]
  53. D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
    [CrossRef]
  54. G. W. Kattawar, T. J. Humphreys, “Electromagnetic scattering from two identical pseudospheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 177–190.
    [CrossRef]
  55. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  56. J. M. Perrin, J. P. Sivan, “Scattering and polarisation of light by rough and porous interstellar grains,” Astron. Astrophys. 247, 497–504 (1991).
  57. 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).
  58. B. T. Draine, S. Malhotra, “On graphite and the 2175 Å extinction profile,” Astrophys. J. 414, 632–645 (1993).
    [CrossRef]
  59. M. F. Iskander, H. Y. Chen, J. E. Penner, “Resonance optical absorption by fractal agglomerates of smoke aerosols,” Atmos. Environ. 25A, 2563–2569 (1991).
  60. R. A. West, “Optical properties of aggregate particles whose outer diameter is comparable to the wavelength,” Appl. Opt. 30, 5316–5324 (1991).
    [CrossRef] [PubMed]
  61. R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
    [CrossRef]
  62. T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates. I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).
  63. T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).
  64. M. J. Wolff, G. C. Clayton, P. G. Martin, R. E. Schulte-Ladbeck, “Modeling composite and fluffy grains: the effects of porosity,” Astrophys. J. (to be published).
  65. S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
    [CrossRef]
  66. J. M. Perrin, P. L. Lamy, “On the validity of effective- medium theories in the case of light extinction by inhomogeneous dust particles,” Astrophys. J. 364, 146–151 (1990).
    [CrossRef]
  67. M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
    [CrossRef]
  68. K. F. Evans, J. Vivekanandan, “Multiparameter radar and microwave radiative transfer modeling of nonspherical atmospheric ice particles,” IEEE Trans. Geosci. Remote Sensing 28, 423–437 (1990).
    [CrossRef]
  69. P. J. Flatau, “Scattering by irregular particles in anomalous diffraction and discrete dipole approximations,” Atmos. Sci. Paper 517 (Department of Atmospheric Science, Colorado State University, Fort Collins, Colo., 1992).

1993 (10)

J. M. Perrin, J. P. Sivan, “Light scattering by dust grains: effects of the state of the surface on the validity of the discrete dipole approximation,” C. R. Acad. Sci. Paris Ser. II 316, 47–53 (1993).

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, K. A. Fuller, D. W. Mackowski, “Scattering by two spheres in contact: comparisons between discrete dipole approximation and modal analysis,” Appl. Opt. 32, 3302–3305 (1993).
[CrossRef] [PubMed]

F. Rouleau, P. G. Martin, “A new method to calculate the extinction properties of irregularly shaped particles,” Astrophys. J. 414, 803–814 (1993).
[CrossRef]

P. J. Flatau, T. Schneider, F. Evans, ccg-pak—fortran. Conjugate gradient package for solving complex matrix equations (1993).Available from pflatau@ucsd.edu.

W. C. Chew, C.-C. Lu, “NEPAL—an algorithm for solving the volume integral equation,” Microwave Opt. Tech. Lett. 6, 185–188 (1993).
[CrossRef]

J. C. Ku, “Comparisons of coupled-dipole solutions and dipole refractive indices for light scattering and absorption by arbitrarily shaped or agglomerated particles,” J. Opt. Soc. Am. A 10, 336–342 (1993).
[CrossRef]

B. T. Draine, S. Malhotra, “On graphite and the 2175 Å extinction profile,” Astrophys. J. 414, 632–645 (1993).
[CrossRef]

S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
[CrossRef]

M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
[CrossRef]

1992 (7)

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates. I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

W. C. Chew, Y. M. Wang, L. Gurel, “Recursive algorithm for wave-scattering using windowed addition theorem,” J. Electromagn. Waves Appl. 6, 1537–1560 (1992).
[CrossRef]

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily- shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

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]

A. Lakhtakia, “General theory of the Purcell-Pennypacker scattering approach and its extension to bianisotropic scatterers,” Astrophys. J. 394, 494–499 (1992).
[CrossRef]

A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields,” Int. J. Mod. Phys. C3, 583–603 (1992).

1991 (12)

C. F. Bohren, S. B. Singham, “Backscattering by non- spherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
[CrossRef]

E. H. Newman, K. Kingsley, “An introduction to the method of moments,” J. Comput. Phys. 68, 1–18 (1991).
[CrossRef]

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]

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]

R. W. Freund, N. M. Nachtigal, “QMR: a quasi-minimal residual method for non-Hermitian linear systems,” Numer. Math. 60, 315–339 (1991).
[CrossRef]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[CrossRef]

K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
[CrossRef] [PubMed]

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

J. M. Perrin, J. P. Sivan, “Scattering and polarisation of light by rough and porous interstellar grains,” Astron. Astrophys. 247, 497–504 (1991).

M. F. Iskander, H. Y. Chen, J. E. Penner, “Resonance optical absorption by fractal agglomerates of smoke aerosols,” Atmos. Environ. 25A, 2563–2569 (1991).

R. A. West, “Optical properties of aggregate particles whose outer diameter is comparable to the wavelength,” Appl. Opt. 30, 5316–5324 (1991).
[CrossRef] [PubMed]

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[CrossRef]

1990 (6)

J. M. Perrin, P. L. Lamy, “On the validity of effective- medium theories in the case of light extinction by inhomogeneous dust particles,” Astrophys. J. 364, 146–151 (1990).
[CrossRef]

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).

K. F. Evans, J. Vivekanandan, “Multiparameter radar and microwave radiative transfer modeling of nonspherical atmospheric ice particles,” IEEE Trans. Geosci. Remote Sensing 28, 423–437 (1990).
[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]

R. Harrington, “Origin and development of the method of moments for field computation,” IEEE Antennas Propag. Mag. 32(3), 31–35 (1990).
[CrossRef]

J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251–259 (1990).
[CrossRef]

1989 (3)

M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aerosols,” Appl. Opt. 28, 3083–3091 (1989).
[CrossRef] [PubMed]

A. W. Glison, “Recent advances in frequency domain techniques for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 25, 2867–2871 (1989).

C. F. Smith, A. F. Peterson, R. Mittra, “A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields,” IEEE Trans. Antennas Propag. 37, 1490–1493 (1989).
[CrossRef]

1988 (7)

A. F. Peterson, C. F. Smith, R. Mittra, “Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propag. 36, 1177–1179 (1988).
[CrossRef]

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]

T. K. Sarkar, X. Yang, E. Arvas, “A limited survey of various conjugate gradient methods for complex matrix equations arising in electromagnetic wave interactions,” Wave Motion 10, 527–546 (1988).
[CrossRef]

E. K. Miller, “A selective survey of computational electromagnetics,” IEEE Trans. Antennas Propag. 36, 1281–1305 (1988).
[CrossRef]

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]

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

E. L. Wright, “The ultraviolet extinction from interstellar graphitic onions,” Nature (London) 366, 227–228 (1988).
[CrossRef]

1987 (2)

S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: a physical reformulation of the coupled-dipoles method,” Opt. Lett. 12, 10–12 (1987).
[CrossRef] [PubMed]

L. Knockaert, “A note on the relationship between the conjugate gradient method and polynomials orthogonal over the spectrum of a linear operator,” IEEE Trans. Antennas Propag. AP-35, 1089–1091 (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).
[CrossRef]

1985 (2)

D. T. Borup, O. P. Gandhi, “Calculation of high- resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
[CrossRef]

T. K. Sarkar, E. Arvas, S. M. Rao, “Application of the fast Fourier transform and the conjugate gradient method for efficient solution of electromagnetic scattering from both electrically large and small conducting bodies,” Electromagnetics 5, 99–122 (1985).
[CrossRef]

1979 (1)

1975 (1)

1974 (1)

D. E. Livesay, K. Chen, “Electromagnetic fields induced inside arbitrarily shaped biological bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
[CrossRef]

1973 (1)

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

1965 (2)

H. DeVoe, “Optical properties of molecular aggregates. II. Classical theory of the refraction, absorption, and optical activity of solutions and crystals,” J. Chem. Phys. 43, 3199–3208 (1965).
[CrossRef]

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross-section shape,” IEEE Trans. Antennas Propag. AP-13, 334–343 (1965).
[CrossRef]

1964 (1)

H. DeVoe, “Optical properties of molecular aggregates. I. Classical model of electronic absorption and refraction,” J. Chem. Phys. 41, 393–400 (1964).
[CrossRef]

Arvas, E.

T. K. Sarkar, X. Yang, E. Arvas, “A limited survey of various conjugate gradient methods for complex matrix equations arising in electromagnetic wave interactions,” Wave Motion 10, 527–546 (1988).
[CrossRef]

T. K. Sarkar, E. Arvas, S. M. Rao, “Application of the fast Fourier transform and the conjugate gradient method for efficient solution of electromagnetic scattering from both electrically large and small conducting bodies,” Electromagnetics 5, 99–122 (1985).
[CrossRef]

Barber, P.

Barber, P. W.

Blum, J.

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates. I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

Bohren, C. F.

S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
[CrossRef]

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]

C. F. Bohren, S. B. Singham, “Backscattering by non- spherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
[CrossRef]

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]

S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: a physical reformulation of the coupled-dipoles method,” Opt. Lett. 12, 10–12 (1987).
[CrossRef] [PubMed]

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

Borup, D. T.

D. T. Borup, O. P. Gandhi, “Calculation of high- resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
[CrossRef]

Bourrely, C.

Chan, C. H.

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, “Numerical implementation of the conjugate gradient method and the CG-FFT for electromagnetic scattering,” in Application of Conjugate Gradient Method to Electromagnetics and Signal Processing, T. K. Sarkar, ed. (Elsevier, New York, 1991), Chap. 5.

Chen, H. Y.

M. F. Iskander, H. Y. Chen, J. E. Penner, “Resonance optical absorption by fractal agglomerates of smoke aerosols,” Atmos. Environ. 25A, 2563–2569 (1991).

M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aerosols,” Appl. Opt. 28, 3083–3091 (1989).
[CrossRef] [PubMed]

Chen, K.

D. E. Livesay, K. Chen, “Electromagnetic fields induced inside arbitrarily shaped biological bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
[CrossRef]

Chew, W. C.

W. C. Chew, C.-C. Lu, “NEPAL—an algorithm for solving the volume integral equation,” Microwave Opt. Tech. Lett. 6, 185–188 (1993).
[CrossRef]

W. C. Chew, Y. M. Wang, L. Gurel, “Recursive algorithm for wave-scattering using windowed addition theorem,” J. Electromagn. Waves Appl. 6, 1537–1560 (1992).
[CrossRef]

Chiappetta, P.

Clayton, G. C.

M. J. Wolff, G. C. Clayton, P. G. Martin, R. E. Schulte-Ladbeck, “Modeling composite and fluffy grains: the effects of porosity,” Astrophys. J. (to be published).

DeVoe, H.

H. DeVoe, “Optical properties of molecular aggregates. II. Classical theory of the refraction, absorption, and optical activity of solutions and crystals,” J. Chem. Phys. 43, 3199–3208 (1965).
[CrossRef]

H. DeVoe, “Optical properties of molecular aggregates. I. Classical model of electronic absorption and refraction,” J. Chem. Phys. 41, 393–400 (1964).
[CrossRef]

Draine, B. T.

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, S. Malhotra, “On graphite and the 2175 Å extinction profile,” Astrophys. J. 414, 632–645 (1993).
[CrossRef]

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]

Dungey, C. E.

Evans, F.

P. J. Flatau, T. Schneider, F. Evans, ccg-pak—fortran. Conjugate gradient package for solving complex matrix equations (1993).Available from pflatau@ucsd.edu.

Evans, K. F.

K. F. Evans, J. Vivekanandan, “Multiparameter radar and microwave radiative transfer modeling of nonspherical atmospheric ice particles,” IEEE Trans. Geosci. Remote Sensing 28, 423–437 (1990).
[CrossRef]

Flatau, P. J.

Freund, R. W.

R. W. Freund, N. M. Nachtigal, “QMR: a quasi-minimal residual method for non-Hermitian linear systems,” Numer. Math. 60, 315–339 (1991).
[CrossRef]

Fuller, K. A.

Gallopoulos, E.

V. Simoncini, E. Gallopoulos, “An iterative method for nonsymmetric systems with multiple right-hand sides,” Tech. Rep. 1242 (Center for Supercomputing Research and Development, University of Illinois at Urbana–Champaign, Champaign, III., 1992).

Gandhi, O. P.

D. T. Borup, O. P. Gandhi, “Calculation of high- resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
[CrossRef]

Glison, A. W.

A. W. Glison, “Recent advances in frequency domain techniques for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 25, 2867–2871 (1989).

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]

Goodman, J. J.

Greenberg, J. M.

T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251–259 (1990).
[CrossRef]

Gurel, L.

W. C. Chew, Y. M. Wang, L. Gurel, “Recursive algorithm for wave-scattering using windowed addition theorem,” J. Electromagn. Waves Appl. 6, 1537–1560 (1992).
[CrossRef]

Hage, J. I.

J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251–259 (1990).
[CrossRef]

Hager, W.

W. Hager, Applied Numerical Linear Algebra (Prentice-Hall, Englewood Cliffs, N.J., 1988).

Harrington, R.

R. Harrington, “Origin and development of the method of moments for field computation,” IEEE Antennas Propag. Mag. 32(3), 31–35 (1990).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

Huffman, D. R.

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

Humphreys, T. J.

G. W. Kattawar, T. J. Humphreys, “Electromagnetic scattering from two identical pseudospheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 177–190.
[CrossRef]

Ishimoto, H.

T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

Iskander, M. F.

M. F. Iskander, H. Y. Chen, J. E. Penner, “Resonance optical absorption by fractal agglomerates of smoke aerosols,” Atmos. Environ. 25A, 2563–2569 (1991).

M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aerosols,” Appl. Opt. 28, 3083–3091 (1989).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electromagnetism (Wiley, New York, 1975).

Joly, P.

P. Joly, “Résolution de systèmes linéaires avec plusieurs members par la méthode du gradient conjugué,” Tech. Rep. R-91012 (Publications du Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Paris, 1991).

Kattawar, G. W.

G. W. Kattawar, T. J. Humphreys, “Electromagnetic scattering from two identical pseudospheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 177–190.
[CrossRef]

Kingsley, K.

E. H. Newman, K. Kingsley, “An introduction to the method of moments,” J. Comput. Phys. 68, 1–18 (1991).
[CrossRef]

Knockaert, L.

L. Knockaert, “A note on the relationship between the conjugate gradient method and polynomials orthogonal over the spectrum of a linear operator,” IEEE Trans. Antennas Propag. AP-35, 1089–1091 (1987).
[CrossRef]

Kozasa, T.

T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates. I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

Ku, J. C.

J. C. Ku, “Comparisons of coupled-dipole solutions and dipole refractive indices for light scattering and absorption by arbitrarily shaped or agglomerated particles,” J. Opt. Soc. Am. A 10, 336–342 (1993).
[CrossRef]

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily- shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, “General theory of the Purcell-Pennypacker scattering approach and its extension to bianisotropic scatterers,” Astrophys. J. 394, 494–499 (1992).
[CrossRef]

A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields,” Int. J. Mod. Phys. C3, 583–603 (1992).

Lamy, P. L.

J. M. Perrin, P. L. Lamy, “On the validity of effective- medium theories in the case of light extinction by inhomogeneous dust particles,” Astrophys. J. 364, 146–151 (1990).
[CrossRef]

Lemaire, T.

Livesay, D. E.

D. E. Livesay, K. Chen, “Electromagnetic fields induced inside arbitrarily shaped biological bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
[CrossRef]

Lorentz, H. A.

H. A. Lorentz, Theory of Electrons (Teubner, Leipzig, 1909).

Lu, C.-C.

W. C. Chew, C.-C. Lu, “NEPAL—an algorithm for solving the volume integral equation,” Microwave Opt. Tech. Lett. 6, 185–188 (1993).
[CrossRef]

Mackowski, D. W.

Malhotra, S.

B. T. Draine, S. Malhotra, “On graphite and the 2175 Å extinction profile,” Astrophys. J. 414, 632–645 (1993).
[CrossRef]

Martin, P. G.

F. Rouleau, P. G. Martin, “A new method to calculate the extinction properties of irregularly shaped particles,” Astrophys. J. 414, 803–814 (1993).
[CrossRef]

M. J. Wolff, G. C. Clayton, P. G. Martin, R. E. Schulte-Ladbeck, “Modeling composite and fluffy grains: the effects of porosity,” Astrophys. J. (to be published).

Miller, E. K.

E. K. Miller, “A selective survey of computational electromagnetics,” IEEE Trans. Antennas Propag. 36, 1281–1305 (1988).
[CrossRef]

Mishchenko, M. I.

Mittra, R.

C. F. Smith, A. F. Peterson, R. Mittra, “A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields,” IEEE Trans. Antennas Propag. 37, 1490–1493 (1989).
[CrossRef]

A. F. Peterson, C. F. Smith, R. Mittra, “Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propag. 36, 1177–1179 (1988).
[CrossRef]

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, “Numerical implementation of the conjugate gradient method and the CG-FFT for electromagnetic scattering,” in Application of Conjugate Gradient Method to Electromagnetics and Signal Processing, T. K. Sarkar, ed. (Elsevier, New York, 1991), Chap. 5.

Mukai, T.

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates. I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

Nachtigal, N. M.

R. W. Freund, N. M. Nachtigal, “QMR: a quasi-minimal residual method for non-Hermitian linear systems,” Numer. Math. 60, 315–339 (1991).
[CrossRef]

Newman, E. H.

E. H. Newman, K. Kingsley, “An introduction to the method of moments,” J. Comput. Phys. 68, 1–18 (1991).
[CrossRef]

O’Brien, S. G.

Penner, J. E.

M. F. Iskander, H. Y. Chen, J. E. Penner, “Resonance optical absorption by fractal agglomerates of smoke aerosols,” Atmos. Environ. 25A, 2563–2569 (1991).

M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aerosols,” Appl. Opt. 28, 3083–3091 (1989).
[CrossRef] [PubMed]

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]

Perrin, J. M.

J. M. Perrin, J. P. Sivan, “Light scattering by dust grains: effects of the state of the surface on the validity of the discrete dipole approximation,” C. R. Acad. Sci. Paris Ser. II 316, 47–53 (1993).

J. M. Perrin, J. P. Sivan, “Scattering and polarisation of light by rough and porous interstellar grains,” Astron. Astrophys. 247, 497–504 (1991).

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).

J. M. Perrin, P. L. Lamy, “On the validity of effective- medium theories in the case of light extinction by inhomogeneous dust particles,” Astrophys. J. 364, 146–151 (1990).
[CrossRef]

Peterson, A. F.

C. F. Smith, A. F. Peterson, R. Mittra, “A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields,” IEEE Trans. Antennas Propag. 37, 1490–1493 (1989).
[CrossRef]

A. F. Peterson, C. F. Smith, R. Mittra, “Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propag. 36, 1177–1179 (1988).
[CrossRef]

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, “Numerical implementation of the conjugate gradient method and the CG-FFT for electromagnetic scattering,” in Application of Conjugate Gradient Method to Electromagnetics and Signal Processing, T. K. Sarkar, ed. (Elsevier, New York, 1991), Chap. 5.

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]

Rao, S. M.

T. K. Sarkar, E. Arvas, S. M. Rao, “Application of the fast Fourier transform and the conjugate gradient method for efficient solution of electromagnetic scattering from both electrically large and small conducting bodies,” Electromagnetics 5, 99–122 (1985).
[CrossRef]

Ray, S. L.

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, “Numerical implementation of the conjugate gradient method and the CG-FFT for electromagnetic scattering,” in Application of Conjugate Gradient Method to Electromagnetics and Signal Processing, T. K. Sarkar, ed. (Elsevier, New York, 1991), Chap. 5.

Richmond, J. H.

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross-section shape,” IEEE Trans. Antennas Propag. AP-13, 334–343 (1965).
[CrossRef]

Rouleau, F.

F. Rouleau, P. G. Martin, “A new method to calculate the extinction properties of irregularly shaped particles,” Astrophys. J. 414, 803–814 (1993).
[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]

Sarkar, T. K.

T. K. Sarkar, X. Yang, E. Arvas, “A limited survey of various conjugate gradient methods for complex matrix equations arising in electromagnetic wave interactions,” Wave Motion 10, 527–546 (1988).
[CrossRef]

T. K. Sarkar, E. Arvas, S. M. Rao, “Application of the fast Fourier transform and the conjugate gradient method for efficient solution of electromagnetic scattering from both electrically large and small conducting bodies,” Electromagnetics 5, 99–122 (1985).
[CrossRef]

Schneider, T.

P. J. Flatau, T. Schneider, F. Evans, ccg-pak—fortran. Conjugate gradient package for solving complex matrix equations (1993).Available from pflatau@ucsd.edu.

Schulte-Ladbeck, R. E.

M. J. Wolff, G. C. Clayton, P. G. Martin, R. E. Schulte-Ladbeck, “Modeling composite and fluffy grains: the effects of porosity,” Astrophys. J. (to be published).

Shim, K.-H.

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily- shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

Simoncini, V.

V. Simoncini, E. Gallopoulos, “An iterative method for nonsymmetric systems with multiple right-hand sides,” Tech. Rep. 1242 (Center for Supercomputing Research and Development, University of Illinois at Urbana–Champaign, Champaign, III., 1992).

Singham, S. B.

S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
[CrossRef]

C. F. Bohren, S. B. Singham, “Backscattering by non- spherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
[CrossRef]

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]

S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: a physical reformulation of the coupled-dipoles method,” Opt. Lett. 12, 10–12 (1987).
[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).
[CrossRef]

Sivan, J. P.

J. M. Perrin, J. P. Sivan, “Light scattering by dust grains: effects of the state of the surface on the validity of the discrete dipole approximation,” C. R. Acad. Sci. Paris Ser. II 316, 47–53 (1993).

J. M. Perrin, J. P. Sivan, “Scattering and polarisation of light by rough and porous interstellar grains,” Astron. Astrophys. 247, 497–504 (1991).

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).

Smith, C. F.

C. F. Smith, A. F. Peterson, R. Mittra, “A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields,” IEEE Trans. Antennas Propag. 37, 1490–1493 (1989).
[CrossRef]

A. F. Peterson, C. F. Smith, R. Mittra, “Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propag. 36, 1177–1179 (1988).
[CrossRef]

Smith, P. H.

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[CrossRef]

Stephens, G. L.

Taubenblatt, M. A.

Torrésani, B.

Tran, T. K.

Vivekanandan, J.

K. F. Evans, J. Vivekanandan, “Multiparameter radar and microwave radiative transfer modeling of nonspherical atmospheric ice particles,” IEEE Trans. Geosci. Remote Sensing 28, 423–437 (1990).
[CrossRef]

Wang, D.-S.

Wang, Y. M.

W. C. Chew, Y. M. Wang, L. Gurel, “Recursive algorithm for wave-scattering using windowed addition theorem,” J. Electromagn. Waves Appl. 6, 1537–1560 (1992).
[CrossRef]

West, R. A.

R. A. West, “Optical properties of aggregate particles whose outer diameter is comparable to the wavelength,” Appl. Opt. 30, 5316–5324 (1991).
[CrossRef] [PubMed]

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[CrossRef]

Wolff, M. J.

M. J. Wolff, G. C. Clayton, P. G. Martin, R. E. Schulte-Ladbeck, “Modeling composite and fluffy grains: the effects of porosity,” Astrophys. J. (to be published).

Wright, E. L.

E. L. Wright, “The ultraviolet extinction from interstellar graphitic onions,” Nature (London) 366, 227–228 (1988).
[CrossRef]

Yang, X.

T. K. Sarkar, X. Yang, E. Arvas, “A limited survey of various conjugate gradient methods for complex matrix equations arising in electromagnetic wave interactions,” Wave Motion 10, 527–546 (1988).
[CrossRef]

Yeh, C.

Appl. Opt. (7)

Astron. Astrophys. (4)

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates. I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

J. M. Perrin, J. P. Sivan, “Scattering and polarisation of light by rough and porous interstellar grains,” Astron. Astrophys. 247, 497–504 (1991).

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. (8)

B. T. Draine, S. Malhotra, “On graphite and the 2175 Å extinction profile,” Astrophys. J. 414, 632–645 (1993).
[CrossRef]

J. M. Perrin, P. L. Lamy, “On the validity of effective- medium theories in the case of light extinction by inhomogeneous dust particles,” Astrophys. J. 364, 146–151 (1990).
[CrossRef]

F. Rouleau, P. G. Martin, “A new method to calculate the extinction properties of irregularly shaped particles,” Astrophys. J. 414, 803–814 (1993).
[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]

J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251–259 (1990).
[CrossRef]

A. Lakhtakia, “General theory of the Purcell-Pennypacker scattering approach and its extension to bianisotropic scatterers,” Astrophys. J. 394, 494–499 (1992).
[CrossRef]

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical 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).
[CrossRef]

Atmos. Environ. (1)

M. F. Iskander, H. Y. Chen, J. E. Penner, “Resonance optical absorption by fractal agglomerates of smoke aerosols,” Atmos. Environ. 25A, 2563–2569 (1991).

C. R. Acad. Sci. Paris Ser. II (1)

J. M. Perrin, J. P. Sivan, “Light scattering by dust grains: effects of the state of the surface on the validity of the discrete dipole approximation,” C. R. Acad. Sci. Paris Ser. II 316, 47–53 (1993).

ccg-pak—fortran. Conjugate gradient package for solving complex matrix equations (1)

P. J. Flatau, T. Schneider, F. Evans, ccg-pak—fortran. Conjugate gradient package for solving complex matrix equations (1993).Available from pflatau@ucsd.edu.

Electromagnetics (1)

T. K. Sarkar, E. Arvas, S. M. Rao, “Application of the fast Fourier transform and the conjugate gradient method for efficient solution of electromagnetic scattering from both electrically large and small conducting bodies,” Electromagnetics 5, 99–122 (1985).
[CrossRef]

Icarus (1)

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

R. Harrington, “Origin and development of the method of moments for field computation,” IEEE Antennas Propag. Mag. 32(3), 31–35 (1990).
[CrossRef]

IEEE Trans. Antennas Propag. (6)

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross-section shape,” IEEE Trans. Antennas Propag. AP-13, 334–343 (1965).
[CrossRef]

A. W. Glison, “Recent advances in frequency domain techniques for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 25, 2867–2871 (1989).

E. K. Miller, “A selective survey of computational electromagnetics,” IEEE Trans. Antennas Propag. 36, 1281–1305 (1988).
[CrossRef]

L. Knockaert, “A note on the relationship between the conjugate gradient method and polynomials orthogonal over the spectrum of a linear operator,” IEEE Trans. Antennas Propag. AP-35, 1089–1091 (1987).
[CrossRef]

A. F. Peterson, C. F. Smith, R. Mittra, “Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propag. 36, 1177–1179 (1988).
[CrossRef]

C. F. Smith, A. F. Peterson, R. Mittra, “A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields,” IEEE Trans. Antennas Propag. 37, 1490–1493 (1989).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (1)

K. F. Evans, J. Vivekanandan, “Multiparameter radar and microwave radiative transfer modeling of nonspherical atmospheric ice particles,” IEEE Trans. Geosci. Remote Sensing 28, 423–437 (1990).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

D. T. Borup, O. P. Gandhi, “Calculation of high- resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
[CrossRef]

D. E. Livesay, K. Chen, “Electromagnetic fields induced inside arbitrarily shaped biological bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
[CrossRef]

Int. J. Mod. Phys. (1)

A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields,” Int. J. Mod. Phys. C3, 583–603 (1992).

J. Chem. Phys. (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]

H. DeVoe, “Optical properties of molecular aggregates. I. Classical model of electronic absorption and refraction,” J. Chem. Phys. 41, 393–400 (1964).
[CrossRef]

H. DeVoe, “Optical properties of molecular aggregates. II. Classical theory of the refraction, absorption, and optical activity of solutions and crystals,” J. Chem. Phys. 43, 3199–3208 (1965).
[CrossRef]

J. Comput. Phys. (1)

E. H. Newman, K. Kingsley, “An introduction to the method of moments,” J. Comput. Phys. 68, 1–18 (1991).
[CrossRef]

J. Electromagn. Waves Appl. (1)

W. C. Chew, Y. M. Wang, L. Gurel, “Recursive algorithm for wave-scattering using windowed addition theorem,” J. Electromagn. Waves Appl. 6, 1537–1560 (1992).
[CrossRef]

J. Geophys. Res. (1)

C. F. Bohren, S. B. Singham, “Backscattering by non- spherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
[CrossRef]

J. Opt. Soc. Am. A (7)

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

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily- shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

Langmuir (1)

S. B. Singham, C. F. Bohren, “Scattering of unpolarized and polarized light by particle aggregates of different size and fractal dimension,” Langmuir 9, 1431–1435 (1993).
[CrossRef]

Microwave Opt. Tech. Lett. (1)

W. C. Chew, C.-C. Lu, “NEPAL—an algorithm for solving the volume integral equation,” Microwave Opt. Tech. Lett. 6, 185–188 (1993).
[CrossRef]

Nature (London) (1)

E. L. Wright, “The ultraviolet extinction from interstellar graphitic onions,” Nature (London) 366, 227–228 (1988).
[CrossRef]

Numer. Math. (1)

R. W. Freund, N. M. Nachtigal, “QMR: a quasi-minimal residual method for non-Hermitian linear systems,” Numer. Math. 60, 315–339 (1991).
[CrossRef]

Opt. Lett. (2)

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]

Wave Motion (1)

T. K. Sarkar, X. Yang, E. Arvas, “A limited survey of various conjugate gradient methods for complex matrix equations arising in electromagnetic wave interactions,” Wave Motion 10, 527–546 (1988).
[CrossRef]

Other (12)

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, “Numerical implementation of the conjugate gradient method and the CG-FFT for electromagnetic scattering,” in Application of Conjugate Gradient Method to Electromagnetics and Signal Processing, T. K. Sarkar, ed. (Elsevier, New York, 1991), Chap. 5.

W. Hager, Applied Numerical Linear Algebra (Prentice-Hall, Englewood Cliffs, N.J., 1988).

J. D. Jackson, Classical Electromagnetism (Wiley, New York, 1975).

H. A. Lorentz, Theory of Electrons (Teubner, Leipzig, 1909).

The fortranprogram ddscat.4b is available from the authors. Direct queries to the Internet address draine@astro.princeton.edu or pflatau@macao.ucsd.edu.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

G. W. Kattawar, T. J. Humphreys, “Electromagnetic scattering from two identical pseudospheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 177–190.
[CrossRef]

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

P. J. Flatau, “Scattering by irregular particles in anomalous diffraction and discrete dipole approximations,” Atmos. Sci. Paper 517 (Department of Atmospheric Science, Colorado State University, Fort Collins, Colo., 1992).

M. J. Wolff, G. C. Clayton, P. G. Martin, R. E. Schulte-Ladbeck, “Modeling composite and fluffy grains: the effects of porosity,” Astrophys. J. (to be published).

P. Joly, “Résolution de systèmes linéaires avec plusieurs members par la méthode du gradient conjugué,” Tech. Rep. R-91012 (Publications du Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Paris, 1991).

V. Simoncini, E. Gallopoulos, “An iterative method for nonsymmetric systems with multiple right-hand sides,” Tech. Rep. 1242 (Center for Supercomputing Research and Development, University of Illinois at Urbana–Champaign, Champaign, III., 1992).

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Figures (10)

Fig. 1
Fig. 1

Scattering and absorption for a sphere with refractive index m = 1.33 + 0.01i. The upper panel shows the exact values of the scattering and absorption efficiency factors Qsca and Qabs, obtained with Mie theory, as functions of ka, where k = 2π/λ. The middle and lower panels show fractional errors in Qsca and Qabs. obtained from DDA pseudospheres, labeled by the number N of dipoles in the pseudosphere.

Fig. 2
Fig. 2

Same as Fig. 1, but for the refractive index m = 2 + i.

Fig. 3
Fig. 3

Differential scattering cross section for pseudospheres with m = 1.33 + 0.01i and ka = 3. The curves are labeled by N, the number of dipoles in the pseudosphere.

Fig. 4
Fig. 4

Same as Fig. 3 but for ka = 5.

Fig. 5
Fig. 5

Same as Fig. 3 but for ka = 7.

Fig. 6
Fig. 6

Same as Fig. 3 but for m = 2 + i.

Fig. 7
Fig. 7

Same as Fig. 3, but for m = 2 + i and ka = 5.

Fig. 8
Fig. 8

Same as Fig. 3, but for m = 2 + i and ka = 7.

Fig. 9
Fig. 9

(a) Q sca C sca / π a eff 2 and Q abs C abs / π a eff 2 (calculated by modal analysis) for two contiguous spheres of refractive index m = 1.33 + 0.01i, for radiation incident at an angle of 30° relative to the axis passing through the center of the two spheres. (b) Fractional error in computed value of Qsca and (c) Qabs for a DDA representation containing N = 2 × 17256 dipoles. Results are shown for three different prescriptions for the dipole polarizabilities: LDR, DGF/VIEF, and CMRR as functions of x = kaeff (source, Ref. 28).

Fig. 10
Fig. 10

Scattering by two contiguous spheres with refractive index m = 1.33 + 0.001i for x = kaeff = 10. Radiation is incident along the axis passing through the centers of the two spheres. Results are shown for two elements (S11 and S22) of the 4×4 scattering matrix.55 S11 and S22 computed with the DDA are compared with exact results (source, Ref. 28).

Equations (11)

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α j CM = 3 d 3 4 π j 1 j + 2 ,
α LDR α C M 1 + ( α C M / d 3 ) [ ( b 1 + m 2 b 2 + m 2 b 3 S ) ( k d ) 2 ( 2 / 3 ) i ( k d ) 3 ] ,
b 1 = 1.891531 , b 2 = 0.1648469 , b 3 = 1.7700004 , S j = 1 3 ( â j ê j ) 2 ,
N > ( 4 π / 3 ) | m | 3 ( k a eff ) 3 .
E j = E inc , j k j A jk P k ,
A j k = exp ( i k r j k ) r j k × [ k 2 ( r ̂ j k r ̂ j k 1 3 ) + i k r j k 1 r j k 2 ( 3 r ̂ j k r ̂ j k 1 3 ) ] , j k ,
k = 1 N A j k P k = E inc , j .
C ext = 4 π k | E 0 | 2 j = 1 N Im ( E inc , j * · P j ) ,
C abs = 4 π k | E 0 | 2 j = 1 N { Im [ P j · ( α j 1 ) * P j * ] 2 3 k 3 | P j | 2 } .
E sca = k 2 exp ( ikr ) r j = 1 N exp ( i k r ̂ · r j ) ( r ̂ r ̂ 1 3 ) P j .
error d Q / d Ω ( DDA ) d Q / d Ω ( Mie ) d Q / d Ω ( Mie ) .

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