Abstract

Calculation of the scattering pattern from aggregates of spheres through the T-matrix approach yields high-precision results but at a high-computational cost, especially when the aggregate concerned is large or is composed of large-size spheres. With reference to a specific but representative aggregate, we discuss how and to what extent the computational effort can be reduced but still preserve the qualitative features of the signature of the aggregate concerned.

© 2003 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. B 127, 1837–1843 (1962).
    [CrossRef]
  3. M. I. Mishchenko, W. J. Wiscombe, J. H. Hovenier, L. D. Travis, “Overview of scattering by nonspherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 30–59.
  4. S. Holler, J.-C. Auger, B. Stout, Y. Pan, J. R. Bottiger, R. K. Chang, G. Videen, “Observations and calculations of light scattering from clusters of spheres,” Appl. Opt. 39, 6873–6887 (2000).
    [CrossRef]
  5. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 3–25.
    [CrossRef]
  6. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  7. F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
    [CrossRef]
  8. F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
    [CrossRef]
  9. F. Borghese, P. Denti, R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484–491 (1994).
    [CrossRef] [PubMed]
  10. P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
  11. E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. 45, 868–875 (1997).
    [CrossRef]
  12. E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
    [CrossRef]
  13. Y.-L. Xu, “Electromagnetic scattering by an aggregate of spheres: far field,” Appl. Opt. 36, 9496–9508 (1997).
    [CrossRef]
  14. F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from non-spherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
    [CrossRef]
  15. R. T. Wang, J. M. Greenberg, D. W. Schuerman, “Experimental results of dependent light scattering by two spheres,” Opt. Lett. 11, 543–545 (1981).
    [CrossRef]
  16. D. W. Schuerman, R. T. Wang, “Experimental results of multiple scattering,” Contractor Rep. ARCSL-CR-81003 (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Grounds, Md., July1980).
  17. B. Stout, J.-C. Auger, J. Lafait, “Individual and aggregate scattering matrices and cross sections: conservation laws and reciprocity,” J. Mod. Opt. 48, 2105–2128 (2001).
  18. D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
    [CrossRef]
  19. M. I. Mishchenko, L. D. Travis, A. Macke, “T-Matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 147–172.
    [CrossRef]
  20. F. Borghese, P. Denti, R. Saija, M. A. Iatì, O. I. Sindoni, “Optical properties of a dispersion of anisotropic particles with nonrandomly distributed orientations. The case of atmospheric ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 70, 237–251 (2001).
    [CrossRef]
  21. W. C. Chew, Waves and Fields in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1990).
  22. M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
    [CrossRef]
  23. J. R. Bottiger, E. S. Fry, R. C. Tompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
    [CrossRef]
  24. M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
    [CrossRef] [PubMed]

2001 (2)

B. Stout, J.-C. Auger, J. Lafait, “Individual and aggregate scattering matrices and cross sections: conservation laws and reciprocity,” J. Mod. Opt. 48, 2105–2128 (2001).

F. Borghese, P. Denti, R. Saija, M. A. Iatì, O. I. Sindoni, “Optical properties of a dispersion of anisotropic particles with nonrandomly distributed orientations. The case of atmospheric ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 70, 237–251 (2001).
[CrossRef]

2000 (1)

1997 (3)

1996 (2)

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

1995 (1)

1994 (1)

1989 (1)

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from non-spherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

1984 (1)

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

1981 (1)

1980 (1)

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1962 (1)

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. B 127, 1837–1843 (1962).
[CrossRef]

Auger, J.-C.

B. Stout, J.-C. Auger, J. Lafait, “Individual and aggregate scattering matrices and cross sections: conservation laws and reciprocity,” J. Mod. Opt. 48, 2105–2128 (2001).

S. Holler, J.-C. Auger, B. Stout, Y. Pan, J. R. Bottiger, R. K. Chang, G. Videen, “Observations and calculations of light scattering from clusters of spheres,” Appl. Opt. 39, 6873–6887 (2000).
[CrossRef]

Borghese, F.

F. Borghese, P. Denti, R. Saija, M. A. Iatì, O. I. Sindoni, “Optical properties of a dispersion of anisotropic particles with nonrandomly distributed orientations. The case of atmospheric ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 70, 237–251 (2001).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. 45, 868–875 (1997).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484–491 (1994).
[CrossRef] [PubMed]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from non-spherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

Bottiger, J. R.

S. Holler, J.-C. Auger, B. Stout, Y. Pan, J. R. Bottiger, R. K. Chang, G. Videen, “Observations and calculations of light scattering from clusters of spheres,” Appl. Opt. 39, 6873–6887 (2000).
[CrossRef]

J. R. Bottiger, E. S. Fry, R. C. Tompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Chang, R. K.

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1990).

Denti, P.

F. Borghese, P. Denti, R. Saija, M. A. Iatì, O. I. Sindoni, “Optical properties of a dispersion of anisotropic particles with nonrandomly distributed orientations. The case of atmospheric ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 70, 237–251 (2001).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. 45, 868–875 (1997).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484–491 (1994).
[CrossRef] [PubMed]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from non-spherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

Fry, E. S.

J. R. Bottiger, E. S. Fry, R. C. Tompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Fucile, E.

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. 45, 868–875 (1997).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

Greenberg, J. M.

Holler, S.

Hovenier, J. H.

M. I. Mishchenko, W. J. Wiscombe, J. H. Hovenier, L. D. Travis, “Overview of scattering by nonspherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 30–59.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 3–25.
[CrossRef]

Iatì, M. A.

F. Borghese, P. Denti, R. Saija, M. A. Iatì, O. I. Sindoni, “Optical properties of a dispersion of anisotropic particles with nonrandomly distributed orientations. The case of atmospheric ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 70, 237–251 (2001).
[CrossRef]

Jackson, J. D.

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

Lafait, J.

B. Stout, J.-C. Auger, J. Lafait, “Individual and aggregate scattering matrices and cross sections: conservation laws and reciprocity,” J. Mod. Opt. 48, 2105–2128 (2001).

Macke, A.

M. I. Mishchenko, L. D. Travis, A. Macke, “T-Matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 147–172.
[CrossRef]

Mackowski, D. W.

Mishchenko, M. I.

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “T-Matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 147–172.
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 3–25.
[CrossRef]

M. I. Mishchenko, W. J. Wiscombe, J. H. Hovenier, L. D. Travis, “Overview of scattering by nonspherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 30–59.

Pan, Y.

Saija, R.

F. Borghese, P. Denti, R. Saija, M. A. Iatì, O. I. Sindoni, “Optical properties of a dispersion of anisotropic particles with nonrandomly distributed orientations. The case of atmospheric ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 70, 237–251 (2001).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. 45, 868–875 (1997).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484–491 (1994).
[CrossRef] [PubMed]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from non-spherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Schuerman, D. W.

R. T. Wang, J. M. Greenberg, D. W. Schuerman, “Experimental results of dependent light scattering by two spheres,” Opt. Lett. 11, 543–545 (1981).
[CrossRef]

D. W. Schuerman, R. T. Wang, “Experimental results of multiple scattering,” Contractor Rep. ARCSL-CR-81003 (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Grounds, Md., July1980).

Sindoni, O. I.

F. Borghese, P. Denti, R. Saija, M. A. Iatì, O. I. Sindoni, “Optical properties of a dispersion of anisotropic particles with nonrandomly distributed orientations. The case of atmospheric ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 70, 237–251 (2001).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. 45, 868–875 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from non-spherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

Stout, B.

B. Stout, J.-C. Auger, J. Lafait, “Individual and aggregate scattering matrices and cross sections: conservation laws and reciprocity,” J. Mod. Opt. 48, 2105–2128 (2001).

S. Holler, J.-C. Auger, B. Stout, Y. Pan, J. R. Bottiger, R. K. Chang, G. Videen, “Observations and calculations of light scattering from clusters of spheres,” Appl. Opt. 39, 6873–6887 (2000).
[CrossRef]

Tompson, R. C.

J. R. Bottiger, E. S. Fry, R. C. Tompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Toscano, G.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “T-Matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 147–172.
[CrossRef]

M. I. Mishchenko, W. J. Wiscombe, J. H. Hovenier, L. D. Travis, “Overview of scattering by nonspherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 30–59.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 3–25.
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Videen, G.

Wang, R. T.

R. T. Wang, J. M. Greenberg, D. W. Schuerman, “Experimental results of dependent light scattering by two spheres,” Opt. Lett. 11, 543–545 (1981).
[CrossRef]

D. W. Schuerman, R. T. Wang, “Experimental results of multiple scattering,” Contractor Rep. ARCSL-CR-81003 (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Grounds, Md., July1980).

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Wiscombe, W. J.

M. I. Mishchenko, W. J. Wiscombe, J. H. Hovenier, L. D. Travis, “Overview of scattering by nonspherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 30–59.

Wyatt, P. J.

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. B 127, 1837–1843 (1962).
[CrossRef]

Xu, Y.-L.

Aerosol Sci. Technol. (1)

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Antennas Propag. (1)

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. 45, 868–875 (1997).
[CrossRef]

J. Aerosol Sci. (1)

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from non-spherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

J. Math. Phys. (1)

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

J. Mod. Opt. (1)

B. Stout, J.-C. Auger, J. Lafait, “Individual and aggregate scattering matrices and cross sections: conservation laws and reciprocity,” J. Mod. Opt. 48, 2105–2128 (2001).

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (2)

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

F. Borghese, P. Denti, R. Saija, M. A. Iatì, O. I. Sindoni, “Optical properties of a dispersion of anisotropic particles with nonrandomly distributed orientations. The case of atmospheric ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 70, 237–251 (2001).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. B 127, 1837–1843 (1962).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Other (8)

D. W. Schuerman, R. T. Wang, “Experimental results of multiple scattering,” Contractor Rep. ARCSL-CR-81003 (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Grounds, Md., July1980).

M. I. Mishchenko, W. J. Wiscombe, J. H. Hovenier, L. D. Travis, “Overview of scattering by nonspherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 30–59.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 3–25.
[CrossRef]

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

J. R. Bottiger, E. S. Fry, R. C. Tompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

W. C. Chew, Waves and Fields in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1990).

M. I. Mishchenko, L. D. Travis, A. Macke, “T-Matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000), pp. 147–172.
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

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Figures (5)

Fig. 1
Fig. 1

Contour plots of the differential scattering cross section (log scale) of the aggregate reduced to 20% of its real size, calculated with the E scheme. The incident field has θ I = 90° and ϕ I = 0°: (a) L M = 3, (b) L M = 5, (c) L M = 8.

Fig. 2
Fig. 2

Differential scattering cross section for the cluster reduced to 20% of its real size, calculated with the E scheme for L M = 2 (light dotted curve), 3 (dot-dash curve), 4 (heavy dotted curve) and 5 (solid curve) for θ I = 90° and ϕ I = 0°: (a) θ S = 90° and (b) θ S = 30°.

Fig. 3
Fig. 3

Comparison of the differential scattering cross section for the cluster reduced to 20% of its real size calculated with the E scheme for L M = 4 (heavy solid curve) with that yielded by the T scheme with L M = 4 and l M = 4 (light solid curve), 6 (dot-dash curve), 8 (dotted curve), 10 (heavy dotted curve), 12 (dashed curve). θ I = 90°, ϕ I = 0°, and θ S = 90°. Note that the heavy solid curve and the dashed curve are almost perfectly superposed on the scale of the figure.

Fig. 4
Fig. 4

Contour plots of the differential scattering cross section for the cluster considered with its real size calculated with the E scheme for θ I = 90° and ϕ I = 0° with (a) L M = 13 and (b) L M = 15.

Fig. 5
Fig. 5

Contour plots of the differential scattering cross section for the cluster considered with its real size calculated with the E scheme for θ I = 45° and ϕ I = 0° with (a) L M = 13 and (b) L M = 15.

Tables (1)

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Table 1 Coordinates of the Centers of Component Spheres in Micrometersa

Equations (26)

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Jlm1r, K=jlKrXlmrˆ, Jlm2r, K=1K ×Jlm1r, K
EIηr=E0plmJlmpr, nkWIηlmp,
Wlmpeˆ, kˆ=4πip+l-1eˆ · Zlmp*kˆ,
Zlm1kˆ=Xlmkˆ, Zlm2kˆ=Xlmkˆ×kˆ.
ESη=E0αplmHlmprα, nkAηαlmp,
ETηα=E0plmJlmprα, nαkCηαlmp.
αplm αlmαlmppAηαlmp=-Wηαlmp,
Wηαlmp=plm αlm0lmppWIηlmp.
αlmαlmpp=Rαlp-1δααδppδllδmm+αlmαlmpp.
Aηαlmp=-plmM-1αlmαlmppWηαlmp,
ESη=E0plmαplmHlmpr, nk×0lmαlmppAηαlmp.
Aηlmp=αplm 0lmαlmppAηαlmp,
Aηlmp=plm SlmlmppWIηlmp,
Slmlmpp=-ααqLMqLM 0lmαLMpq×M-1αLMαLMqqαLM0lmqp.
ESη=E0expinkrrfηkˆS, kˆI=E0expinkrnkrplm-il+pZlmpkˆSAηlmp,
ESη · ûSη=E0expikrr fηη,
fηη=- i4πnkplmplm WSηlmp*SlmlmppWIηlmp
Iηη= |E0|2r2 |fηηkˆS, kˆI|2.
plm WSηlmp*0lmαLMpq, plm αLM0lmqpWIηlmp,
expikI · r=expikI · RαexpikI · rα.
Wηαlmp=expikI · RαWIηlmp.
plm αlm0lmppWIηlmp=expikI · RαWIηlmp.
plm αlm0lmpp*WSηlmp*=exp-ikS · RαWSηlmp*,
αlm0lmpp*=0lmαlmpp,
plm WSηlmp*0lmαlmpp=exp-ikS · RαWSηlmp*.
fηη= i4πnkpLMpLMαα WSηLMp*exp-ikS · Rα×M-1αLMαLMppexpikI · RαWIηLMp.

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