Abstract

We study the orientation average scattering cross section of various isolated aggregates of identical spherical particles as functions of their size, optical properties, and spatial configurations. Two kinds of aggregates are studied: latex particles in water and rutile titanium dioxide pigments in a polymeric resin, with size parameters varying from 0.6 to 2.3. Calculations are performed by using a recursive centered T-matrix algorithm solution of the multiple scattering equation that we previously developed [J. Quant. Spectrosc. Radiat. Transfer 79–80, 533 (2003) ]. We show that for a specific size of the constituent spheres, their respective couplings apparently vanish, regardless of the aggregate configuration, and that the scattering cross section of the entire cluster behaves as if its constituents were isolated. We found that the particular radius for which this phenomenon occurs is a function of the relative refractive index of the system. We also study the correlations between the strength of the coupling among the constituent spheres, and the pseudofractal dimension of the aggregate as it varies from 1 to 30.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
  3. F. Borghese, P. Denti, “Electromagnetic scattering by a cluster of spheres,” Appl. Opt. 18, 116–120 (1979).
    [CrossRef] [PubMed]
  4. A.-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by a system of multilayered dielectric spheres,” IEEE Trans. Antennas Propag. 41, 172–175 (1992).
  5. A. Rahmani, C. Benoit, R. Jullien, G. Poussigue, A. Sakout, “Light scattering in fractals with scalar and bond-bending models,” J. Phys.: Condens. Matter 9, 2149–2164 (1997).
  6. M. Quinten, J. Stier, “Absorption of scattered light in colloidal systems of aggregated particles,” Colloid Polym. Sci. 273, 233–241 (1995).
    [CrossRef]
  7. S. Fitzwater, J. W. Hook, “Dependent scattering theory: a new approach to predicting scattering in paints,” J. Coat. Technol. 57, 39–47 (1985).
  8. Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag., 1881, pp. 12–81.
  9. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  10. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  11. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
    [CrossRef]
  12. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
  13. M. A. Morgan, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
    [CrossRef]
  14. P. P. Silvester, R. L. Ferrari, Finite Elements for Electrical Engineers (Cambridge U. Press, 1996).
    [CrossRef]
  15. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
  16. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).
  17. P. Yang, K.-N. Liou, “Finite-difference time domain method for light scattering by non spherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 173–221.
    [CrossRef]
  18. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  19. U. Frisch, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A. T. Barucha-Reid, ed. (Academic, 1968), Vol. 1, pp. 75–191.
  20. F. Curiel, W. Vargas, R. G. Barrera, “Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra,” Appl. Opt. 41, 5968–5978 (2002).
    [CrossRef]
  21. D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transf. 56, 591–607 (1996).
    [CrossRef]
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  23. P. Rannou, C. P. McKay, R. Botet, M. Cabane, “Semi-empirical model of absorption and scattering by isotropic fractal aggregates of sphere,” Planet. Space Sci. 47, 385–396 (1999).
    [CrossRef]
  24. R. Botet, P. Rannou, “Optical anisotropy of an ensemble of aligned fractal aggregates,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 569–576 (2003).
    [CrossRef]
  25. R. Botet, P. Rannou, M. Cabane, “Mean-field approximation of Mie scattering by fractal aggregates of identical spheres,” Appl. Opt. 36, 8791–8796 (1997).
    [CrossRef]
  26. J. C. Auger, B. Stout, “A recursive T-matrix algorithm to solve the multiple scattering equation: numerical validation,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 533–547 (2003).
    [CrossRef]
  27. B. Stout, J. C. Auger, J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
    [CrossRef]
  28. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  29. S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).
  30. D. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
    [CrossRef]
  31. 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).
  32. J. C. Auger, R. G. Barrera, B. Stout, “Scattering efficiencies of aggregates of spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 521–531 (2003).
    [CrossRef]
  33. R. Julien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, 1987).
  34. E. S. Thiele, R. H. French, “Light-scattering properties of representative, morphological rutile titania particles studied using a finite-element method,” J. Am. Ceram. Soc. 81, 469–479 (1998).
    [CrossRef]

2003

R. Botet, P. Rannou, “Optical anisotropy of an ensemble of aligned fractal aggregates,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 569–576 (2003).
[CrossRef]

J. C. Auger, B. Stout, “A recursive T-matrix algorithm to solve the multiple scattering equation: numerical validation,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 533–547 (2003).
[CrossRef]

J. C. Auger, R. G. Barrera, B. Stout, “Scattering efficiencies of aggregates of spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 521–531 (2003).
[CrossRef]

2002

B. Stout, J. C. Auger, J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

F. Curiel, W. Vargas, R. G. Barrera, “Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra,” Appl. Opt. 41, 5968–5978 (2002).
[CrossRef]

2001

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).

1999

P. Rannou, C. P. McKay, R. Botet, M. Cabane, “Semi-empirical model of absorption and scattering by isotropic fractal aggregates of sphere,” Planet. Space Sci. 47, 385–396 (1999).
[CrossRef]

1998

E. S. Thiele, R. H. French, “Light-scattering properties of representative, morphological rutile titania particles studied using a finite-element method,” J. Am. Ceram. Soc. 81, 469–479 (1998).
[CrossRef]

1997

R. Botet, P. Rannou, M. Cabane, “Mean-field approximation of Mie scattering by fractal aggregates of identical spheres,” Appl. Opt. 36, 8791–8796 (1997).
[CrossRef]

A. Rahmani, C. Benoit, R. Jullien, G. Poussigue, A. Sakout, “Light scattering in fractals with scalar and bond-bending models,” J. Phys.: Condens. Matter 9, 2149–2164 (1997).

1996

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transf. 56, 591–607 (1996).
[CrossRef]

1995

M. Quinten, J. Stier, “Absorption of scattered light in colloidal systems of aggregated particles,” Colloid Polym. Sci. 273, 233–241 (1995).
[CrossRef]

1994

1993

1992

A.-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by a system of multilayered dielectric spheres,” IEEE Trans. Antennas Propag. 41, 172–175 (1992).

1985

S. Fitzwater, J. W. Hook, “Dependent scattering theory: a new approach to predicting scattering in paints,” J. Coat. Technol. 57, 39–47 (1985).

1979

M. A. Morgan, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

F. Borghese, P. Denti, “Electromagnetic scattering by a cluster of spheres,” Appl. Opt. 18, 116–120 (1979).
[CrossRef] [PubMed]

1973

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

1971

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

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

1965

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

1961

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

1881

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag., 1881, pp. 12–81.

Auger, J. C.

J. C. Auger, B. Stout, “A recursive T-matrix algorithm to solve the multiple scattering equation: numerical validation,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 533–547 (2003).
[CrossRef]

J. C. Auger, R. G. Barrera, B. Stout, “Scattering efficiencies of aggregates of spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 521–531 (2003).
[CrossRef]

B. Stout, J. C. Auger, J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

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).

Barrera, R. G.

J. C. Auger, R. G. Barrera, B. Stout, “Scattering efficiencies of aggregates of spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 521–531 (2003).
[CrossRef]

F. Curiel, W. Vargas, R. G. Barrera, “Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra,” Appl. Opt. 41, 5968–5978 (2002).
[CrossRef]

Benoit, C.

A. Rahmani, C. Benoit, R. Jullien, G. Poussigue, A. Sakout, “Light scattering in fractals with scalar and bond-bending models,” J. Phys.: Condens. Matter 9, 2149–2164 (1997).

Bhanti, D.

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transf. 56, 591–607 (1996).
[CrossRef]

Bohren, C. F.

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

Borghese, F.

Botet, R.

R. Botet, P. Rannou, “Optical anisotropy of an ensemble of aligned fractal aggregates,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 569–576 (2003).
[CrossRef]

P. Rannou, C. P. McKay, R. Botet, M. Cabane, “Semi-empirical model of absorption and scattering by isotropic fractal aggregates of sphere,” Planet. Space Sci. 47, 385–396 (1999).
[CrossRef]

R. Botet, P. Rannou, M. Cabane, “Mean-field approximation of Mie scattering by fractal aggregates of identical spheres,” Appl. Opt. 36, 8791–8796 (1997).
[CrossRef]

R. Julien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, 1987).

Cabane, M.

P. Rannou, C. P. McKay, R. Botet, M. Cabane, “Semi-empirical model of absorption and scattering by isotropic fractal aggregates of sphere,” Planet. Space Sci. 47, 385–396 (1999).
[CrossRef]

R. Botet, P. Rannou, M. Cabane, “Mean-field approximation of Mie scattering by fractal aggregates of identical spheres,” Appl. Opt. 36, 8791–8796 (1997).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Ciric, I. R.

A.-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by a system of multilayered dielectric spheres,” IEEE Trans. Antennas Propag. 41, 172–175 (1992).

Curiel, F.

F. Curiel, W. Vargas, R. G. Barrera, “Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra,” Appl. Opt. 41, 5968–5978 (2002).
[CrossRef]

Denti, P.

Ferrari, R. L.

P. P. Silvester, R. L. Ferrari, Finite Elements for Electrical Engineers (Cambridge U. Press, 1996).
[CrossRef]

Fitzwater, S.

S. Fitzwater, J. W. Hook, “Dependent scattering theory: a new approach to predicting scattering in paints,” J. Coat. Technol. 57, 39–47 (1985).

French, R. H.

E. S. Thiele, R. H. French, “Light-scattering properties of representative, morphological rutile titania particles studied using a finite-element method,” J. Am. Ceram. Soc. 81, 469–479 (1998).
[CrossRef]

Frisch, U.

U. Frisch, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A. T. Barucha-Reid, ed. (Academic, 1968), Vol. 1, pp. 75–191.

Gustafson, B. A. S.

Hamid, A.-K.

A.-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by a system of multilayered dielectric spheres,” IEEE Trans. Antennas Propag. 41, 172–175 (1992).

Hamid, M.

A.-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by a system of multilayered dielectric spheres,” IEEE Trans. Antennas Propag. 41, 172–175 (1992).

Hook, J. W.

S. Fitzwater, J. W. Hook, “Dependent scattering theory: a new approach to predicting scattering in paints,” J. Coat. Technol. 57, 39–47 (1985).

Huffman, D. R.

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

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Julien, R.

R. Julien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, 1987).

Jullien, R.

A. Rahmani, C. Benoit, R. Jullien, G. Poussigue, A. Sakout, “Light scattering in fractals with scalar and bond-bending models,” J. Phys.: Condens. Matter 9, 2149–2164 (1997).

Kong, J.

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Lafait, J.

B. Stout, J. C. Auger, J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

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).

Liou, K.-N.

P. Yang, K.-N. Liou, “Finite-difference time domain method for light scattering by non spherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 173–221.
[CrossRef]

Mackowski, D.

Manickavasagam, S.

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transf. 56, 591–607 (1996).
[CrossRef]

McKay, C. P.

P. Rannou, C. P. McKay, R. Botet, M. Cabane, “Semi-empirical model of absorption and scattering by isotropic fractal aggregates of sphere,” Planet. Space Sci. 47, 385–396 (1999).
[CrossRef]

Mei, K. K.

M. A. Morgan, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

Mengüç, M. P.

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transf. 56, 591–607 (1996).
[CrossRef]

Mishchenko, M. I.

Morgan, M. A.

M. A. Morgan, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

Pennypacker, C. R.

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

Poussigue, G.

A. Rahmani, C. Benoit, R. Jullien, G. Poussigue, A. Sakout, “Light scattering in fractals with scalar and bond-bending models,” J. Phys.: Condens. Matter 9, 2149–2164 (1997).

Purcell, E. M.

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

Quinten, M.

M. Quinten, J. Stier, “Absorption of scattered light in colloidal systems of aggregated particles,” Colloid Polym. Sci. 273, 233–241 (1995).
[CrossRef]

Rahmani, A.

A. Rahmani, C. Benoit, R. Jullien, G. Poussigue, A. Sakout, “Light scattering in fractals with scalar and bond-bending models,” J. Phys.: Condens. Matter 9, 2149–2164 (1997).

Rannou, P.

R. Botet, P. Rannou, “Optical anisotropy of an ensemble of aligned fractal aggregates,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 569–576 (2003).
[CrossRef]

P. Rannou, C. P. McKay, R. Botet, M. Cabane, “Semi-empirical model of absorption and scattering by isotropic fractal aggregates of sphere,” Planet. Space Sci. 47, 385–396 (1999).
[CrossRef]

R. Botet, P. Rannou, M. Cabane, “Mean-field approximation of Mie scattering by fractal aggregates of identical spheres,” Appl. Opt. 36, 8791–8796 (1997).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag., 1881, pp. 12–81.

Sakout, A.

A. Rahmani, C. Benoit, R. Jullien, G. Poussigue, A. Sakout, “Light scattering in fractals with scalar and bond-bending models,” J. Phys.: Condens. Matter 9, 2149–2164 (1997).

Schultz, K.

Shin, R.

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Silvester, P. P.

P. P. Silvester, R. L. Ferrari, Finite Elements for Electrical Engineers (Cambridge U. Press, 1996).
[CrossRef]

Stein, S.

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

Stier, J.

M. Quinten, J. Stier, “Absorption of scattered light in colloidal systems of aggregated particles,” Colloid Polym. Sci. 273, 233–241 (1995).
[CrossRef]

Stout, B.

J. C. Auger, R. G. Barrera, B. Stout, “Scattering efficiencies of aggregates of spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 521–531 (2003).
[CrossRef]

J. C. Auger, B. Stout, “A recursive T-matrix algorithm to solve the multiple scattering equation: numerical validation,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 533–547 (2003).
[CrossRef]

B. Stout, J. C. Auger, J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

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).

Taflove, A.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).

Thiele, E. S.

E. S. Thiele, R. H. French, “Light-scattering properties of representative, morphological rutile titania particles studied using a finite-element method,” J. Am. Ceram. Soc. 81, 469–479 (1998).
[CrossRef]

Thiele-Corbach, E.

Tsang, L.

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Vargas, W.

F. Curiel, W. Vargas, R. G. Barrera, “Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra,” Appl. Opt. 41, 5968–5978 (2002).
[CrossRef]

Waterman, P. C.

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

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Yang, P.

P. Yang, K.-N. Liou, “Finite-difference time domain method for light scattering by non spherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 173–221.
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Zerull, R. H.

Appl. Opt.

Astrophys. J.

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

Colloid Polym. Sci.

M. Quinten, J. Stier, “Absorption of scattered light in colloidal systems of aggregated particles,” Colloid Polym. Sci. 273, 233–241 (1995).
[CrossRef]

IEEE Trans. Antennas Propag.

A.-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by a system of multilayered dielectric spheres,” IEEE Trans. Antennas Propag. 41, 172–175 (1992).

M. A. Morgan, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

J. Am. Ceram. Soc.

E. S. Thiele, R. H. French, “Light-scattering properties of representative, morphological rutile titania particles studied using a finite-element method,” J. Am. Ceram. Soc. 81, 469–479 (1998).
[CrossRef]

J. Coat. Technol.

S. Fitzwater, J. W. Hook, “Dependent scattering theory: a new approach to predicting scattering in paints,” J. Coat. Technol. 57, 39–47 (1985).

J. Mod. Opt.

B. Stout, J. C. Auger, J. Lafait, “A transfer matrix approach to local field calculations in multiple scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

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

J. Phys.: Condens. Matter

A. Rahmani, C. Benoit, R. Jullien, G. Poussigue, A. Sakout, “Light scattering in fractals with scalar and bond-bending models,” J. Phys.: Condens. Matter 9, 2149–2164 (1997).

J. Quant. Spectrosc. Radiat. Transf.

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transf. 56, 591–607 (1996).
[CrossRef]

J. C. Auger, R. G. Barrera, B. Stout, “Scattering efficiencies of aggregates of spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 521–531 (2003).
[CrossRef]

R. Botet, P. Rannou, “Optical anisotropy of an ensemble of aligned fractal aggregates,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 569–576 (2003).
[CrossRef]

J. C. Auger, B. Stout, “A recursive T-matrix algorithm to solve the multiple scattering equation: numerical validation,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 533–547 (2003).
[CrossRef]

Philos. Mag.

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag., 1881, pp. 12–81.

Phys. Rev. D

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

Planet. Space Sci.

P. Rannou, C. P. McKay, R. Botet, M. Cabane, “Semi-empirical model of absorption and scattering by isotropic fractal aggregates of sphere,” Planet. Space Sci. 47, 385–396 (1999).
[CrossRef]

Proc. IEEE

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Q. Appl. Math.

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

Other

R. Julien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, 1987).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

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Figures (9)

Fig. 1
Fig. 1

Aggregate composed of 21 spheres generated from the RLPCA process.

Fig. 2
Fig. 2

Aggregate composed of 21 spheres generated from the DLCCA process.

Fig. 3
Fig. 3

OASCS C sca as a function of 1000 different configurations. The aggregates are composed of 12 spheres of radius r s = 0.132 μ m generated from the RLPCA process with index of refraction n s = 1.5 embedded in water with index of refraction n m = 1.33 . The wavelength of the incident radiation is 0.546 μ m .

Fig. 4
Fig. 4

Histogram constructed from the values of Fig. 3, where the occupation frequency is plotted as a function of C sca and fitted with a Gaussian probability function.

Fig. 5
Fig. 5

Gaussian adjustments for the 6-, 9-, 12-, 15-, 18-, and 21-sphere clusters of rutile titanium dioxide ( n s = 2.8 ) in a polymer resin ( n m = 1.5 ) for 1000 different configurations. The solid and dashed curves indicate aggregates generated from the DLCCA and RLPCA, respectively. The radii of the spheres are equal to (a) 0.040 μ m , (b) 0.080 μ m , and (c) 0.132 μ m .

Fig. 6
Fig. 6

(a) Variation of C ext c as a function of the number of particles for the (a) RLPCA, (b) DLCCA, and (c) linear chain with respective fractal dimensions of 3.0, 1.8, and 1.0, together with the value of C ext c in the case of isolated scatterers (d) for a cluster of rutile titanium dioxide particles in a polymer resin. The radius of the constituent spheres is r s = 0.04 μ m . (b) Same as (a) but for r s = 0.08 μ m . (c) Same as (a) but for r s = 0.132 μ m .

Fig. 7
Fig. 7

(a) Variation of C ext c as a function of the number of particles for the (a) RLPCA, (b) DLCCA, and (c) linear chain with respective fractal dimensions of 3.0, 1.8, and 1.0, together with the value of C ext c in the case of isolated scatterers (d) for a cluster of latex particles in water. The radius of the constituent spheres is r s = 0.04 μ m . (b) Same as (a) but for r s = 0.132 μ m .

Fig. 8
Fig. 8

Transition radius R T as a function of relative refraction index N re for a polymer resin host medium ( n m = 1.5 ) and a wavelength of 0.546 μ m .

Fig. 9
Fig. 9

Variation of C sca N as a function of the number of particles for the (a) RLPCA, (b) DLCCA, and (c) linear chain with respective fractal dimensions of 3.0, 1.8, and 1.0, together with the value of C sca N of isolated scatterers (d) for clusters of rutile titanium dioxide particles in water. The radius of the constituent spheres is r s = 0.132 μ m .

Tables (2)

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Table 1 Normalized Size of the Overlapping Areas for RLPCA and DLPCA Clusters

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Table 2 Adjustment Coefficients Given by the Power Law Functions

Equations (7)

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T ¯ i ( N ) = T ¯ i ( 1 ) [ I ¯ + j = 1 j i N H ¯ ( i , j ) T ¯ j ( N ) J ¯ ( j , i ) ] , i = 1 , , N ,
T ¯ i ( N ) = j = 1 j = N τ ¯ N ( i , j ) J ¯ ( j , i ) .
C ext = 2 π k 0 2 Tr i = 1 N j = 1 N τ ¯ N ( i , j ) J ¯ ( j , i ) ,
τ ¯ N ( N , N ) = [ I ¯ T ¯ N ( 1 ) i = 1 i = N 1 H ¯ ( N , i ) j = 1 j = N 1 τ ¯ N 1 ( i , j ) H ¯ ( j , N ) ] 1 T ¯ N ( 1 ) ,
τ ¯ N ( N , j ) = τ ¯ N ( N , N ) i = 1 i = N 1 H ¯ ( N , i ) τ ¯ N 1 ( i , j ) , j N ,
τ ¯ N ( k , i ) = τ ¯ N 1 ( k , i ) + j = 1 j = N 1 τ ¯ N 1 ( k , j ) H ¯ ( j , N ) τ ¯ N ( N , i ) , i N ,
τ ¯ N ( k , N ) = j = 1 j = N 1 τ ¯ N 1 ( k , j ) H ¯ ( j , N ) τ ¯ N ( N , N ) , i = N .

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