Abstract

We study theoretically the extinction of collimated light in random systems of highly scattering particles embedded in nonabsorbing media. We aim to provide rough guidelines on the behavior of the extinction coefficient in the so-called dependent-scattering regime. We base our analysis on Keller’s second order perturbative approximation to the effective propagation constant. To gain physical insight, we also analyze a simple model based on the physical notion that particles in a dense system scatter light in an effective medium.

© 2013 Optical Society of America

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).
  2. Y. Huang and E. M. Sevick-Muraca, “Validating the assumption to the interference approximation by use of measurements of absorption efficiency and hindered scattering in dense suspensions,” Appl. Opt. 43, 814–819 (2004).
    [CrossRef]
  3. G. Zaccanti, S. Del Bianco, and F. Martelli, “Measurements of optical properties of high-density media,” Appl. Opt. 42, 4023–4030 (2003).
    [CrossRef]
  4. J.-C. Auger, V. Martínez, and B. Stout, “Absorption and scattering properties of dense ensembles of nonspherical particles,” J. Opt. Soc. Am. A 24, 3508–3516 (2007).
    [CrossRef]
  5. V. A. Loiko and G. I. Ruban, “Absorption by a layer of densely packed subwavelength-sized particles,” J. Quant. Spectrosc. Radiat. Transfer 89, 271–278 (2004).
    [CrossRef]
  6. V. K. Varadan, V. N. Bringi, and V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed dielectric scatterers,” Phys. Rev. D 19, 2480–2489 (1979).
    [CrossRef]
  7. V. N. Bringi, V. V. Varandan, and V. K. Varandan, “The effects of pair correlation function on coherent wave attenuation in discrete random media,” IEEE Trans. Antennas Propag. 30, 805–808 (1982).
    [CrossRef]
  8. V. N. Bringi, V. K. Varandan, and V. V. Varandan, “Coherent wave attenuation by a random distribution of particles,” Radio Sci. 17, 946–952 (1982).
    [CrossRef]
  9. A. Ishimaru and Y. Kuga, “Attenuation constant of coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
    [CrossRef]
  10. V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
    [CrossRef]
  11. R. West, D. Gibbs, L. Tsang, and A. K. Fund, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1854–1858 (1994).
    [CrossRef]
  12. V. P. Dick, V. A. Loiko, and A. P. Ivanov, “Angular structure of radiation scattered by monolayer of particles: experimental study,” Appl. Opt. 36, 4235–4240 (1997).
    [CrossRef]
  13. 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]
  14. V. P. Dick and A. P. Ivanov, “Extinction of light in dispersive media with high particle concentrations: applicability limits of the interference approximation,” J. Opt. Soc. Am. A 16, 1034–1038 (1999).
    [CrossRef]
  15. L. Tsang and J. A. Kong, “Multiple scattering theory for discrete scatterers,” Scattering of Electromagnetic Waves: Advanced Topics (Wiley, 2001), Chap. 5, pp. 128–130.
  16. M. Lax, “Multiple scattering of waves II: effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
    [CrossRef]
  17. 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]
  18. J. B. Keller, “Stochastic equations and wave propagation in random media,” Proc. Symp. Appl. Math. 16, 145–170 (1964).
    [CrossRef]
  19. 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]
  20. S. Durant, O. Calvo-Perez, N. Vukadinovic, and J.-J. Greffet, “Light scattering by a random distribution of particles embedded in absorbing media: full-wave Monte Carlo solutions of the extinction coefficient,” J. Opt. Soc. Am. A 24, 2953–2961 (2007).
    [CrossRef]
  21. R. G. Barrera and A. García-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
    [CrossRef]
  22. R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
    [CrossRef]
  23. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  24. K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
    [CrossRef]
  25. H. Zhang, P. Zhu, Y. Xu, H. Zhu, and M. Xu, “Effective medium theory for random media composed of two-layered spheres,” J. Opt. Soc. Am. A 28, 2292–2297 (2011).
    [CrossRef]

2011 (1)

2007 (4)

2004 (2)

V. A. Loiko and G. I. Ruban, “Absorption by a layer of densely packed subwavelength-sized particles,” J. Quant. Spectrosc. Radiat. Transfer 89, 271–278 (2004).
[CrossRef]

Y. Huang and E. M. Sevick-Muraca, “Validating the assumption to the interference approximation by use of measurements of absorption efficiency and hindered scattering in dense suspensions,” Appl. Opt. 43, 814–819 (2004).
[CrossRef]

2003 (2)

2001 (1)

1999 (2)

1997 (1)

1996 (1)

K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
[CrossRef]

1994 (1)

1983 (1)

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

1982 (3)

V. N. Bringi, V. V. Varandan, and V. K. Varandan, “The effects of pair correlation function on coherent wave attenuation in discrete random media,” IEEE Trans. Antennas Propag. 30, 805–808 (1982).
[CrossRef]

V. N. Bringi, V. K. Varandan, and V. V. Varandan, “Coherent wave attenuation by a random distribution of particles,” Radio Sci. 17, 946–952 (1982).
[CrossRef]

A. Ishimaru and Y. Kuga, “Attenuation constant of coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
[CrossRef]

1979 (1)

V. K. Varadan, V. N. Bringi, and V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed dielectric scatterers,” Phys. Rev. D 19, 2480–2489 (1979).
[CrossRef]

1964 (1)

J. B. Keller, “Stochastic equations and wave propagation in random media,” Proc. Symp. Appl. Math. 16, 145–170 (1964).
[CrossRef]

1952 (1)

M. Lax, “Multiple scattering of waves II: effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
[CrossRef]

Auger, J.-C.

Barrera, R. G.

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[CrossRef]

R. G. Barrera and A. García-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
[CrossRef]

Bohren, C. F.

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

Bringi, V. N.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

V. N. Bringi, V. V. Varandan, and V. K. Varandan, “The effects of pair correlation function on coherent wave attenuation in discrete random media,” IEEE Trans. Antennas Propag. 30, 805–808 (1982).
[CrossRef]

V. N. Bringi, V. K. Varandan, and V. V. Varandan, “Coherent wave attenuation by a random distribution of particles,” Radio Sci. 17, 946–952 (1982).
[CrossRef]

V. K. Varadan, V. N. Bringi, and V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed dielectric scatterers,” Phys. Rev. D 19, 2480–2489 (1979).
[CrossRef]

Busch, K.

K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
[CrossRef]

Calvo-Perez, O.

Del Bianco, S.

Dick, V. P.

Durant, S.

Fund, A. K.

García-Valenzuela, A.

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[CrossRef]

R. G. Barrera and A. García-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
[CrossRef]

Gibbs, D.

Greffet, J.-J.

Hespel, L.

Huang, Y.

Huffman, D. R.

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

Ishimaru, A.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

A. Ishimaru and Y. Kuga, “Attenuation constant of coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

Ivanov, A. P.

Keller, J. B.

J. B. Keller, “Stochastic equations and wave propagation in random media,” Proc. Symp. Appl. Math. 16, 145–170 (1964).
[CrossRef]

Kong, J. A.

L. Tsang and J. A. Kong, “Multiple scattering theory for discrete scatterers,” Scattering of Electromagnetic Waves: Advanced Topics (Wiley, 2001), Chap. 5, pp. 128–130.

Kuga, Y.

Lax, M.

M. Lax, “Multiple scattering of waves II: effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
[CrossRef]

Loiko, V. A.

Mainguy, S.

Martelli, F.

Martínez, V.

Reyes-Coronado, A.

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[CrossRef]

Ruban, G. I.

V. A. Loiko and G. I. Ruban, “Absorption by a layer of densely packed subwavelength-sized particles,” J. Quant. Spectrosc. Radiat. Transfer 89, 271–278 (2004).
[CrossRef]

Sevick-Muraca, E. M.

Soukoulis, C. M.

K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
[CrossRef]

Stout, B.

Tsang, L.

R. West, D. Gibbs, L. Tsang, and A. K. Fund, “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 and J. A. Kong, “Multiple scattering theory for discrete scatterers,” Scattering of Electromagnetic Waves: Advanced Topics (Wiley, 2001), Chap. 5, pp. 128–130.

Varadan, V. K.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

V. K. Varadan, V. N. Bringi, and V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed dielectric scatterers,” Phys. Rev. D 19, 2480–2489 (1979).
[CrossRef]

Varadan, V. V.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

V. K. Varadan, V. N. Bringi, and V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed dielectric scatterers,” Phys. Rev. D 19, 2480–2489 (1979).
[CrossRef]

Varandan, V. K.

V. N. Bringi, V. V. Varandan, and V. K. Varandan, “The effects of pair correlation function on coherent wave attenuation in discrete random media,” IEEE Trans. Antennas Propag. 30, 805–808 (1982).
[CrossRef]

V. N. Bringi, V. K. Varandan, and V. V. Varandan, “Coherent wave attenuation by a random distribution of particles,” Radio Sci. 17, 946–952 (1982).
[CrossRef]

Varandan, V. V.

V. N. Bringi, V. K. Varandan, and V. V. Varandan, “Coherent wave attenuation by a random distribution of particles,” Radio Sci. 17, 946–952 (1982).
[CrossRef]

V. N. Bringi, V. V. Varandan, and V. K. Varandan, “The effects of pair correlation function on coherent wave attenuation in discrete random media,” IEEE Trans. Antennas Propag. 30, 805–808 (1982).
[CrossRef]

Vukadinovic, N.

West, R.

Xu, M.

Xu, Y.

Zaccanti, G.

Zhang, H.

Zhu, H.

Zhu, P.

Appl. Opt. (4)

IEEE Trans. Antennas Propag. (1)

V. N. Bringi, V. V. Varandan, and V. K. Varandan, “The effects of pair correlation function on coherent wave attenuation in discrete random media,” IEEE Trans. Antennas Propag. 30, 805–808 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (8)

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]

R. G. Barrera and A. García-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
[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]

S. Durant, O. Calvo-Perez, N. Vukadinovic, and J.-J. Greffet, “Light scattering by a random distribution of particles embedded in absorbing media: full-wave Monte Carlo solutions of the extinction coefficient,” J. Opt. Soc. Am. A 24, 2953–2961 (2007).
[CrossRef]

J.-C. Auger, V. Martínez, and B. Stout, “Absorption and scattering properties of dense ensembles of nonspherical particles,” J. Opt. Soc. Am. A 24, 3508–3516 (2007).
[CrossRef]

H. Zhang, P. Zhu, Y. Xu, H. Zhu, and M. Xu, “Effective medium theory for random media composed of two-layered spheres,” J. Opt. Soc. Am. A 28, 2292–2297 (2011).
[CrossRef]

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

V. P. Dick and A. P. Ivanov, “Extinction of light in dispersive media with high particle concentrations: applicability limits of the interference approximation,” J. Opt. Soc. Am. A 16, 1034–1038 (1999).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

V. A. Loiko and G. I. Ruban, “Absorption by a layer of densely packed subwavelength-sized particles,” J. Quant. Spectrosc. Radiat. Transfer 89, 271–278 (2004).
[CrossRef]

Phys. Rev. (1)

M. Lax, “Multiple scattering of waves II: effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
[CrossRef]

Phys. Rev. B (2)

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[CrossRef]

K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
[CrossRef]

Phys. Rev. D (1)

V. K. Varadan, V. N. Bringi, and V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed dielectric scatterers,” Phys. Rev. D 19, 2480–2489 (1979).
[CrossRef]

Proc. Symp. Appl. Math. (1)

J. B. Keller, “Stochastic equations and wave propagation in random media,” Proc. Symp. Appl. Math. 16, 145–170 (1964).
[CrossRef]

Radio Sci. (2)

V. N. Bringi, V. K. Varandan, and V. V. Varandan, “Coherent wave attenuation by a random distribution of particles,” Radio Sci. 17, 946–952 (1982).
[CrossRef]

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Other (3)

L. Tsang and J. A. Kong, “Multiple scattering theory for discrete scatterers,” Scattering of Electromagnetic Waves: Advanced Topics (Wiley, 2001), Chap. 5, pp. 128–130.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

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

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