Abstract

We present a numerical investigation of the light scattering in an absorbing medium with randomly distributed scatterers. The extinction coefficient is derived from an ensemble of numerical solutions of Maxwell’s equations for many different realizations of the system. Results are in good agreement with the predictions given by the effective medium theory under the independent-scattering approximation. Beyond the independent-scattering approximation, we explore the domain of validity of an effective medium theory that takes into account correlations between pairs of scatterers. A good agreement is obtained with a filling ratio up to 30% for scatterers with a relative refractive index contrast lower than 20% and size parameters near unity.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S.Chandrasekhar, Radiative Transfer (Dover, 1960).
  2. K.M.Case and P.F.Zweifel, Linear Transport Theory (Addison-Wesley, 1967).
  3. A.Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vols. I and II.
  4. L.Apresyan and Y.Kravtsov, Radiation Transfer, Statistical and Wave Aspects (Gordon and Breach, 1996).
  5. G.E.Thomas and K.Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, 1999).
    [CrossRef]
  6. L.Tsang, J.A.Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Theories and Applications (Wiley, 2000).
    [CrossRef]
  7. P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 10, 505-509 (1957).
  8. P. W. Anderson, "The question of classical localization: a theory of white paint?" Philos. Mag. B 52, 505-509 (1985).
    [CrossRef]
  9. S. Durant, O. Calvo-Perez, N. Vukadinovic, and J.-J. Greffet, "Light scattering by a random distribution of particles embedded in absorbing media: diagrammatic expansion of the extinction coefficient," J. Opt. Soc. Am. A 24, 2943-2952 (2007).
    [CrossRef]
  10. W. C. Mundy, J. A. Roux, and A. M. Smith, "Mie scattering by spheres in an absorbing medium," J. Opt. Soc. Am. 64, 1593-1597 (1974).
    [CrossRef]
  11. P. Chylek, "Light scattering by small particles in an absorbing medium," J. Opt. Soc. Am. 67, 561-563 (1977).
    [CrossRef]
  12. P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium," Waves Random Media 3, 147-156 (1993).
    [CrossRef]
  13. G. Fardella and S. Berthier, "Infrared emissivity of inhomogeneous media," Physica A 207, 346-351 (1994).
    [CrossRef]
  14. M. Quinten and J. Rostalski, "Lorenz-Mie theory for spheres immersed in an absorbing host medium," Part. Part. Syst. Charact. 13, 89-96 (1996).
    [CrossRef]
  15. A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, "Optical extinction by spherical particles in an absorbing media: application to composite absorbing films," Eur. Phys. J. D 6, 365-373 (1999).
    [CrossRef]
  16. A. N. Lebedev and O. Stenzel, "Optical extinction of an assembly of spherical particles in an absorbing medium: application to silver cluster in absorbing organic materials," Eur. Phys. J. D 7, 83-88 (1999).
    [CrossRef]
  17. Q. Fu and W. Sun, "Mie theory for light scattering by a spherical particle in an absorbing medium," Appl. Opt. 40, 1354-1361 (2001).
    [CrossRef]
  18. I. W. Sudiarta and P. Chylek, "Mie-scattering formalism for spherical particles embedded in an absorbing medium," J. Opt. Soc. Am. A 18, 1275-1278 (2001).
    [CrossRef]
  19. I. W. Sudiarta and P. Chylek, "Mie scattering efficiency of a large spherical particle embedded in an absorbing medium," J. Quant. Spectrosc. Radiat. Transf. 70, 709-714 (2001).
    [CrossRef]
  20. P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, and S. K. Park, "Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium," Appl. Opt. 41, 2740-2759 (2002).
    [CrossRef] [PubMed]
  21. G. Videen and W. Sun, "Yet another look at light scattering from particles in absorbing media," Appl. Opt. 42, 6724-6727 (2003).
    [CrossRef] [PubMed]
  22. C. F. Bohren and D. P. Gilra, "Extinction by a spherical particle in an absorbing medium," J. Colloid Interface Sci. 72, 215-221 (1979).
    [CrossRef]
  23. L. Foldy, "General theory of isotropic scattering by randomly distributed scatterers," Phys. Rev. 67, 107-119 (1945).
    [CrossRef]
  24. M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951).
    [CrossRef]
  25. J. B. Keller, "Stochastic equation and wave propagation in random media," Proc. Symp. Appl. Math. 13, 145-170 (1964).
  26. U.Frisch, "Wave propagation in random media," in Probabilistic Methods in Applied Mathematics, A.T.Bharuch-Reid, ed. (Academic, 1968), Vol. 1, pp. 75-198.
  27. V. Twersky, "On propagation in random media of discrete scatterers," Proc. Am. Math. Soc. 16, 84-116 (1964).
  28. P.Sheng, Introduction to Wave Scattering Localization and Mesoscopic Phenomena (Academic, 1995).
  29. L.Tsang and J.A.Kong, Scattering of Electromagnetic Waves, Volume II: Advanced Topics (Wiley, 2001).
    [CrossRef]
  30. S. Durant, "Propagation de la lumière en milieu aléatoire. Rôle de l'absorption, de la diffusion dépendante et du couplage surface-volume," Ph.D. thesis (Ecole Centrale Paris, 2003).
  31. V. A. Loiko, V. P. Dick, and A. P. Ivanov, "Features in coherent transmittance of a monolayer of particles," J. Opt. Soc. Am. A 17, 2040-2045 (2000).
    [CrossRef]
  32. C.F.Bohren and D.R.Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  33. V. A. Loiko and A. Miskevich, "The adding method for coherent transmittance and reflectance of a densely packed layer," J. Quant. Spectrosc. Radiat. Transf. 88, 125-138 (2004).
    [CrossRef]
  34. V. A. Loiko and A. Miskevich, "Light propagation through a monolayer of discrete scatterers: analysis of coherent transmission and reflection coefficients," Appl. Opt. 44, 3759-3768 (2005).
    [CrossRef] [PubMed]
  35. V. A. Loiko, V. P. Dick, and A. P. Ivanov, "Passage of light through a dispersion medium with a high concentration of discrete inhomogeneities: experiment," Appl. Opt. 38, 2640-2646 (1999).
    [CrossRef]
  36. Y. Kuga, F. T. Ulaby, T. F. Haddock, and R. D. DeRoo, "Millimeter-wave radar scattering from snow. 1. Radiative transfer model," Radio Sci. 26, 329-341 (1991).
    [CrossRef]
  37. L. Tsang, C. E. Mandt, and K. H. Ding, "Monte Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell's equations," Opt. Lett. 17, 314-316 (1992).
    [CrossRef] [PubMed]
  38. L. M. Zurk, L. Tsang, K. H. Ding, and D. P. Winebrenner, "Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries," J. Opt. Soc. Am. A 12, 1772-1781 (1995).
    [CrossRef]
  39. K. Sarabandi and P. R. Siqueira, "Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity," IEEE Trans. Antennas Propag. 45, 858-867 (1997).
    [CrossRef]
  40. L. Tsang, K. H. Ding, S. E. Shih, and J. A. Kong, "Scattering of electromagnetic waves from dense distribution of spheroidal particles based on Monte Carlo simulations," J. Opt. Soc. Am. A 15, 2660-2669 (1998).
    [CrossRef]
  41. P. R. Siqueira and K. Sarabandi, "Method of moments evaluation of the two-dimensional quasi-crystalline approximation," IEEE Trans. Antennas Propag. 44, 1067-1077 (2000).
    [CrossRef]
  42. P. R. Siqueira and K. Sarabandi, "T-matrix determination of effective permittivity for three-dimensional dense random media," IEEE Trans. Antennas Propag. 48, 317-327 (2000).
    [CrossRef]
  43. P. Mallet, C. A. Guerin, and A. Sentenac, "Maxwell-Garnett mixing rule in the presence of multiple scattering: derivation and accuracy," Phys. Rev. B 72, 014205 (2005).
    [CrossRef]
  44. C. A. Guerin, P. Mallet, and A. Sentenac, "Effective-medium theory for finite-size aggregates," J. Opt. Soc. Am. A 23, 349-358 (2006).
    [CrossRef]
  45. R. West, D. Gibbs, L. Tsang, and A. K. Fung, "Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media," J. Opt. Soc. Am. A , 11, 1854-1858 (1994).
    [CrossRef]
  46. A. Nashashibi and K. Sarabandi, "Experimental characterization of the effective propagation constant of dense random media," IEEE Trans. Antennas Propag. 47, 1454-1462 (1999).
    [CrossRef]
  47. L. Hespel, S. Mainguy, and J. J. Greffet, "Theoretical and experimental investigation of the extinction in a dense distribution of particles: nonlocal effects," J. Opt. Soc. Am. A 18, 3072-3076 (2001).
    [CrossRef]
  48. A. Derode, V. Mamou, and A. Tourin, "Influence of correlations between scatterers on the attenuation of the coherent wave in a random media," Phys. Rev. E 74, 036606 (2006).
    [CrossRef]
  49. L. Dombrovsky, J. Randrianalisoa, and D. Baillis, "Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements," J. Opt. Soc. Am. A 23, 91-98 (2006).
    [CrossRef]
  50. J. Randrianalisoa, D. Baillis, and L. Pilon, "Improved inverse method for radiative characteristics of closed-cell absorbing porous media," J. Thermophys. Heat Transfer 20, 871-883 (2006).
    [CrossRef]
  51. JohnsonJ. H.Wang, Generalized Moment Methods in Electromagnetics: Formulation and Computer Solution of Integral Equations (Wiley-Interscience, 1991).
    [PubMed]
  52. L. Roux, P. Mareschal, N. Vukadinovic, J.-B. Thibaud, and J.-J. Greffet, "Scattering by a slab containing randomly located cylinders: comparison between radiative transfer and electromagnetic simulation," J. Opt. Soc. Am. A 18, 374-384 (2001).
    [CrossRef]
  53. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  54. W. Wiscombe, "Improved Mie scattering algorithms," Appl. Opt. 19, 1505-1509 (1980).
    [CrossRef] [PubMed]
  55. J. K. Percus and G. J. Yevick, "Analysis of classical statistical mechanics by means of collective coordinates," Phys. Rev. 110, 1-13 (1958).
    [CrossRef]
  56. J. Randrianalisoa, D. Baillis, and L. Pilon, "Modeling radiation characteristics of semitransparent media containing bubbles or particles," J. Opt. Soc. Am. A 23, 1645-1656 (2006).
    [CrossRef]
  57. J. Yin and L. Pilon, "Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium," J. Opt. Soc. Am. A 23, 2784-2796 (2006).
    [CrossRef]

2007

2006

2005

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

V. A. Loiko and A. Miskevich, "Light propagation through a monolayer of discrete scatterers: analysis of coherent transmission and reflection coefficients," Appl. Opt. 44, 3759-3768 (2005).
[CrossRef] [PubMed]

2004

V. A. Loiko and A. Miskevich, "The adding method for coherent transmittance and reflectance of a densely packed layer," J. Quant. Spectrosc. Radiat. Transf. 88, 125-138 (2004).
[CrossRef]

2003

2002

2001

2000

P. R. Siqueira and K. Sarabandi, "Method of moments evaluation of the two-dimensional quasi-crystalline approximation," IEEE Trans. Antennas Propag. 44, 1067-1077 (2000).
[CrossRef]

P. R. Siqueira and K. Sarabandi, "T-matrix determination of effective permittivity for three-dimensional dense random media," IEEE Trans. Antennas Propag. 48, 317-327 (2000).
[CrossRef]

V. A. Loiko, V. P. Dick, and A. P. Ivanov, "Features in coherent transmittance of a monolayer of particles," J. Opt. Soc. Am. A 17, 2040-2045 (2000).
[CrossRef]

1999

V. A. Loiko, V. P. Dick, and A. P. Ivanov, "Passage of light through a dispersion medium with a high concentration of discrete inhomogeneities: experiment," Appl. Opt. 38, 2640-2646 (1999).
[CrossRef]

A. Nashashibi and K. Sarabandi, "Experimental characterization of the effective propagation constant of dense random media," IEEE Trans. Antennas Propag. 47, 1454-1462 (1999).
[CrossRef]

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, "Optical extinction by spherical particles in an absorbing media: application to composite absorbing films," Eur. Phys. J. D 6, 365-373 (1999).
[CrossRef]

A. N. Lebedev and O. Stenzel, "Optical extinction of an assembly of spherical particles in an absorbing medium: application to silver cluster in absorbing organic materials," Eur. Phys. J. D 7, 83-88 (1999).
[CrossRef]

1998

1997

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

K. Sarabandi and P. R. Siqueira, "Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity," IEEE Trans. Antennas Propag. 45, 858-867 (1997).
[CrossRef]

1996

M. Quinten and J. Rostalski, "Lorenz-Mie theory for spheres immersed in an absorbing host medium," Part. Part. Syst. Charact. 13, 89-96 (1996).
[CrossRef]

1995

1994

1993

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium," Waves Random Media 3, 147-156 (1993).
[CrossRef]

1992

1991

Y. Kuga, F. T. Ulaby, T. F. Haddock, and R. D. DeRoo, "Millimeter-wave radar scattering from snow. 1. Radiative transfer model," Radio Sci. 26, 329-341 (1991).
[CrossRef]

1985

P. W. Anderson, "The question of classical localization: a theory of white paint?" Philos. Mag. B 52, 505-509 (1985).
[CrossRef]

1980

1979

C. F. Bohren and D. P. Gilra, "Extinction by a spherical particle in an absorbing medium," J. Colloid Interface Sci. 72, 215-221 (1979).
[CrossRef]

1977

1974

1964

J. B. Keller, "Stochastic equation and wave propagation in random media," Proc. Symp. Appl. Math. 13, 145-170 (1964).

V. Twersky, "On propagation in random media of discrete scatterers," Proc. Am. Math. Soc. 16, 84-116 (1964).

1958

J. K. Percus and G. J. Yevick, "Analysis of classical statistical mechanics by means of collective coordinates," Phys. Rev. 110, 1-13 (1958).
[CrossRef]

1957

P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 10, 505-509 (1957).

1951

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951).
[CrossRef]

1945

L. Foldy, "General theory of isotropic scattering by randomly distributed scatterers," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

Anderson, P. W.

P. W. Anderson, "The question of classical localization: a theory of white paint?" Philos. Mag. B 52, 505-509 (1985).
[CrossRef]

P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 10, 505-509 (1957).

Baillis, D.

Baum, B. A.

Berthier, S.

G. Fardella and S. Berthier, "Infrared emissivity of inhomogeneous media," Physica A 207, 346-351 (1994).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. P. Gilra, "Extinction by a spherical particle in an absorbing medium," J. Colloid Interface Sci. 72, 215-221 (1979).
[CrossRef]

Bruscaglioni, P.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium," Waves Random Media 3, 147-156 (1993).
[CrossRef]

Calvo-Perez, O.

Chylek, P.

Derode, A.

A. Derode, V. Mamou, and A. Tourin, "Influence of correlations between scatterers on the attenuation of the coherent wave in a random media," Phys. Rev. E 74, 036606 (2006).
[CrossRef]

DeRoo, R. D.

Y. Kuga, F. T. Ulaby, T. F. Haddock, and R. D. DeRoo, "Millimeter-wave radar scattering from snow. 1. Radiative transfer model," Radio Sci. 26, 329-341 (1991).
[CrossRef]

Dick, V. P.

Ding, K. H.

Dombrovsky, L.

Durant, S.

S. Durant, O. Calvo-Perez, N. Vukadinovic, and J.-J. Greffet, "Light scattering by a random distribution of particles embedded in absorbing media: diagrammatic expansion of the extinction coefficient," J. Opt. Soc. Am. A 24, 2943-2952 (2007).
[CrossRef]

S. Durant, "Propagation de la lumière en milieu aléatoire. Rôle de l'absorption, de la diffusion dépendante et du couplage surface-volume," Ph.D. thesis (Ecole Centrale Paris, 2003).

Fardella, G.

G. Fardella and S. Berthier, "Infrared emissivity of inhomogeneous media," Physica A 207, 346-351 (1994).
[CrossRef]

Foldy, L.

L. Foldy, "General theory of isotropic scattering by randomly distributed scatterers," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

Fu, Q.

Fung, A. K.

Gao, B.-C.

Gartz, M.

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, "Optical extinction by spherical particles in an absorbing media: application to composite absorbing films," Eur. Phys. J. D 6, 365-373 (1999).
[CrossRef]

Gibbs, D.

Gilra, D. P.

C. F. Bohren and D. P. Gilra, "Extinction by a spherical particle in an absorbing medium," J. Colloid Interface Sci. 72, 215-221 (1979).
[CrossRef]

Greffet, J. J.

Greffet, J.-J.

Guerin, C. A.

C. A. Guerin, P. Mallet, and A. Sentenac, "Effective-medium theory for finite-size aggregates," J. Opt. Soc. Am. A 23, 349-358 (2006).
[CrossRef]

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

Haddock, T. F.

Y. Kuga, F. T. Ulaby, T. F. Haddock, and R. D. DeRoo, "Millimeter-wave radar scattering from snow. 1. Radiative transfer model," Radio Sci. 26, 329-341 (1991).
[CrossRef]

Hespel, L.

Hu, Y. X.

Huang, H.-L.

Ismaelli, A.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium," Waves Random Media 3, 147-156 (1993).
[CrossRef]

Ivanov, A. P.

Keller, J. B.

J. B. Keller, "Stochastic equation and wave propagation in random media," Proc. Symp. Appl. Math. 13, 145-170 (1964).

Kong, J. A.

Kreibig, U.

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, "Optical extinction by spherical particles in an absorbing media: application to composite absorbing films," Eur. Phys. J. D 6, 365-373 (1999).
[CrossRef]

Kuga, Y.

Y. Kuga, F. T. Ulaby, T. F. Haddock, and R. D. DeRoo, "Millimeter-wave radar scattering from snow. 1. Radiative transfer model," Radio Sci. 26, 329-341 (1991).
[CrossRef]

Lax, M.

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951).
[CrossRef]

Lebedev, A. N.

A. N. Lebedev and O. Stenzel, "Optical extinction of an assembly of spherical particles in an absorbing medium: application to silver cluster in absorbing organic materials," Eur. Phys. J. D 7, 83-88 (1999).
[CrossRef]

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, "Optical extinction by spherical particles in an absorbing media: application to composite absorbing films," Eur. Phys. J. D 6, 365-373 (1999).
[CrossRef]

Li, L.

Loiko, V. A.

Mainguy, S.

Mallet, P.

C. A. Guerin, P. Mallet, and A. Sentenac, "Effective-medium theory for finite-size aggregates," J. Opt. Soc. Am. A 23, 349-358 (2006).
[CrossRef]

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

Mamou, V.

A. Derode, V. Mamou, and A. Tourin, "Influence of correlations between scatterers on the attenuation of the coherent wave in a random media," Phys. Rev. E 74, 036606 (2006).
[CrossRef]

Mandt, C. E.

Mareschal, P.

Mishchenko, M. I.

Miskevich, A.

V. A. Loiko and A. Miskevich, "Light propagation through a monolayer of discrete scatterers: analysis of coherent transmission and reflection coefficients," Appl. Opt. 44, 3759-3768 (2005).
[CrossRef] [PubMed]

V. A. Loiko and A. Miskevich, "The adding method for coherent transmittance and reflectance of a densely packed layer," J. Quant. Spectrosc. Radiat. Transf. 88, 125-138 (2004).
[CrossRef]

Mundy, W. C.

Nashashibi, A.

A. Nashashibi and K. Sarabandi, "Experimental characterization of the effective propagation constant of dense random media," IEEE Trans. Antennas Propag. 47, 1454-1462 (1999).
[CrossRef]

Park, S. K.

Percus, J. K.

J. K. Percus and G. J. Yevick, "Analysis of classical statistical mechanics by means of collective coordinates," Phys. Rev. 110, 1-13 (1958).
[CrossRef]

Pilon, L.

Platnick, S. E.

Quinten, M.

M. Quinten and J. Rostalski, "Lorenz-Mie theory for spheres immersed in an absorbing host medium," Part. Part. Syst. Charact. 13, 89-96 (1996).
[CrossRef]

Randrianalisoa, J.

Rostalski, J.

M. Quinten and J. Rostalski, "Lorenz-Mie theory for spheres immersed in an absorbing host medium," Part. Part. Syst. Charact. 13, 89-96 (1996).
[CrossRef]

Roux, J. A.

Roux, L.

Sarabandi, K.

P. R. Siqueira and K. Sarabandi, "Method of moments evaluation of the two-dimensional quasi-crystalline approximation," IEEE Trans. Antennas Propag. 44, 1067-1077 (2000).
[CrossRef]

P. R. Siqueira and K. Sarabandi, "T-matrix determination of effective permittivity for three-dimensional dense random media," IEEE Trans. Antennas Propag. 48, 317-327 (2000).
[CrossRef]

A. Nashashibi and K. Sarabandi, "Experimental characterization of the effective propagation constant of dense random media," IEEE Trans. Antennas Propag. 47, 1454-1462 (1999).
[CrossRef]

K. Sarabandi and P. R. Siqueira, "Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity," IEEE Trans. Antennas Propag. 45, 858-867 (1997).
[CrossRef]

Sentenac, A.

C. A. Guerin, P. Mallet, and A. Sentenac, "Effective-medium theory for finite-size aggregates," J. Opt. Soc. Am. A 23, 349-358 (2006).
[CrossRef]

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

Shih, S. E.

Siqueira, P. R.

P. R. Siqueira and K. Sarabandi, "T-matrix determination of effective permittivity for three-dimensional dense random media," IEEE Trans. Antennas Propag. 48, 317-327 (2000).
[CrossRef]

P. R. Siqueira and K. Sarabandi, "Method of moments evaluation of the two-dimensional quasi-crystalline approximation," IEEE Trans. Antennas Propag. 44, 1067-1077 (2000).
[CrossRef]

K. Sarabandi and P. R. Siqueira, "Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity," IEEE Trans. Antennas Propag. 45, 858-867 (1997).
[CrossRef]

Smith, A. M.

Stenzel, O.

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, "Optical extinction by spherical particles in an absorbing media: application to composite absorbing films," Eur. Phys. J. D 6, 365-373 (1999).
[CrossRef]

A. N. Lebedev and O. Stenzel, "Optical extinction of an assembly of spherical particles in an absorbing medium: application to silver cluster in absorbing organic materials," Eur. Phys. J. D 7, 83-88 (1999).
[CrossRef]

Sudiarta, I. W.

I. W. Sudiarta and P. Chylek, "Mie-scattering formalism for spherical particles embedded in an absorbing medium," J. Opt. Soc. Am. A 18, 1275-1278 (2001).
[CrossRef]

I. W. Sudiarta and P. Chylek, "Mie scattering efficiency of a large spherical particle embedded in an absorbing medium," J. Quant. Spectrosc. Radiat. Transf. 70, 709-714 (2001).
[CrossRef]

Sun, W.

Thibaud, J.-B.

Tourin, A.

A. Derode, V. Mamou, and A. Tourin, "Influence of correlations between scatterers on the attenuation of the coherent wave in a random media," Phys. Rev. E 74, 036606 (2006).
[CrossRef]

Tsang, L.

Tsay, S.-C.

Twersky, V.

V. Twersky, "On propagation in random media of discrete scatterers," Proc. Am. Math. Soc. 16, 84-116 (1964).

Ulaby, F. T.

Y. Kuga, F. T. Ulaby, T. F. Haddock, and R. D. DeRoo, "Millimeter-wave radar scattering from snow. 1. Radiative transfer model," Radio Sci. 26, 329-341 (1991).
[CrossRef]

Videen, G.

Vukadinovic, N.

West, R.

Winebrenner, D. P.

Winker, D. M.

Wiscombe, W.

Wiscombe, W. J.

Yang, P.

Yevick, G. J.

J. K. Percus and G. J. Yevick, "Analysis of classical statistical mechanics by means of collective coordinates," Phys. Rev. 110, 1-13 (1958).
[CrossRef]

Yin, J.

Zaccanti, G.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium," Waves Random Media 3, 147-156 (1993).
[CrossRef]

Zurk, L. M.

Appl. Opt.

Eur. Phys. J. D

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, "Optical extinction by spherical particles in an absorbing media: application to composite absorbing films," Eur. Phys. J. D 6, 365-373 (1999).
[CrossRef]

A. N. Lebedev and O. Stenzel, "Optical extinction of an assembly of spherical particles in an absorbing medium: application to silver cluster in absorbing organic materials," Eur. Phys. J. D 7, 83-88 (1999).
[CrossRef]

IEEE Trans. Antennas Propag.

P. R. Siqueira and K. Sarabandi, "Method of moments evaluation of the two-dimensional quasi-crystalline approximation," IEEE Trans. Antennas Propag. 44, 1067-1077 (2000).
[CrossRef]

P. R. Siqueira and K. Sarabandi, "T-matrix determination of effective permittivity for three-dimensional dense random media," IEEE Trans. Antennas Propag. 48, 317-327 (2000).
[CrossRef]

K. Sarabandi and P. R. Siqueira, "Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity," IEEE Trans. Antennas Propag. 45, 858-867 (1997).
[CrossRef]

A. Nashashibi and K. Sarabandi, "Experimental characterization of the effective propagation constant of dense random media," IEEE Trans. Antennas Propag. 47, 1454-1462 (1999).
[CrossRef]

J. Colloid Interface Sci.

C. F. Bohren and D. P. Gilra, "Extinction by a spherical particle in an absorbing medium," J. Colloid Interface Sci. 72, 215-221 (1979).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

V. A. Loiko, V. P. Dick, and A. P. Ivanov, "Features in coherent transmittance of a monolayer of particles," J. Opt. Soc. Am. A 17, 2040-2045 (2000).
[CrossRef]

L. Roux, P. Mareschal, N. Vukadinovic, J.-B. Thibaud, and J.-J. Greffet, "Scattering by a slab containing randomly located cylinders: comparison between radiative transfer and electromagnetic simulation," J. Opt. Soc. Am. A 18, 374-384 (2001).
[CrossRef]

I. W. Sudiarta and P. Chylek, "Mie-scattering formalism for spherical particles embedded in an absorbing medium," J. Opt. Soc. Am. A 18, 1275-1278 (2001).
[CrossRef]

L. Hespel, S. Mainguy, and J. J. Greffet, "Theoretical and experimental investigation of the extinction in a dense distribution of particles: nonlocal effects," J. Opt. Soc. Am. A 18, 3072-3076 (2001).
[CrossRef]

L. M. Zurk, L. Tsang, K. H. Ding, and D. P. Winebrenner, "Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries," J. Opt. Soc. Am. A 12, 1772-1781 (1995).
[CrossRef]

L. Dombrovsky, J. Randrianalisoa, and D. Baillis, "Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements," J. Opt. Soc. Am. A 23, 91-98 (2006).
[CrossRef]

C. A. Guerin, P. Mallet, and A. Sentenac, "Effective-medium theory for finite-size aggregates," J. Opt. Soc. Am. A 23, 349-358 (2006).
[CrossRef]

J. Randrianalisoa, D. Baillis, and L. Pilon, "Modeling radiation characteristics of semitransparent media containing bubbles or particles," J. Opt. Soc. Am. A 23, 1645-1656 (2006).
[CrossRef]

J. Yin and L. Pilon, "Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium," J. Opt. Soc. Am. A 23, 2784-2796 (2006).
[CrossRef]

S. Durant, O. Calvo-Perez, N. Vukadinovic, and J.-J. Greffet, "Light scattering by a random distribution of particles embedded in absorbing media: diagrammatic expansion of the extinction coefficient," J. Opt. Soc. Am. A 24, 2943-2952 (2007).
[CrossRef]

R. West, D. Gibbs, L. Tsang, and A. K. Fung, "Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media," J. Opt. Soc. Am. A , 11, 1854-1858 (1994).
[CrossRef]

L. Tsang, K. H. Ding, S. E. Shih, and J. A. Kong, "Scattering of electromagnetic waves from dense distribution of spheroidal particles based on Monte Carlo simulations," J. Opt. Soc. Am. A 15, 2660-2669 (1998).
[CrossRef]

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf.

V. A. Loiko and A. Miskevich, "The adding method for coherent transmittance and reflectance of a densely packed layer," J. Quant. Spectrosc. Radiat. Transf. 88, 125-138 (2004).
[CrossRef]

I. W. Sudiarta and P. Chylek, "Mie scattering efficiency of a large spherical particle embedded in an absorbing medium," J. Quant. Spectrosc. Radiat. Transf. 70, 709-714 (2001).
[CrossRef]

J. Thermophys. Heat Transfer

J. Randrianalisoa, D. Baillis, and L. Pilon, "Improved inverse method for radiative characteristics of closed-cell absorbing porous media," J. Thermophys. Heat Transfer 20, 871-883 (2006).
[CrossRef]

Opt. Lett.

Part. Part. Syst. Charact.

M. Quinten and J. Rostalski, "Lorenz-Mie theory for spheres immersed in an absorbing host medium," Part. Part. Syst. Charact. 13, 89-96 (1996).
[CrossRef]

Philos. Mag. B

P. W. Anderson, "The question of classical localization: a theory of white paint?" Philos. Mag. B 52, 505-509 (1985).
[CrossRef]

Phys. Rev.

P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 10, 505-509 (1957).

L. Foldy, "General theory of isotropic scattering by randomly distributed scatterers," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

J. K. Percus and G. J. Yevick, "Analysis of classical statistical mechanics by means of collective coordinates," Phys. Rev. 110, 1-13 (1958).
[CrossRef]

Phys. Rev. B

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

Phys. Rev. E

A. Derode, V. Mamou, and A. Tourin, "Influence of correlations between scatterers on the attenuation of the coherent wave in a random media," Phys. Rev. E 74, 036606 (2006).
[CrossRef]

Physica A

G. Fardella and S. Berthier, "Infrared emissivity of inhomogeneous media," Physica A 207, 346-351 (1994).
[CrossRef]

Proc. Am. Math. Soc.

V. Twersky, "On propagation in random media of discrete scatterers," Proc. Am. Math. Soc. 16, 84-116 (1964).

Proc. Symp. Appl. Math.

J. B. Keller, "Stochastic equation and wave propagation in random media," Proc. Symp. Appl. Math. 13, 145-170 (1964).

Radio Sci.

Y. Kuga, F. T. Ulaby, T. F. Haddock, and R. D. DeRoo, "Millimeter-wave radar scattering from snow. 1. Radiative transfer model," Radio Sci. 26, 329-341 (1991).
[CrossRef]

Rev. Mod. Phys.

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951).
[CrossRef]

Waves Random Media

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium," Waves Random Media 3, 147-156 (1993).
[CrossRef]

Other

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

K.M.Case and P.F.Zweifel, Linear Transport Theory (Addison-Wesley, 1967).

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

L.Apresyan and Y.Kravtsov, Radiation Transfer, Statistical and Wave Aspects (Gordon and Breach, 1996).

G.E.Thomas and K.Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, 1999).
[CrossRef]

L.Tsang, J.A.Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Theories and Applications (Wiley, 2000).
[CrossRef]

P.Sheng, Introduction to Wave Scattering Localization and Mesoscopic Phenomena (Academic, 1995).

L.Tsang and J.A.Kong, Scattering of Electromagnetic Waves, Volume II: Advanced Topics (Wiley, 2001).
[CrossRef]

S. Durant, "Propagation de la lumière en milieu aléatoire. Rôle de l'absorption, de la diffusion dépendante et du couplage surface-volume," Ph.D. thesis (Ecole Centrale Paris, 2003).

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

U.Frisch, "Wave propagation in random media," in Probabilistic Methods in Applied Mathematics, A.T.Bharuch-Reid, ed. (Academic, 1968), Vol. 1, pp. 75-198.

JohnsonJ. H.Wang, Generalized Moment Methods in Electromagnetics: Formulation and Computer Solution of Integral Equations (Wiley-Interscience, 1991).
[PubMed]

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 (6)

Fig. 1
Fig. 1

Two-dimensional geometry that was investigated. The slab of thickness e is filled by a random distribution of an infinitely long cylinder with a circular section with a radius a, with an index n p embedded into an absorbing medium, and with an index n h . For each realization, Maxwell’s equations were solved from a method of moments with periodic boundary conditions with a period L λ 0 and the statistical average E of the electric field was computed. The resulting effective geometry as seen by the mean field is shown on the right.

Fig. 2
Fig. 2

Pair-correlation function g 2 as a function of the distance between the particles’ center R normalized by their radius a at several filling ratios f. The two top panels consider a distribution of spherical particles. The pair-correlation function computed with either the PY model or the Monte Carlo simulation yields essentially the same results. The bottom panel is the result for the 2D random distribution of cylinders computed with a Monte Carlo simulation that can be implemented very conveniently. The results give g 2 = 1 for R < 2 a because only the case of hard particles that do not overlap are considered in this study.

Fig. 3
Fig. 3

Ratio between the extinction coefficient computed from the nonlocal EMT, including correlations between pairs of particles ( K e x t 2 ) , and that computed from EMT under independent-scattering approximation ( K e x t 1 ) . (a), (b) Numerical results without absorption [ I m ( n h ) = 0 ] ; (c), (d) results with absorbing host medium I m ( n h ) = 0.02 . The index of particles and the host medium are, respectively, n p = 1.59 and R e ( n h ) = 1.33 .

Fig. 4
Fig. 4

Monte Carlo rigorous solution of the imaginary part of the effective index, equivalent to the extinction coefficient, is plotted as a function of the filling ratio f with the following parameters: The real part of the host medium index is R e ( n h ) = 1.46 , the index of particles is n p = 2.21 , and the radius is a = 0.3 λ 0 . The case of nonabsorbing host medium is reported in (a) I m ( n h ) = 0 . Results for the absorbing [ I m ( n h ) = 0.03 ] and highly absorbing [ I m ( n h ) = 0.1 ] host media are reported in (b) and (c), respectively. Exact results are compared with EMT, nonlocal EMT (dependent scattering), and Kuga’s model.

Fig. 5
Fig. 5

Monte Carlo rigorous solution of the imaginary part of the effective index, equivalent to the extinction coefficient, is plotted as a function of the filling ratio f with parameters described in the inset of each panel. Exact results are compared with the EMT, nonlocal EMT (dependent scattering), and Kuga’s model.

Fig. 6
Fig. 6

Imaginary part of the effective index as a function of (a), (c) the size parameter X = R e ( k h a ) or (b), (d) the filling ratio f. Results are computed from our model, referred by EMT under independent-scattering approximation, and are compared with the Kuga et al. and Yang et al. formulations.

Equations (9)

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

K e x t = 2 I m ( k e f f ) .
k 2 = k h 2 + i f v p 4 π S k h ( 0 ) k h ,
k 2 = k h 2 + i f v p 4 π S k h ( 0 ) k h + ( i f v p 4 π S k h ( 0 ) k h ) 2 1 k 0 e i k h r sin ( k r ) g 2 ( r ) d r ,
k 2 = k 0 2 n e f f 2 ( ω , k ) ,
K e x t = 2 k 0 I m ( n h ) ( 1 f ) + f v p C e x t ,
K e x t = 2 k 0 I m ( n h ) + f v p ( C a b s + e 2 I m ( n h ) k 0 a C s c a , a ) ,
k 2 = k h 2 + i f s p 4 S k h 2 D ( 0 ) ,
k 2 = k h 2 + i f s p 4 S k h 2 D ( 0 ) + ( i f s p 4 S k h 2 D ( 0 ) ) 2 0 i π 2 H 0 ( 1 ) ( k h r ) J 0 ( k r ) r g 2 ( r ) d r .
E = E + δ E ,

Metrics