Abstract

We present Monte Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres that occupy up to 25% by volume and size parameter ka = 0.2. Maxwell’s equations in multiple-scattering form are solved iteratively for each realization. Convergence is demonstrated numerically by varying the number of iterations, the number of spheres up to 4000, and the number of realizations. Results are compared with that of the independent-scattering approximation, Foldy’s approximation, the quasi-crystalline approximation, and the quasi-crystalline approximation with coherent potential. The simulations are in good agreement with the last two approximations.

© 1992 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), Vols. 1 and 2.
  2. A. Ishimaru, Y. Kuga, J. Opt. Soc. Am. 72, 1317 (1982).
    [CrossRef]
  3. G. S. Brown, Radio Sci. 15, 705 (1980).
    [CrossRef]
  4. V. Twersky, J. Math. Phys. N.Y. 19, 215 (1978).
    [CrossRef]
  5. L. Tsang, J. A. Kong, J. Appl. Phys. 53, 7162 (1982).
    [CrossRef]
  6. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
  7. L. Tsang, J. A. Kong, J. Appl. Phys. 15, 3465 (1980).
    [CrossRef]
  8. J. K. Percus, G. J. Yevick, Phys. Rev. 110, 1 (1958).
    [CrossRef]
  9. K. H. Ding, C. E. Mandt, L. Tsang, J. A. Kong, “Monte Carlo simulations of pair distribution functions of dense discrete media with multiple sizes of particles,”J. Electromagn. Waves Appl. (to be published).
  10. B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, IEEE Trans. Geosci. Remote Sensing 28, 46 (1990).
    [CrossRef]

1990 (1)

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, IEEE Trans. Geosci. Remote Sensing 28, 46 (1990).
[CrossRef]

1982 (2)

A. Ishimaru, Y. Kuga, J. Opt. Soc. Am. 72, 1317 (1982).
[CrossRef]

L. Tsang, J. A. Kong, J. Appl. Phys. 53, 7162 (1982).
[CrossRef]

1980 (2)

L. Tsang, J. A. Kong, J. Appl. Phys. 15, 3465 (1980).
[CrossRef]

G. S. Brown, Radio Sci. 15, 705 (1980).
[CrossRef]

1978 (1)

V. Twersky, J. Math. Phys. N.Y. 19, 215 (1978).
[CrossRef]

1958 (1)

J. K. Percus, G. J. Yevick, Phys. Rev. 110, 1 (1958).
[CrossRef]

Brown, G. S.

G. S. Brown, Radio Sci. 15, 705 (1980).
[CrossRef]

Ding, K. H.

K. H. Ding, C. E. Mandt, L. Tsang, J. A. Kong, “Monte Carlo simulations of pair distribution functions of dense discrete media with multiple sizes of particles,”J. Electromagn. Waves Appl. (to be published).

Ishimaru, A.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, IEEE Trans. Geosci. Remote Sensing 28, 46 (1990).
[CrossRef]

A. Ishimaru, Y. Kuga, J. Opt. Soc. Am. 72, 1317 (1982).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. 1 and 2.

Kong, J. A.

L. Tsang, J. A. Kong, J. Appl. Phys. 53, 7162 (1982).
[CrossRef]

L. Tsang, J. A. Kong, J. Appl. Phys. 15, 3465 (1980).
[CrossRef]

K. H. Ding, C. E. Mandt, L. Tsang, J. A. Kong, “Monte Carlo simulations of pair distribution functions of dense discrete media with multiple sizes of particles,”J. Electromagn. Waves Appl. (to be published).

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

Kuga, Y.

Mandt, C. E.

K. H. Ding, C. E. Mandt, L. Tsang, J. A. Kong, “Monte Carlo simulations of pair distribution functions of dense discrete media with multiple sizes of particles,”J. Electromagn. Waves Appl. (to be published).

Percus, J. K.

J. K. Percus, G. J. Yevick, Phys. Rev. 110, 1 (1958).
[CrossRef]

Shin, R. T.

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

Tsang, L.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, IEEE Trans. Geosci. Remote Sensing 28, 46 (1990).
[CrossRef]

L. Tsang, J. A. Kong, J. Appl. Phys. 53, 7162 (1982).
[CrossRef]

L. Tsang, J. A. Kong, J. Appl. Phys. 15, 3465 (1980).
[CrossRef]

K. H. Ding, C. E. Mandt, L. Tsang, J. A. Kong, “Monte Carlo simulations of pair distribution functions of dense discrete media with multiple sizes of particles,”J. Electromagn. Waves Appl. (to be published).

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

Twersky, V.

V. Twersky, J. Math. Phys. N.Y. 19, 215 (1978).
[CrossRef]

Wen, B.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, IEEE Trans. Geosci. Remote Sensing 28, 46 (1990).
[CrossRef]

Winebrenner, D. P.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, IEEE Trans. Geosci. Remote Sensing 28, 46 (1990).
[CrossRef]

Yevick, G. J.

J. K. Percus, G. J. Yevick, Phys. Rev. 110, 1 (1958).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (1)

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, IEEE Trans. Geosci. Remote Sensing 28, 46 (1990).
[CrossRef]

J. Appl. Phys. (2)

L. Tsang, J. A. Kong, J. Appl. Phys. 15, 3465 (1980).
[CrossRef]

L. Tsang, J. A. Kong, J. Appl. Phys. 53, 7162 (1982).
[CrossRef]

J. Math. Phys. N.Y. (1)

V. Twersky, J. Math. Phys. N.Y. 19, 215 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. (1)

J. K. Percus, G. J. Yevick, Phys. Rev. 110, 1 (1958).
[CrossRef]

Radio Sci. (1)

G. S. Brown, Radio Sci. 15, 705 (1980).
[CrossRef]

Other (3)

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

K. H. Ding, C. E. Mandt, L. Tsang, J. A. Kong, “Monte Carlo simulations of pair distribution functions of dense discrete media with multiple sizes of particles,”J. Electromagn. Waves Appl. (to be published).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. 1 and 2.

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Figures (3)

Fig. 1
Fig. 1

Convergence of extinction rate versus number of realizations and number of iterations for fractional volume f = 15% and N = 2000 and 4000. The extinction rate is normalized to the independent scattering case. Other parameters are s = 3.20 and ka = 0.2.

Fig. 2
Fig. 2

Convergence of extinction rate versus number of realizations and number of iterations for fractional volume f = 25% and N = 2000 and 4000. The extinction rate is normalized to the independent scattering case. Other parameters are s = 3.20 and ka = 0.2.

Fig. 3
Fig. 3

Extinction rate normalized to the free-space wave number as a function of the fractional volume of scatterers. The plots show calculations based on independent scattering, Foldy’s formula, QCA–PY, QCA–CP–PY, and Monte Carlo simulations. Other parameters are s = 3.20 and ka = 0.2.

Tables (1)

Tables Icon

Table 1 Numerical Values of the Ratio κe/(κe)ind

Equations (9)

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w ( α ) = β = 1 β α N σ ( k r α r β ) T ( β ) w ( β ) + exp ( i k i r α ) a inc ,
a s ( α ) = T ( α ) w ( α ) .
E s = exp ( i k R ) k R m n γ m n [ a m n s ( M ) C m n ( θ s , ϕ s ) i n 1 + a m n s ( N ) B m n ( θ s , ϕ s ) i n ] ,
a s ( α ) = β = 1 β α N T ( α ) σ ( k r α r β ) a s ( β ) + exp ( i k i r α ) T ( α ) a inc .
E s = R N r σ = 1 N r E s σ ,
σ b N ( k ˆ s , k ˆ i ) = R 2 | s σ | 2 = R 2 N r σ = 1 N r | s σ | 2 .
σ s N = 0 π d θ s sin θ s 0 2 π d ϕ s σ b N ( k ˆ s , k ˆ i ) .
κ e ( κ e ) ind = σ s N V n 0 σ s = σ s N N σ s .
a s ( α ) ( υ + 1 ) = exp ( i k i r α ) T ( α ) a inc + β = 1 β α N T ( α ) σ ( k r α r β ) a s ( β ) ( υ ) ,

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