OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 11, Iss. 4 — Apr. 1, 1994
  • pp: 1491–1499

Discrete-Dipole Approximation For Scattering Calculations

Bruce T. Draine and Piotr J. Flatau  »View Author Affiliations

JOSA A, Vol. 11, Issue 4, pp. 1491-1499 (1994)

View Full Text Article

Enhanced HTML    Acrobat PDF (1174 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

Original Manuscript: July 20, 1993
Revised Manuscript: October 12, 1993
Manuscript Accepted: October 18, 1993
Published: April 1, 1994

Bruce T. Draine and Piotr J. Flatau, "Discrete-Dipole Approximation For Scattering Calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited