Abstract
The discretedipole approximation (DDA) for scattering calculations, including the relationship between the DDA and other methods, is reviewed. Computational considerations, i.e., the use of complexconjugate gradient algorithms and fastFouriertransform 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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References
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 Year
 
 Author
 
 Publication
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[Crossref]  The fortranprogram ddscat.4b is available from the authors. Direct queries to the Internet address draine@astro.princeton.edu or pflatau@macao.ucsd.edu.
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[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 discretedipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[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] 
S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: a physical reformulation of the coupleddipoles method,” Opt. Lett. 12, 10–12 (1987).
[Crossref] [PubMed]  H. A. Lorentz, Theory of Electrons (Teubner, Leipzig, 1909).
 E. L. Wright, “The ultraviolet extinction from interstellar graphitic onions,” Nature (London) 366, 227–228 (1988).
[Crossref]  A. Lakhtakia, “General theory of the PurcellPennypacker 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 timeharmonic electromagnetic fields,” Int. J. Mod. Phys. C3, 583–603 (1992).
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[Crossref]  R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
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[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]  D. E. Livesay, K. Chen, “Electromagnetic fields induced inside arbitrarily shaped biological bodies,” IEEE Trans. Microwave Theory Tech. MTT22, 1273–1280 (1974).
[Crossref]  A. W. Glison, “Recent advances in frequency domain techniques for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 25, 2867–2871 (1989).
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[Crossref] 
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]  J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251–259 (1990).
[Crossref]  E. H. Newman, K. Kingsley, “An introduction to the method of moments,” J. Comput. Phys. 68, 1–18 (1991).
[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]  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).
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[Crossref] 
C. E. Dungey, C. F. Bohren, “Light scattering by nonspherical particles: a refinement to the coupleddipole method,” J. Opt. Soc. Am. A 8, 81–87 (1991).
[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]  W. Hager, Applied Numerical Linear Algebra (PrenticeHall, Englewood Cliffs, N.J., 1988).

P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discretedipole approximation: a new algorithm exploiting the blockToeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990).
[Crossref] 
J. J. Goodman, B. T. Draine, P. J. Flatau, “Application of fastFouriertransform techniques to the discretedipole approximation,” Opt. Lett. 16, 1198–1200 (1991).
[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]  A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, “Numerical implementation of the conjugate gradient method and the CGFFT for electromagnetic scattering,” in Application of Conjugate Gradient Method to Electromagnetics and Signal Processing, T. K. Sarkar, ed. (Elsevier, New York, 1991), Chap. 5.
 R. W. Freund, N. M. Nachtigal, “QMR: a quasiminimal residual method for nonHermitian linear systems,” Numer. Math. 60, 315–339 (1991).
[Crossref] 
S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: the scattering order formulation of the coupleddipole method,” J. Opt. Soc. Am. A 5, 1867–1872 (1988).
[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. AP35, 1089–1091 (1987).
[Crossref]  A. F. Peterson, C. F. Smith, R. Mittra, “Eigenvalues of the momentmethod 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]  P. Joly, “Résolution de systèmes linéaires avec plusieurs members par la méthode du gradient conjugué,” Tech. Rep. R91012 (Publications du Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Paris, 1991).
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 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. MTT33, 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] 
P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[Crossref] [PubMed] 
D.S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
[Crossref] [PubMed] 
M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[Crossref]  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 wavescattering 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] 
J. C. Ku, “Comparisons of coupleddipole 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] 
K. A. Fuller, “Optical resonances and twosphere 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]  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).
 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).
 B. T. Draine, S. Malhotra, “On graphite and the 2175 Å extinction profile,” Astrophys. J. 414, 632–645 (1993).
[Crossref]  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]  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).
 M. J. Wolff, G. C. Clayton, P. G. Martin, R. E. SchulteLadbeck, “Modeling composite and fluffy grains: the effects of porosity,” Astrophys. J. (to be published).
 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]  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] 
M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupleddipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
[Crossref]  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, “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, T. Schneider, F. Evans, ccgpak—fortran. Conjugate gradient package for solving complex matrix equations (1993).Available from pflatau@ucsd.edu.
F. Rouleau, P. G. Martin, “A new method to calculate the extinction properties of irregularly shaped particles,” Astrophys. J. 414, 803–814 (1993).
[Crossref]
W. C. Chew, C.C. Lu, “NEPAL—an algorithm for solving the volume integral equation,” Microwave Opt. Tech. Lett. 6, 185–188 (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]
J. C. Ku, “Comparisons of coupleddipole 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]
M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupleddipole method,” J. Opt. Soc. Am. A 10, 912–919 (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]
1992 (7)
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]
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 wavescattering 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]
A. Lakhtakia, “General theory of the PurcellPennypacker 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 timeharmonic 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]
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, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[Crossref]
R. W. Freund, N. M. Nachtigal, “QMR: a quasiminimal residual method for nonHermitian linear systems,” Numer. Math. 60, 315–339 (1991).
[Crossref]
K. A. Fuller, “Optical resonances and twosphere systems,” Appl. Opt. 30, 4716–4731 (1991).
[Crossref]
[PubMed]
R. A. West, “Optical properties of aggregate particles whose outer diameter is comparable to the wavelength,” Appl. Opt. 30, 5316–5324 (1991).
[Crossref]
[PubMed]
J. J. Goodman, B. T. Draine, P. J. Flatau, “Application of fastFouriertransform techniques to the discretedipole approximation,” Opt. Lett. 16, 1198–1200 (1991).
[Crossref]
[PubMed]
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 coupleddipole method,” J. Opt. Soc. Am. A 8, 81–87 (1991).
[Crossref]
M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[Crossref]
1990 (6)
P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discretedipole approximation: a new algorithm exploiting the blockToeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990).
[Crossref]
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]
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).
J. I. Hage, J. M. Greenberg, “A model for the optical properties of porous grains,” Astrophys. J. 361, 251–259 (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]
1989 (3)
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]
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]
1988 (7)
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]
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]
S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: the scattering order formulation of the coupleddipole method,” J. Opt. Soc. Am. A 5, 1867–1872 (1988).
[Crossref]
[PubMed]
E. K. Miller, “A selective survey of computational electromagnetics,” IEEE Trans. Antennas Propag. 36, 1281–1305 (1988).
[Crossref]
E. L. Wright, “The ultraviolet extinction from interstellar graphitic onions,” Nature (London) 366, 227–228 (1988).
[Crossref]
A. F. Peterson, C. F. Smith, R. Mittra, “Eigenvalues of the momentmethod matrix and their effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propag. 36, 1177–1179 (1988).
[Crossref]
B. T. Draine, “The discretedipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]
1987 (2)
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. AP35, 1089–1091 (1987).
[Crossref]
S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: a physical reformulation of the coupleddipoles method,” Opt. Lett. 12, 10–12 (1987).
[Crossref]
[PubMed]
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. MTT33, 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)
D.S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
[Crossref]
[PubMed]
1975 (1)
P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[Crossref]
[PubMed]
1974 (1)
D. E. Livesay, K. Chen, “Electromagnetic fields induced inside arbitrarily shaped biological bodies,” IEEE Trans. Microwave Theory Tech. MTT22, 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 crosssection shape,” IEEE Trans. Antennas Propag. AP13, 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.
P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[Crossref]
[PubMed]
Barber, P. W.
D.S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
[Crossref]
[PubMed]
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 coupleddipole 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 coupleddipole 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 coupleddipoles 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. MTT33, 417–419 (1985).
[Crossref]
Bourrely, C.
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]
Chan, C. H.
A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, “Numerical implementation of the conjugate gradient method and the CGFFT 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. MTT22, 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]
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Appl. Opt. (7)
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Astron. Astrophys. (4)
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Astrophys. J. (8)
B. T. Draine, S. Malhotra, “On graphite and the 2175 Å extinction profile,” Astrophys. J. 414, 632–645 (1993).
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Atmos. Environ. (1)
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C. R. Acad. Sci. Paris Ser. II (1)
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ccgpak—fortran. Conjugate gradient package for solving complex matrix equations (1)
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Electromagnetics (1)
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J. Opt. Soc. Am. A (7)
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Langmuir (1)
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Numer. Math. (1)
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Proc. R. Soc. London Ser. A (1)
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Wave Motion (1)
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The fortranprogram ddscat.4b is available from the authors. Direct queries to the Internet address draine@astro.princeton.edu or pflatau@macao.ucsd.edu.
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C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
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Figures (10)
Scattering and absorption for a sphere with refractive index
Same as Fig. 1, but for the refractive index
Differential scattering cross section for pseudospheres with
Same as Fig. 3 but for
Same as Fig. 3 but for
Same as Fig. 3 but for
Same as Fig. 3, but for
Same as Fig. 3, but for
(a)
Scattering by two contiguous spheres with refractive index
Equations (11)
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