Abstract

The effect of absorption on the diffusion constant of classical waves propagating in media with randomly positioned Mie scatterers is studied. Profound changes including a significant increase in the diffusion constant are found and attributed to the growth of the transport mean free path in the vicinity of Mie resonances.

© 1995 Optical Society of America

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References

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  2. S. John, "Localization of light," Phys. Today 44 (5), 32 (1991).
    [CrossRef]
  3. Z. Q. Zhang and P. Sheng, in Scattering and Localization of Classical Waves in Random Media P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 137–178.
    [CrossRef]
  4. M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, "Speed of propagation of classical waves in strongly scattering media," Phys. Rev. Lett. 62, 3132 (1991).
    [CrossRef]
  5. G. Cwilich and Y. Fu, "Scattering delay and renormalization of the wave-diffusion constant," Phys. Rev. B 46, 12015 (1992).
    [CrossRef]
  6. E. Kogan and M. Kaveh, "Diffusion constant in a random system near resonance," Phys. Rev. B 46, 10636 (1992).
    [CrossRef]
  7. J. Kroha, C. M. Soukoulis, and P. Wolffe, "Localization of classical waves in random medium: a self-consistent theory," Phys. Rev. B 47, 9208 (1992).
  8. A. Z. Genack, N. Garcia, J. H. Li, and A. A. Lisyansky, in Photonic Band Gaps and Localization, C. M. Soukoulis, ed. (Wiley, New York, 1993), p. 23.
  9. B. A. van Tiggelen and A. Lagendijk, "Rigorous treatment of the speed of diffusing classical waves," Europhys. Lett. 23, 311 (1993).
    [CrossRef]
  10. D. Livdan and A. A. Lisyansky, "Diffusion of classical waves in random media with microstructure resonances," Department of Physics, Queens College, Flushing, N.Y. 11367 (preprint, 1994).
  11. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9, p. 123.

1993 (1)

B. A. van Tiggelen and A. Lagendijk, "Rigorous treatment of the speed of diffusing classical waves," Europhys. Lett. 23, 311 (1993).
[CrossRef]

1992 (3)

G. Cwilich and Y. Fu, "Scattering delay and renormalization of the wave-diffusion constant," Phys. Rev. B 46, 12015 (1992).
[CrossRef]

E. Kogan and M. Kaveh, "Diffusion constant in a random system near resonance," Phys. Rev. B 46, 10636 (1992).
[CrossRef]

J. Kroha, C. M. Soukoulis, and P. Wolffe, "Localization of classical waves in random medium: a self-consistent theory," Phys. Rev. B 47, 9208 (1992).

1991 (2)

S. John, "Localization of light," Phys. Today 44 (5), 32 (1991).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, "Speed of propagation of classical waves in strongly scattering media," Phys. Rev. Lett. 62, 3132 (1991).
[CrossRef]

Albada, M. P. van

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, "Speed of propagation of classical waves in strongly scattering media," Phys. Rev. Lett. 62, 3132 (1991).
[CrossRef]

Cwilich, G.

G. Cwilich and Y. Fu, "Scattering delay and renormalization of the wave-diffusion constant," Phys. Rev. B 46, 12015 (1992).
[CrossRef]

Fu, Y.

G. Cwilich and Y. Fu, "Scattering delay and renormalization of the wave-diffusion constant," Phys. Rev. B 46, 12015 (1992).
[CrossRef]

Garcia, N.

A. Z. Genack, N. Garcia, J. H. Li, and A. A. Lisyansky, in Photonic Band Gaps and Localization, C. M. Soukoulis, ed. (Wiley, New York, 1993), p. 23.

Genack, A. Z.

A. Z. Genack, N. Garcia, J. H. Li, and A. A. Lisyansky, in Photonic Band Gaps and Localization, C. M. Soukoulis, ed. (Wiley, New York, 1993), p. 23.

Hulst, H. C. van de

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9, p. 123.

Ishimaru, A.

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

John, S.

S. John, "Localization of light," Phys. Today 44 (5), 32 (1991).
[CrossRef]

Kaveh, M.

E. Kogan and M. Kaveh, "Diffusion constant in a random system near resonance," Phys. Rev. B 46, 10636 (1992).
[CrossRef]

Kogan, E.

E. Kogan and M. Kaveh, "Diffusion constant in a random system near resonance," Phys. Rev. B 46, 10636 (1992).
[CrossRef]

Kroha, J.

J. Kroha, C. M. Soukoulis, and P. Wolffe, "Localization of classical waves in random medium: a self-consistent theory," Phys. Rev. B 47, 9208 (1992).

Lagendijk, A.

B. A. van Tiggelen and A. Lagendijk, "Rigorous treatment of the speed of diffusing classical waves," Europhys. Lett. 23, 311 (1993).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, "Speed of propagation of classical waves in strongly scattering media," Phys. Rev. Lett. 62, 3132 (1991).
[CrossRef]

Li, J. H.

A. Z. Genack, N. Garcia, J. H. Li, and A. A. Lisyansky, in Photonic Band Gaps and Localization, C. M. Soukoulis, ed. (Wiley, New York, 1993), p. 23.

Lisyansky, A. A.

A. Z. Genack, N. Garcia, J. H. Li, and A. A. Lisyansky, in Photonic Band Gaps and Localization, C. M. Soukoulis, ed. (Wiley, New York, 1993), p. 23.

D. Livdan and A. A. Lisyansky, "Diffusion of classical waves in random media with microstructure resonances," Department of Physics, Queens College, Flushing, N.Y. 11367 (preprint, 1994).

Livdan, D.

D. Livdan and A. A. Lisyansky, "Diffusion of classical waves in random media with microstructure resonances," Department of Physics, Queens College, Flushing, N.Y. 11367 (preprint, 1994).

Sheng, P.

Z. Q. Zhang and P. Sheng, in Scattering and Localization of Classical Waves in Random Media P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 137–178.
[CrossRef]

Soukoulis, C. M.

J. Kroha, C. M. Soukoulis, and P. Wolffe, "Localization of classical waves in random medium: a self-consistent theory," Phys. Rev. B 47, 9208 (1992).

Tiggelen, B. A. van

B. A. van Tiggelen and A. Lagendijk, "Rigorous treatment of the speed of diffusing classical waves," Europhys. Lett. 23, 311 (1993).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, "Speed of propagation of classical waves in strongly scattering media," Phys. Rev. Lett. 62, 3132 (1991).
[CrossRef]

Tip, A.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, "Speed of propagation of classical waves in strongly scattering media," Phys. Rev. Lett. 62, 3132 (1991).
[CrossRef]

Wolffe, P.

J. Kroha, C. M. Soukoulis, and P. Wolffe, "Localization of classical waves in random medium: a self-consistent theory," Phys. Rev. B 47, 9208 (1992).

Zhang, Z. Q.

Z. Q. Zhang and P. Sheng, in Scattering and Localization of Classical Waves in Random Media P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 137–178.
[CrossRef]

Europhys. Lett. (1)

B. A. van Tiggelen and A. Lagendijk, "Rigorous treatment of the speed of diffusing classical waves," Europhys. Lett. 23, 311 (1993).
[CrossRef]

Phys. Rev. B (3)

G. Cwilich and Y. Fu, "Scattering delay and renormalization of the wave-diffusion constant," Phys. Rev. B 46, 12015 (1992).
[CrossRef]

E. Kogan and M. Kaveh, "Diffusion constant in a random system near resonance," Phys. Rev. B 46, 10636 (1992).
[CrossRef]

J. Kroha, C. M. Soukoulis, and P. Wolffe, "Localization of classical waves in random medium: a self-consistent theory," Phys. Rev. B 47, 9208 (1992).

Phys. Rev. Lett. (1)

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, "Speed of propagation of classical waves in strongly scattering media," Phys. Rev. Lett. 62, 3132 (1991).
[CrossRef]

Phys. Today (1)

S. John, "Localization of light," Phys. Today 44 (5), 32 (1991).
[CrossRef]

Other (5)

Z. Q. Zhang and P. Sheng, in Scattering and Localization of Classical Waves in Random Media P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 137–178.
[CrossRef]

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

A. Z. Genack, N. Garcia, J. H. Li, and A. A. Lisyansky, in Photonic Band Gaps and Localization, C. M. Soukoulis, ed. (Wiley, New York, 1993), p. 23.

D. Livdan and A. A. Lisyansky, "Diffusion of classical waves in random media with microstructure resonances," Department of Physics, Queens College, Flushing, N.Y. 11367 (preprint, 1994).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9, p. 123.

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Figures (3)

Fig. 1
Fig. 1

Correction to the diffusion constant a(x = k0R) normalized by a volume of a single scatterer plotted for an absorbing medium, m = 2.73 − i0.005 (thick curve), and in the absence of absorption, m = 2.73 (thin curve). Because this correction decreases D according to Eq. (1), in the figure the negative value of a(x) is plotted. It can be seen that absorption significantly decreases the magnitude of resonances. To preserve the important details of these plots we have shortened the vertical scale of the figure. The magnitude of peaks omitted from the figure can be as large as 3000.

Fig. 2
Fig. 2

Correction to the diffusion constant Δ(x) normalized by a volume of a single scatterer for two different values of the index of refraction m = 2.73 − i0.005 (thick curve) and m = 2.73 (thin curve).

Fig. 3
Fig. 3

Total correction to the diffusion constant Δ(x) − a(x) normalized by a volume of a single scatterer for the same values of m as in Figs. 1 and 2, m = 2.73 − i0.005 (thick curve) and m = 2.73 (thin curve).

Equations (9)

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D ( Ω ) = D 0 1 + n a ( Ω ) ( c c p ) 2 [ 1 + n Δ ( Ω ) ] ,
T = 1 n ( 1 - μ ) t kk 2 μ ,
Δ ( Ω ) = 2 Re ( t kk k 2 ) k = k 0 + i Ω 2 π c p ( 1 + μ ) K ( k , k ) μ ,
K ( k , k ) = i Im [ ( t kk k 2 + 1 - μ k 2 t kk μ ) t kk * ] .
a ( Ω ) = m r 2 - 1 2 m r k 0 σ abs ( Ω ) m i
t kk = - 4 π i k 0 l = 0 ( 2 l + 1 ) P l ( μ ) b l * ( x ) ,
σ abs ( x ) = 4 π R 2 x 2 l = 0 ( 2 l + 1 ) [ Re b l ( x ) - b l ( x ) 2 ] .
v ( Ω ) = c 2 c p 1 1 + n a ( Ω ) .
( Ω ) = T [ 1 + n Δ ( Ω ) ] .

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