Abstract

The extinction efficiencies as well as the scattering properties of particles of different porosity are studied. Calculations are performed for porous pseudospheres with small size (Rayleigh) inclusions using the discrete dipole approximation. Five refractive indices of materials covering the range from 1.20+0.00i to 1.75+0.58i were selected. They correspond to biological particles, dirty ice, silicate, and amorphous carbon and soot in the visual part of the spectrum. We attempt to describe the optical properties of such particles using Lorenz–Mie theory and a refractive index found from some effective medium theory (EMT) assuming the particle is homogeneous. We refer to this as the effective model. It is found that the deviations are minimal when utilizing the EMT based on the Bruggeman mixing rule. Usually the deviations in the extinction factor do not exceed 5% for particle porosity P=00.9 and size parameters xporous=2πrs, porous /λ25. The deviations are larger for scattering and absorption efficiencies and smaller for particle albedo and the asymmetry parameter. Our calculations made for spheroids confirm these conclusions. Preliminary consideration shows that the effective model represents the intensity and polarization of radiation scattered by fluffy aggregates quite well. Thus the effective models of spherical and nonspherical particles can be used to significantly simplify the computations of the optical properties of aggregates containing only Rayleigh inclusions.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. I. Mishchenko, J. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles (Academic, 2000).
  2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  3. P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, "Effective medium approximations for heterogeneous particles," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 274-308.
  4. A. H. Sihvola, Electromagnetic Mixing Formulas and Applications (Institute of Electrical Engineers, Electromagnetic Waves Series 47, 1999).
  5. L. Kolokolova and B. Å. S. Gustafson, "Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theory," J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
    [CrossRef]
  6. N. Maron and O. Maron, "On the mixing rules for astrophysical inhomogeneous grains," Mon. Not. R. Astron. Soc. 357, 873-880 (2005).
    [CrossRef]
  7. B. T. Draine, "The discrete dipole approximation for light scattering by irregular targets," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 131-145.
  8. M. Min, C. Dominik, J. W. Hovenier, A. de Koter, and L. B. F. M. Waters, "The 10 μm amorphous silicate feature of fractal aggregates and compact particles with complex shapes," Astron. Astrophys. 445, 1005-1014 (2006).
    [CrossRef]
  9. N. V. Voshchinnikov, V. B. Il'in, and Th. Henning, "Modelling the optical properties of composite and porous interstellar grains," Astron. Astrophys. 429, 371-381 (2005).
    [CrossRef]
  10. B. T. Draine and P. J. Flatau, User Guide for the Discrete Dipole Approximation Code DDSCAT.6.0, astro-ph/0309069, pp. 1-46 (2003).
  11. Th. Henning and R. Stognienko, "Porous grains and polarization: the silicate features," Astron. Astrophys. 280, 609-616 (1993).
  12. K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
    [CrossRef]
  13. M. J. Wolff, G. C. Clayton, P. G. Martin, and R. E. Schulte-Ladbeck, "Modeling composite and fluffy grains: the effects of porosity," Astrophys. J. 423, 412-425 (1994).
    [CrossRef]
  14. A. Doicu and Th. Wriedt, "Equivalent refractive index of a sphere with multiple spherical inclusions," J. Opt. A 3, 204-209 (2001).
    [CrossRef]
  15. P. Mallet, C. A. Guérin, and A. Sentenac, "Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy," Phys. Rev. B 72, 014205-014209 (2005).
    [CrossRef]
  16. M. Kocifaj, M. Gangl, F. Kundracík, H. Horvath, and G. Videen, "Simulation of the optical properties of single composite aerosols," J. Aerosol Sci. 37, 1683-1695 (2006).
    [CrossRef]
  17. Y. Guéguen, M. Le Ravalec, and L. Ricard, "Upscaling: effective medium theory, numerical methods and the fractal dream," Pure Appl. Geophys. 163, 1175-1192 (2006).
    [CrossRef]
  18. N. V. Voshchinnikov, "Optics of Cosmic Dust. I," Astrophys. Space Phys. Rev. 12, 1-182 (2004).
  19. Th. Henning, V. B. Il'in, N. A. Krivova, B. Michel, and N. V. Voshchinnikov, "WWW Database on Optical Constants for Astronomy," Astron. Astrophys. Suppl. sen. 136, 405-406 (1999).
    [CrossRef]
  20. C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
    [CrossRef]
  21. H. Chang and T. T. Charalampopoulos, "Determination of the wavelength dependence of refractive indices of flame soot," Proc. R. Soc. London Sen. A 430, 577-591 (1990).
    [CrossRef]
  22. N. V. Voshchinnikov and V. G. Farafonov, "Optical properties of spheroidal particles," Astrophys. Space Sci. 204, 19-86 (1993).
    [CrossRef]

2006 (3)

M. Min, C. Dominik, J. W. Hovenier, A. de Koter, and L. B. F. M. Waters, "The 10 μm amorphous silicate feature of fractal aggregates and compact particles with complex shapes," Astron. Astrophys. 445, 1005-1014 (2006).
[CrossRef]

M. Kocifaj, M. Gangl, F. Kundracík, H. Horvath, and G. Videen, "Simulation of the optical properties of single composite aerosols," J. Aerosol Sci. 37, 1683-1695 (2006).
[CrossRef]

Y. Guéguen, M. Le Ravalec, and L. Ricard, "Upscaling: effective medium theory, numerical methods and the fractal dream," Pure Appl. Geophys. 163, 1175-1192 (2006).
[CrossRef]

2005 (3)

N. V. Voshchinnikov, V. B. Il'in, and Th. Henning, "Modelling the optical properties of composite and porous interstellar grains," Astron. Astrophys. 429, 371-381 (2005).
[CrossRef]

N. Maron and O. Maron, "On the mixing rules for astrophysical inhomogeneous grains," Mon. Not. R. Astron. Soc. 357, 873-880 (2005).
[CrossRef]

P. Mallet, C. A. Guérin, and A. Sentenac, "Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy," Phys. Rev. B 72, 014205-014209 (2005).
[CrossRef]

2004 (1)

N. V. Voshchinnikov, "Optics of Cosmic Dust. I," Astrophys. Space Phys. Rev. 12, 1-182 (2004).

2003 (1)

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

2001 (2)

A. Doicu and Th. Wriedt, "Equivalent refractive index of a sphere with multiple spherical inclusions," J. Opt. A 3, 204-209 (2001).
[CrossRef]

L. Kolokolova and B. Å. S. Gustafson, "Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theory," J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
[CrossRef]

1999 (1)

Th. Henning, V. B. Il'in, N. A. Krivova, B. Michel, and N. V. Voshchinnikov, "WWW Database on Optical Constants for Astronomy," Astron. Astrophys. Suppl. sen. 136, 405-406 (1999).
[CrossRef]

1994 (2)

K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
[CrossRef]

M. J. Wolff, G. C. Clayton, P. G. Martin, and R. E. Schulte-Ladbeck, "Modeling composite and fluffy grains: the effects of porosity," Astrophys. J. 423, 412-425 (1994).
[CrossRef]

1993 (2)

Th. Henning and R. Stognienko, "Porous grains and polarization: the silicate features," Astron. Astrophys. 280, 609-616 (1993).

N. V. Voshchinnikov and V. G. Farafonov, "Optical properties of spheroidal particles," Astrophys. Space Sci. 204, 19-86 (1993).
[CrossRef]

1990 (1)

H. Chang and T. T. Charalampopoulos, "Determination of the wavelength dependence of refractive indices of flame soot," Proc. R. Soc. London Sen. A 430, 577-591 (1990).
[CrossRef]

Bohren, C. F.

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

Chang, H.

H. Chang and T. T. Charalampopoulos, "Determination of the wavelength dependence of refractive indices of flame soot," Proc. R. Soc. London Sen. A 430, 577-591 (1990).
[CrossRef]

Charalampopoulos, T. T.

H. Chang and T. T. Charalampopoulos, "Determination of the wavelength dependence of refractive indices of flame soot," Proc. R. Soc. London Sen. A 430, 577-591 (1990).
[CrossRef]

Chýlek, P.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, "Effective medium approximations for heterogeneous particles," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 274-308.

Clayton, G. C.

M. J. Wolff, G. C. Clayton, P. G. Martin, and R. E. Schulte-Ladbeck, "Modeling composite and fluffy grains: the effects of porosity," Astrophys. J. 423, 412-425 (1994).
[CrossRef]

de Koter, A.

M. Min, C. Dominik, J. W. Hovenier, A. de Koter, and L. B. F. M. Waters, "The 10 μm amorphous silicate feature of fractal aggregates and compact particles with complex shapes," Astron. Astrophys. 445, 1005-1014 (2006).
[CrossRef]

Dobbie, J. S.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, "Effective medium approximations for heterogeneous particles," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 274-308.

Doicu, A.

A. Doicu and Th. Wriedt, "Equivalent refractive index of a sphere with multiple spherical inclusions," J. Opt. A 3, 204-209 (2001).
[CrossRef]

Dominik, C.

M. Min, C. Dominik, J. W. Hovenier, A. de Koter, and L. B. F. M. Waters, "The 10 μm amorphous silicate feature of fractal aggregates and compact particles with complex shapes," Astron. Astrophys. 445, 1005-1014 (2006).
[CrossRef]

Draine, B. T.

B. T. Draine, "The discrete dipole approximation for light scattering by irregular targets," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 131-145.

B. T. Draine and P. J. Flatau, User Guide for the Discrete Dipole Approximation Code DDSCAT.6.0, astro-ph/0309069, pp. 1-46 (2003).

Fabian, D.

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

Farafonov, V. G.

N. V. Voshchinnikov and V. G. Farafonov, "Optical properties of spheroidal particles," Astrophys. Space Sci. 204, 19-86 (1993).
[CrossRef]

Flatau, P. J.

B. T. Draine and P. J. Flatau, User Guide for the Discrete Dipole Approximation Code DDSCAT.6.0, astro-ph/0309069, pp. 1-46 (2003).

Gangl, M.

M. Kocifaj, M. Gangl, F. Kundracík, H. Horvath, and G. Videen, "Simulation of the optical properties of single composite aerosols," J. Aerosol Sci. 37, 1683-1695 (2006).
[CrossRef]

Geldart, D. J. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, "Effective medium approximations for heterogeneous particles," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 274-308.

Guéguen, Y.

Y. Guéguen, M. Le Ravalec, and L. Ricard, "Upscaling: effective medium theory, numerical methods and the fractal dream," Pure Appl. Geophys. 163, 1175-1192 (2006).
[CrossRef]

Guérin, C. A.

P. Mallet, C. A. Guérin, and A. Sentenac, "Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy," Phys. Rev. B 72, 014205-014209 (2005).
[CrossRef]

Gustafson, B. Å. S.

L. Kolokolova and B. Å. S. Gustafson, "Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theory," J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
[CrossRef]

Henning, T.

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

Henning, Th.

N. V. Voshchinnikov, V. B. Il'in, and Th. Henning, "Modelling the optical properties of composite and porous interstellar grains," Astron. Astrophys. 429, 371-381 (2005).
[CrossRef]

Th. Henning, V. B. Il'in, N. A. Krivova, B. Michel, and N. V. Voshchinnikov, "WWW Database on Optical Constants for Astronomy," Astron. Astrophys. Suppl. sen. 136, 405-406 (1999).
[CrossRef]

Horvath, H.

M. Kocifaj, M. Gangl, F. Kundracík, H. Horvath, and G. Videen, "Simulation of the optical properties of single composite aerosols," J. Aerosol Sci. 37, 1683-1695 (2006).
[CrossRef]

Hovenier, J.

M. I. Mishchenko, J. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles (Academic, 2000).

Hovenier, J. W.

M. Min, C. Dominik, J. W. Hovenier, A. de Koter, and L. B. F. M. Waters, "The 10 μm amorphous silicate feature of fractal aggregates and compact particles with complex shapes," Astron. Astrophys. 445, 1005-1014 (2006).
[CrossRef]

Huffman, D. R.

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

Il'in, V. B.

N. V. Voshchinnikov, V. B. Il'in, and Th. Henning, "Modelling the optical properties of composite and porous interstellar grains," Astron. Astrophys. 429, 371-381 (2005).
[CrossRef]

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

Th. Henning, V. B. Il'in, N. A. Krivova, B. Michel, and N. V. Voshchinnikov, "WWW Database on Optical Constants for Astronomy," Astron. Astrophys. Suppl. sen. 136, 405-406 (1999).
[CrossRef]

Jäger, C.

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

Kocifaj, M.

M. Kocifaj, M. Gangl, F. Kundracík, H. Horvath, and G. Videen, "Simulation of the optical properties of single composite aerosols," J. Aerosol Sci. 37, 1683-1695 (2006).
[CrossRef]

Kolokolova, L.

L. Kolokolova and B. Å. S. Gustafson, "Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theory," J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
[CrossRef]

Krivova, N. A.

Th. Henning, V. B. Il'in, N. A. Krivova, B. Michel, and N. V. Voshchinnikov, "WWW Database on Optical Constants for Astronomy," Astron. Astrophys. Suppl. sen. 136, 405-406 (1999).
[CrossRef]

Kundracík, F.

M. Kocifaj, M. Gangl, F. Kundracík, H. Horvath, and G. Videen, "Simulation of the optical properties of single composite aerosols," J. Aerosol Sci. 37, 1683-1695 (2006).
[CrossRef]

Le Ravalec, M.

Y. Guéguen, M. Le Ravalec, and L. Ricard, "Upscaling: effective medium theory, numerical methods and the fractal dream," Pure Appl. Geophys. 163, 1175-1192 (2006).
[CrossRef]

Lumme, K.

K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
[CrossRef]

Mallet, P.

P. Mallet, C. A. Guérin, and A. Sentenac, "Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy," Phys. Rev. B 72, 014205-014209 (2005).
[CrossRef]

Maron, N.

N. Maron and O. Maron, "On the mixing rules for astrophysical inhomogeneous grains," Mon. Not. R. Astron. Soc. 357, 873-880 (2005).
[CrossRef]

Maron, O.

N. Maron and O. Maron, "On the mixing rules for astrophysical inhomogeneous grains," Mon. Not. R. Astron. Soc. 357, 873-880 (2005).
[CrossRef]

Martin, P. G.

M. J. Wolff, G. C. Clayton, P. G. Martin, and R. E. Schulte-Ladbeck, "Modeling composite and fluffy grains: the effects of porosity," Astrophys. J. 423, 412-425 (1994).
[CrossRef]

Michel, B.

Th. Henning, V. B. Il'in, N. A. Krivova, B. Michel, and N. V. Voshchinnikov, "WWW Database on Optical Constants for Astronomy," Astron. Astrophys. Suppl. sen. 136, 405-406 (1999).
[CrossRef]

Min, M.

M. Min, C. Dominik, J. W. Hovenier, A. de Koter, and L. B. F. M. Waters, "The 10 μm amorphous silicate feature of fractal aggregates and compact particles with complex shapes," Astron. Astrophys. 445, 1005-1014 (2006).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, J. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles (Academic, 2000).

Mutschke, H.

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

Rahola, J.

K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
[CrossRef]

Ricard, L.

Y. Guéguen, M. Le Ravalec, and L. Ricard, "Upscaling: effective medium theory, numerical methods and the fractal dream," Pure Appl. Geophys. 163, 1175-1192 (2006).
[CrossRef]

Schulte-Ladbeck, R. E.

M. J. Wolff, G. C. Clayton, P. G. Martin, and R. E. Schulte-Ladbeck, "Modeling composite and fluffy grains: the effects of porosity," Astrophys. J. 423, 412-425 (1994).
[CrossRef]

Semenov, D. A.

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

Sentenac, A.

P. Mallet, C. A. Guérin, and A. Sentenac, "Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy," Phys. Rev. B 72, 014205-014209 (2005).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, J. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles (Academic, 2000).

Tso, H. C. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, "Effective medium approximations for heterogeneous particles," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 274-308.

Videen, G.

M. Kocifaj, M. Gangl, F. Kundracík, H. Horvath, and G. Videen, "Simulation of the optical properties of single composite aerosols," J. Aerosol Sci. 37, 1683-1695 (2006).
[CrossRef]

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, "Effective medium approximations for heterogeneous particles," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 274-308.

Voshchinnikov, N. V.

N. V. Voshchinnikov, V. B. Il'in, and Th. Henning, "Modelling the optical properties of composite and porous interstellar grains," Astron. Astrophys. 429, 371-381 (2005).
[CrossRef]

N. V. Voshchinnikov, "Optics of Cosmic Dust. I," Astrophys. Space Phys. Rev. 12, 1-182 (2004).

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

Th. Henning, V. B. Il'in, N. A. Krivova, B. Michel, and N. V. Voshchinnikov, "WWW Database on Optical Constants for Astronomy," Astron. Astrophys. Suppl. sen. 136, 405-406 (1999).
[CrossRef]

N. V. Voshchinnikov and V. G. Farafonov, "Optical properties of spheroidal particles," Astrophys. Space Sci. 204, 19-86 (1993).
[CrossRef]

Waters, L. B. F. M.

M. Min, C. Dominik, J. W. Hovenier, A. de Koter, and L. B. F. M. Waters, "The 10 μm amorphous silicate feature of fractal aggregates and compact particles with complex shapes," Astron. Astrophys. 445, 1005-1014 (2006).
[CrossRef]

Wolff, M. J.

M. J. Wolff, G. C. Clayton, P. G. Martin, and R. E. Schulte-Ladbeck, "Modeling composite and fluffy grains: the effects of porosity," Astrophys. J. 423, 412-425 (1994).
[CrossRef]

Wriedt, Th.

A. Doicu and Th. Wriedt, "Equivalent refractive index of a sphere with multiple spherical inclusions," J. Opt. A 3, 204-209 (2001).
[CrossRef]

Astron. Astrophys. (3)

M. Min, C. Dominik, J. W. Hovenier, A. de Koter, and L. B. F. M. Waters, "The 10 μm amorphous silicate feature of fractal aggregates and compact particles with complex shapes," Astron. Astrophys. 445, 1005-1014 (2006).
[CrossRef]

N. V. Voshchinnikov, V. B. Il'in, and Th. Henning, "Modelling the optical properties of composite and porous interstellar grains," Astron. Astrophys. 429, 371-381 (2005).
[CrossRef]

Th. Henning and R. Stognienko, "Porous grains and polarization: the silicate features," Astron. Astrophys. 280, 609-616 (1993).

Astron. Astrophys. Suppl. sen. (1)

Th. Henning, V. B. Il'in, N. A. Krivova, B. Michel, and N. V. Voshchinnikov, "WWW Database on Optical Constants for Astronomy," Astron. Astrophys. Suppl. sen. 136, 405-406 (1999).
[CrossRef]

Astrophys. J. (2)

K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
[CrossRef]

M. J. Wolff, G. C. Clayton, P. G. Martin, and R. E. Schulte-Ladbeck, "Modeling composite and fluffy grains: the effects of porosity," Astrophys. J. 423, 412-425 (1994).
[CrossRef]

Astrophys. Space Phys. Rev. (1)

N. V. Voshchinnikov, "Optics of Cosmic Dust. I," Astrophys. Space Phys. Rev. 12, 1-182 (2004).

Astrophys. Space Sci. (1)

N. V. Voshchinnikov and V. G. Farafonov, "Optical properties of spheroidal particles," Astrophys. Space Sci. 204, 19-86 (1993).
[CrossRef]

J. Aerosol Sci. (1)

M. Kocifaj, M. Gangl, F. Kundracík, H. Horvath, and G. Videen, "Simulation of the optical properties of single composite aerosols," J. Aerosol Sci. 37, 1683-1695 (2006).
[CrossRef]

J. Opt. A (1)

A. Doicu and Th. Wriedt, "Equivalent refractive index of a sphere with multiple spherical inclusions," J. Opt. A 3, 204-209 (2001).
[CrossRef]

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

C. Jäger, V. B. Il'in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, "A database of optical constants of cosmic dust analogs," J. Quant. Spectrosc. Radiat. Transfer 79-80, 765-774 (2003).
[CrossRef]

L. Kolokolova and B. Å. S. Gustafson, "Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theory," J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

N. Maron and O. Maron, "On the mixing rules for astrophysical inhomogeneous grains," Mon. Not. R. Astron. Soc. 357, 873-880 (2005).
[CrossRef]

Phys. Rev. B (1)

P. Mallet, C. A. Guérin, and A. Sentenac, "Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy," Phys. Rev. B 72, 014205-014209 (2005).
[CrossRef]

Proc. R. Soc. London Sen. (1)

H. Chang and T. T. Charalampopoulos, "Determination of the wavelength dependence of refractive indices of flame soot," Proc. R. Soc. London Sen. A 430, 577-591 (1990).
[CrossRef]

Pure Appl. Geophys. (1)

Y. Guéguen, M. Le Ravalec, and L. Ricard, "Upscaling: effective medium theory, numerical methods and the fractal dream," Pure Appl. Geophys. 163, 1175-1192 (2006).
[CrossRef]

Other (6)

B. T. Draine, "The discrete dipole approximation for light scattering by irregular targets," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 131-145.

B. T. Draine and P. J. Flatau, User Guide for the Discrete Dipole Approximation Code DDSCAT.6.0, astro-ph/0309069, pp. 1-46 (2003).

M. I. Mishchenko, J. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles (Academic, 2000).

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

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, "Effective medium approximations for heterogeneous particles," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 274-308.

A. H. Sihvola, Electromagnetic Mixing Formulas and Applications (Institute of Electrical Engineers, Electromagnetic Waves Series 47, 1999).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Size dependence of the extinction efficiency factors calculated for spheres with inclusions of different sizes (DDA computations) and with the Lorenz–Mie theory using the Bruggeman EMT. The refractive index of inclusions is m compact = 1.33 + 0.01 i . The effective refractive indices of porous particles are indicated in Table 3. The porosity of particles is P = 0.33 (upper panel) and P = 0.9 (lower panel). For a given porosity the particles of the same size parameter x porous have the same mass. The effect of variations of the size of inclusions is illustrated.

Fig. 2
Fig. 2

Porosity dependence of the normalized extinction cross sections calculated for spheres with small inclusions (DDA computations) and with the Lorenz–Mie theory using different EMTs ( m compact = 1.33 + 0.010 i ) . The effects of variations of the EMT and particle size are illustrated.

Fig. 3
Fig. 3

Dependence of the relative deviations of the extinction cross sections calculated with the DDA and EMT [see Eq. (4)] on the particle porosity. The particle parameters are the same as in Fig. 2 (middle panel).

Fig. 4
Fig. 4

Porosity dependence of the normalized extinction cross sections calculated for spheres with small inclusions (DDA computations) and with the Lorenz–Mie theory using the three EMTs and two values of m compact . The effect of variations of the EMT and refractive index is illustrated.

Fig. 5
Fig. 5

Size dependence of the extinction efficiency factors (upper panel) calculated for spheres with small inclusions (DDA computations) and with the Lorenz–Mie theory using the Bruggeman EMT. The porosity of the particles is P = 0.33 . The effective refractive indices of the porous particles are indicated in Table 3. The lower panel shows the percent difference between the DDA results and the Bruggeman EMT calculations as defined by Eq. (4). The effect of variations of the refractive indices of the inclusions is illustrated.

Fig. 6
Fig. 6

Same as in Fig. 5 but now for porosity P = 0.9 .

Fig. 7
Fig. 7

Size dependence of the scattering ( Q sca ) and absorption ( Q abs ) efficiency factors, albedo Λ and the asymmetry parameter g for pseudospheres with small inclusions using DDA computations and the Bruggeman effective model. The refractive indices of inclusions are m compact = 1.33 + 0.01 i . The porosity of particles is P = 0.9 .

Fig. 8
Fig. 8

Size dependence of the extinction efficiency factors calculated for prolate spheroids with small inclusions using DDA computations and the Bruggeman effective model. The refractive indices of inclusions are m compact = 1.33 + 0.01 i , and the porosity of particles is P = 0.9 . The effect of variations of the particle shape is illustrated.

Fig. 9
Fig. 9

Intensity and polarization of the scattered radiation calculated for pseudospheres with small inclusions (DDA computations) and effective models (Bruggeman–SVM computations). The refractive indices of the inclusions are m compact = 1.33 + 0.01 i , and the porosity of particles is P = 0.9 .

Tables (3)

Tables Icon

Table 1 Mixing Rules for the Refractive Indices

Tables Icon

Table 2 Effective Refractive Indices m = n + ki of Porous Particles Calculated Using Different EMTs Presented in Fig. 2 a

Tables Icon

Table 3 Effective Refractive Indices m = n + ki of Porous Particles Calculated Using the Bruggeman EMT Presented in Figs. 5 and 6

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

P = V vac / V total = 1 V solid / V total ,
x porous = 2 π r s,porous λ = x compact ( 1 P ) 1 / 3 = x compact ( V solid / V total ) 1 / 3 .
C ( n ) = C ( porous   particle ) C ( compact   particle   of   same   mass )
=  ( 1 P ) 2 / 3 Q ( porous   particle ) Q ( compact   particle   of   same   mass ) .
Deviation = Q ( EMT-Mie ) Q ( DDA ) Q ( DDA ) 100 % .
Λ = Q sca Q ext ,
g = cos   Θ = 4 π F ( Θ , Φ ) cos   Θ d ω 4 π F ( Θ , Φ ) d ω .

Metrics