Abstract

In a dense medium, the failure to properly take into account multiple-scattering effects could lead to significant errors. This has been demonstrated in the past from extensive theoretical, numerical, and experimental studies of electromagnetic wave scattering by densely packed dielectric spheres. Here, electromagnetic wave scattering by densely packed dielectric spheroids with aligned orientation is studied analytically through quasi-crystalline approximation (QCA) and QCA with coherent potential (QCA-CP). We assume that the spheroids are electrically small so that single-particle scattering is simple. Low-frequency QCA and QCA-CP solutions are obtained for the average Green’s function and the effective permittivity tensor. For QCA-CP, the low-frequency expansion of the uniaxial dyadic Green’s function is required. The real parts of the effective permittivities from QCA and QCA-CP are compared with the Maxwell–Garnett mixing formula. QCA gives results identical to those with the mixing formula, while QCA-CP gives slightly higher values. The extinction coefficients from QCA and QCA-CP are compared with results from Monte Carlo simulations. Both QCA and QCA-CP agree well with simulations, although qualitative disagreement is evident at higher fractional volumes.

© 2002 Optical Society of America

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  1. L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, New York, 2000).
  2. A. H. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, London, 1999).
  3. L. Tsang, J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley-Interscience, New York, 2001).
  4. L. Tsang, J. A. Kong, K.-H. Ding, C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, New York, 2001).
  5. L. Tsang, J. A. Kong, “Scattering of electromagnetic waves from a dense medium consisting of correlated Mie scatterers with size distributions and applications to dry snow,” J. Electromagn. Waves Appl. 6, 265–286 (1992).
    [CrossRef]
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  7. L. Tsang, K. H. Ding, S. E. Shih, J. A. Kong, “Scattering of electromagnetic waves from dense distributions of spheroidal particles based on Monte Carlo simulations,” J. Opt. Soc. Am. A 15, 2660–2669 (1998).
    [CrossRef]
  8. L. Tsang, J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
    [CrossRef]
  9. L. Tsang, C. Mandt, 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]
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  14. V. V. Varadan, Y. Ma, V. K. Varadan, “Anisotropic dielectric properties of media containing aligned nonspherical scatterers,” IEEE Trans. Antennas Propag. AP-33, 886–890 (1987).
  15. V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
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  22. N. Metropolis, A. W. Rosenbluth, N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculation by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
    [CrossRef]
  23. J. L. Lebowitz, J. W. Perram, “Correlation functions for nematic liquid crystals,” Mol. Phys. 50, 1207–1214 (1983).
    [CrossRef]
  24. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
  25. M. Lax, “The multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
    [CrossRef]
  26. B. L. Gyorffy, “Electronic states in liquid metals: a generalization of the coherent-potential approximation for a system with short-range order,” Phys. Rev. B 1, 3290–3299 (1970).
    [CrossRef]
  27. J. Korringa, R. L. Mills, “Coherent-potential approximation for random systems with short range correlations,” Phys. Rev. B 5, 1654–1655 (1972).
    [CrossRef]
  28. K.-H. Ding, L. Tsang, “Effective propagation constants and attenuation rates in media of densely distributedcoated dielectric particles with size distributions,” J. Electromagn. Waves Appl. 5, 117–142 (1991).
    [CrossRef]
  29. A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
    [CrossRef]
  30. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
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    [CrossRef]
  33. A. H. Sihvola, J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
    [CrossRef]
  34. L. M. Zurk, L. Tsang, D. P. Winebrenner, “Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow,” Radio Sci. 31, 803–819 (1996).
    [CrossRef]
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    [CrossRef]
  36. G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
    [CrossRef] [PubMed]
  37. J. A. Barker, D. Henderson, “What is “liquid”? Understanding the states of matter,” Rev. Mod. Phys. 48, (1976).
  38. J. A. Kong, Electromagnetic Wave Theory (EMW, Cambridge, Mass., 2000).
  39. H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-Free Approach (McGraw-Hill, New York, 1983).
  40. W. S. Weiglhofer, “Dyadic Green’s functions for general uniaxial media,” IEE Proc. H 137, 5–10 (1990).

2000 (1)

B. E. Barrowes, C. O. Ao, F. L. Teixeira, J. A. Kong, L. Tsang, “Monte Carlo simulation of electromagnetic wave propagation in dense random media with dielectric spheroids,” IEICE Trans. Electron. E83-C, 1797–1802 (2000).

1999 (1)

N. Harfield, “Conductivity calculation for a two-phase composite with spheroidal inclusions,” J. Phys. D 32, 1104–1113 (1999).
[CrossRef]

1998 (1)

1996 (1)

L. M. Zurk, L. Tsang, D. P. Winebrenner, “Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow,” Radio Sci. 31, 803–819 (1996).
[CrossRef]

1994 (1)

1992 (3)

L. Tsang, C. Mandt, 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]

C. Mandt, Y. Kuga, L. Tsang, A. Ishimaru, “Microwave propagation and scattering in a dense distribution of spherical particles: experiment and theory,” Waves Random Media 2, 225–234 (1992).
[CrossRef]

L. Tsang, J. A. Kong, “Scattering of electromagnetic waves from a dense medium consisting of correlated Mie scatterers with size distributions and applications to dry snow,” J. Electromagn. Waves Appl. 6, 265–286 (1992).
[CrossRef]

1991 (1)

K.-H. Ding, L. Tsang, “Effective propagation constants and attenuation rates in media of densely distributedcoated dielectric particles with size distributions,” J. Electromagn. Waves Appl. 5, 117–142 (1991).
[CrossRef]

1990 (1)

W. S. Weiglhofer, “Dyadic Green’s functions for general uniaxial media,” IEE Proc. H 137, 5–10 (1990).

1988 (2)

A. H. Sihvola, J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
[CrossRef]

G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
[CrossRef] [PubMed]

1987 (2)

V. V. Varadan, Y. Ma, V. K. Varadan, “Anisotropic dielectric properties of media containing aligned nonspherical scatterers,” IEEE Trans. Antennas Propag. AP-33, 886–890 (1987).

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

1984 (1)

L. Tsang, “Scattering of electromagnetic waves from a half space of nonspherical particles,” Radio Sci. 19, 1450–1460 (1984).
[CrossRef]

1983 (1)

J. L. Lebowitz, J. W. Perram, “Correlation functions for nematic liquid crystals,” Mol. Phys. 50, 1207–1214 (1983).
[CrossRef]

1982 (1)

L. Tsang, J. A. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71, 552–558 (1982).
[CrossRef]

1980 (2)

L. Tsang, J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
[CrossRef]

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

1978 (1)

V. Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

1977 (1)

V. Twersky, “Coherent scalar field in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 18, 2468–2486 (1977).
[CrossRef]

1976 (1)

J. A. Barker, D. Henderson, “What is “liquid”? Understanding the states of matter,” Rev. Mod. Phys. 48, (1976).

1972 (1)

J. Korringa, R. L. Mills, “Coherent-potential approximation for random systems with short range correlations,” Phys. Rev. B 5, 1654–1655 (1972).
[CrossRef]

1970 (1)

B. L. Gyorffy, “Electronic states in liquid metals: a generalization of the coherent-potential approximation for a system with short-range order,” Phys. Rev. B 1, 3290–3299 (1970).
[CrossRef]

1963 (2)

M. S. Wertheim, “Exact solution of the Percus–Yevick integral equation for hard spheres,” Phys. Rev. Lett. 20, 321–323 (1963).
[CrossRef]

E. Thiele, “Equation of state for hard spheres,” J. Comput. Phys. 39, 474–479 (1963).

1958 (1)

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

1953 (1)

N. Metropolis, A. W. Rosenbluth, N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculation by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

1952 (1)

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

Allen, M. P.

M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids (Oxford U. Press, New York, 1989).

Ao, C. O.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, J. A. Kong, L. Tsang, “Monte Carlo simulation of electromagnetic wave propagation in dense random media with dielectric spheroids,” IEICE Trans. Electron. E83-C, 1797–1802 (2000).

L. Tsang, J. A. Kong, K.-H. Ding, C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, New York, 2001).

Barker, J. A.

J. A. Barker, D. Henderson, “What is “liquid”? Understanding the states of matter,” Rev. Mod. Phys. 48, (1976).

Barrowes, B. E.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, J. A. Kong, L. Tsang, “Monte Carlo simulation of electromagnetic wave propagation in dense random media with dielectric spheroids,” IEICE Trans. Electron. E83-C, 1797–1802 (2000).

Chen, H. C.

H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-Free Approach (McGraw-Hill, New York, 1983).

Ding, K. H.

Ding, K.-H.

K.-H. Ding, L. Tsang, “Effective propagation constants and attenuation rates in media of densely distributedcoated dielectric particles with size distributions,” J. Electromagn. Waves Appl. 5, 117–142 (1991).
[CrossRef]

L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, New York, 2000).

L. Tsang, J. A. Kong, K.-H. Ding, C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, New York, 2001).

Draine, B. T.

Flatau, P. J.

Goedecke, G. H.

Gyorffy, B. L.

B. L. Gyorffy, “Electronic states in liquid metals: a generalization of the coherent-potential approximation for a system with short-range order,” Phys. Rev. B 1, 3290–3299 (1970).
[CrossRef]

Habashy, T.

L. Tsang, J. A. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71, 552–558 (1982).
[CrossRef]

Hansen, J. P.

J. P. Hansen, I. R. McDonald, Theory of Simple Liquids (Academic, New York, 1986).

Harfield, N.

N. Harfield, “Conductivity calculation for a two-phase composite with spheroidal inclusions,” J. Phys. D 32, 1104–1113 (1999).
[CrossRef]

Henderson, D.

J. A. Barker, D. Henderson, “What is “liquid”? Understanding the states of matter,” Rev. Mod. Phys. 48, (1976).

Ishimaru, A.

C. Mandt, Y. Kuga, L. Tsang, A. Ishimaru, “Microwave propagation and scattering in a dense distribution of spherical particles: experiment and theory,” Waves Random Media 2, 225–234 (1992).
[CrossRef]

Kong, J. A.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, J. A. Kong, L. Tsang, “Monte Carlo simulation of electromagnetic wave propagation in dense random media with dielectric spheroids,” IEICE Trans. Electron. E83-C, 1797–1802 (2000).

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

L. Tsang, J. A. Kong, “Scattering of electromagnetic waves from a dense medium consisting of correlated Mie scatterers with size distributions and applications to dry snow,” J. Electromagn. Waves Appl. 6, 265–286 (1992).
[CrossRef]

A. H. Sihvola, J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
[CrossRef]

L. Tsang, J. A. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71, 552–558 (1982).
[CrossRef]

L. Tsang, J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
[CrossRef]

L. Tsang, J. A. Kong, K.-H. Ding, C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, New York, 2001).

L. Tsang, J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley-Interscience, New York, 2001).

L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, New York, 2000).

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

J. A. Kong, Electromagnetic Wave Theory (EMW, Cambridge, Mass., 2000).

Korringa, J.

J. Korringa, R. L. Mills, “Coherent-potential approximation for random systems with short range correlations,” Phys. Rev. B 5, 1654–1655 (1972).
[CrossRef]

Kuga, Y.

C. Mandt, Y. Kuga, L. Tsang, A. Ishimaru, “Microwave propagation and scattering in a dense distribution of spherical particles: experiment and theory,” Waves Random Media 2, 225–234 (1992).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, UK, 1984).

Lax, M.

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

Lebowitz, J. L.

J. L. Lebowitz, J. W. Perram, “Correlation functions for nematic liquid crystals,” Mol. Phys. 50, 1207–1214 (1983).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, UK, 1984).

Ma, Y.

V. V. Varadan, Y. Ma, V. K. Varadan, “Anisotropic dielectric properties of media containing aligned nonspherical scatterers,” IEEE Trans. Antennas Propag. AP-33, 886–890 (1987).

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

Mandt, C.

L. Tsang, C. Mandt, 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]

C. Mandt, Y. Kuga, L. Tsang, A. Ishimaru, “Microwave propagation and scattering in a dense distribution of spherical particles: experiment and theory,” Waves Random Media 2, 225–234 (1992).
[CrossRef]

McDonald, I. R.

J. P. Hansen, I. R. McDonald, Theory of Simple Liquids (Academic, New York, 1986).

Metropolis, N.

N. Metropolis, A. W. Rosenbluth, N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculation by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Mills, R. L.

J. Korringa, R. L. Mills, “Coherent-potential approximation for random systems with short range correlations,” Phys. Rev. B 5, 1654–1655 (1972).
[CrossRef]

O’Brien, S. G.

Percus, J. K.

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

Perram, J. W.

J. L. Lebowitz, J. W. Perram, “Correlation functions for nematic liquid crystals,” Mol. Phys. 50, 1207–1214 (1983).
[CrossRef]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, UK, 1984).

Rosenbluth, A. W.

N. Metropolis, A. W. Rosenbluth, N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculation by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Rosenbluth, N.

N. Metropolis, A. W. Rosenbluth, N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculation by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Shih, S. E.

Shin, R. T.

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

Sihvola, A. H.

A. H. Sihvola, J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
[CrossRef]

A. H. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, London, 1999).

Steele, W. A.

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Teixeira, F. L.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, J. A. Kong, L. Tsang, “Monte Carlo simulation of electromagnetic wave propagation in dense random media with dielectric spheroids,” IEICE Trans. Electron. E83-C, 1797–1802 (2000).

Teller, A. H.

N. Metropolis, A. W. Rosenbluth, N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculation by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Teller, E.

N. Metropolis, A. W. Rosenbluth, N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculation by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Thiele, E.

E. Thiele, “Equation of state for hard spheres,” J. Comput. Phys. 39, 474–479 (1963).

Tildesley, D. J.

M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids (Oxford U. Press, New York, 1989).

Tsang, L.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, J. A. Kong, L. Tsang, “Monte Carlo simulation of electromagnetic wave propagation in dense random media with dielectric spheroids,” IEICE Trans. Electron. E83-C, 1797–1802 (2000).

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

L. M. Zurk, L. Tsang, D. P. Winebrenner, “Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow,” Radio Sci. 31, 803–819 (1996).
[CrossRef]

L. Tsang, J. A. Kong, “Scattering of electromagnetic waves from a dense medium consisting of correlated Mie scatterers with size distributions and applications to dry snow,” J. Electromagn. Waves Appl. 6, 265–286 (1992).
[CrossRef]

L. Tsang, C. Mandt, 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]

C. Mandt, Y. Kuga, L. Tsang, A. Ishimaru, “Microwave propagation and scattering in a dense distribution of spherical particles: experiment and theory,” Waves Random Media 2, 225–234 (1992).
[CrossRef]

K.-H. Ding, L. Tsang, “Effective propagation constants and attenuation rates in media of densely distributedcoated dielectric particles with size distributions,” J. Electromagn. Waves Appl. 5, 117–142 (1991).
[CrossRef]

L. Tsang, “Scattering of electromagnetic waves from a half space of nonspherical particles,” Radio Sci. 19, 1450–1460 (1984).
[CrossRef]

L. Tsang, J. A. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71, 552–558 (1982).
[CrossRef]

L. Tsang, J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
[CrossRef]

L. Tsang, J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley-Interscience, New York, 2001).

L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, New York, 2000).

L. Tsang, J. A. Kong, K.-H. Ding, C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, New York, 2001).

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

Twersky, V.

V. Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

V. Twersky, “Coherent scalar field in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 18, 2468–2486 (1977).
[CrossRef]

Varadan, V. K.

V. V. Varadan, Y. Ma, V. K. Varadan, “Anisotropic dielectric properties of media containing aligned nonspherical scatterers,” IEEE Trans. Antennas Propag. AP-33, 886–890 (1987).

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

Varadan, V. V.

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

V. V. Varadan, Y. Ma, V. K. Varadan, “Anisotropic dielectric properties of media containing aligned nonspherical scatterers,” IEEE Trans. Antennas Propag. AP-33, 886–890 (1987).

Weiglhofer, W. S.

W. S. Weiglhofer, “Dyadic Green’s functions for general uniaxial media,” IEE Proc. H 137, 5–10 (1990).

Wertheim, M. S.

M. S. Wertheim, “Exact solution of the Percus–Yevick integral equation for hard spheres,” Phys. Rev. Lett. 20, 321–323 (1963).
[CrossRef]

Winebrenner, D. P.

L. M. Zurk, L. Tsang, D. P. Winebrenner, “Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow,” Radio Sci. 31, 803–819 (1996).
[CrossRef]

Yaghjian, A. D.

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

Yevick, G. J.

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

Zurk, L. M.

L. M. Zurk, L. Tsang, D. P. Winebrenner, “Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow,” Radio Sci. 31, 803–819 (1996).
[CrossRef]

Appl. Opt. (1)

IEE Proc. H (1)

W. S. Weiglhofer, “Dyadic Green’s functions for general uniaxial media,” IEE Proc. H 137, 5–10 (1990).

IEEE Trans. Antennas Propag. (1)

V. V. Varadan, Y. Ma, V. K. Varadan, “Anisotropic dielectric properties of media containing aligned nonspherical scatterers,” IEEE Trans. Antennas Propag. AP-33, 886–890 (1987).

IEEE Trans. Geosci. Remote Sens. (1)

A. H. Sihvola, J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
[CrossRef]

IEICE Trans. Electron. (1)

B. E. Barrowes, C. O. Ao, F. L. Teixeira, J. A. Kong, L. Tsang, “Monte Carlo simulation of electromagnetic wave propagation in dense random media with dielectric spheroids,” IEICE Trans. Electron. E83-C, 1797–1802 (2000).

J. Acoust. Soc. Am. (1)

L. Tsang, J. A. Kong, T. Habashy, “Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with quasicrystalline and Percus–Yevick approximation,” J. Acoust. Soc. Am. 71, 552–558 (1982).
[CrossRef]

J. Appl. Phys. (1)

L. Tsang, J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485 (1980).
[CrossRef]

J. Chem. Phys. (1)

N. Metropolis, A. W. Rosenbluth, N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculation by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

J. Comput. Phys. (1)

E. Thiele, “Equation of state for hard spheres,” J. Comput. Phys. 39, 474–479 (1963).

J. Electromagn. Waves Appl. (2)

K.-H. Ding, L. Tsang, “Effective propagation constants and attenuation rates in media of densely distributedcoated dielectric particles with size distributions,” J. Electromagn. Waves Appl. 5, 117–142 (1991).
[CrossRef]

L. Tsang, J. A. Kong, “Scattering of electromagnetic waves from a dense medium consisting of correlated Mie scatterers with size distributions and applications to dry snow,” J. Electromagn. Waves Appl. 6, 265–286 (1992).
[CrossRef]

J. Math. Phys. (2)

V. Twersky, “Coherent scalar field in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 18, 2468–2486 (1977).
[CrossRef]

V. Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. D (1)

N. Harfield, “Conductivity calculation for a two-phase composite with spheroidal inclusions,” J. Phys. D 32, 1104–1113 (1999).
[CrossRef]

Mol. Phys. (1)

J. L. Lebowitz, J. W. Perram, “Correlation functions for nematic liquid crystals,” Mol. Phys. 50, 1207–1214 (1983).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (2)

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

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

Phys. Rev. B (2)

B. L. Gyorffy, “Electronic states in liquid metals: a generalization of the coherent-potential approximation for a system with short-range order,” Phys. Rev. B 1, 3290–3299 (1970).
[CrossRef]

J. Korringa, R. L. Mills, “Coherent-potential approximation for random systems with short range correlations,” Phys. Rev. B 5, 1654–1655 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

M. S. Wertheim, “Exact solution of the Percus–Yevick integral equation for hard spheres,” Phys. Rev. Lett. 20, 321–323 (1963).
[CrossRef]

Proc. IEEE (1)

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

Radio Sci. (3)

L. M. Zurk, L. Tsang, D. P. Winebrenner, “Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow,” Radio Sci. 31, 803–819 (1996).
[CrossRef]

L. Tsang, “Scattering of electromagnetic waves from a half space of nonspherical particles,” Radio Sci. 19, 1450–1460 (1984).
[CrossRef]

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

Rev. Mod. Phys. (1)

J. A. Barker, D. Henderson, “What is “liquid”? Understanding the states of matter,” Rev. Mod. Phys. 48, (1976).

Waves Random Media (1)

C. Mandt, Y. Kuga, L. Tsang, A. Ishimaru, “Microwave propagation and scattering in a dense distribution of spherical particles: experiment and theory,” Waves Random Media 2, 225–234 (1992).
[CrossRef]

Other (11)

L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, New York, 2000).

A. H. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, London, 1999).

L. Tsang, J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley-Interscience, New York, 2001).

L. Tsang, J. A. Kong, K.-H. Ding, C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, New York, 2001).

M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids (Oxford U. Press, New York, 1989).

J. P. Hansen, I. R. McDonald, Theory of Simple Liquids (Academic, New York, 1986).

J. A. Kong, Electromagnetic Wave Theory (EMW, Cambridge, Mass., 2000).

H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-Free Approach (McGraw-Hill, New York, 1983).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, UK, 1984).

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

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Figures (7)

Fig. 1
Fig. 1

Scattering of electromagnetic waves by densely packed aligned prolate spheroids. The symmetry axis of the spheroid is chosen to be in the zˆ direction.

Fig. 2
Fig. 2

Effective permittivity as a function of fractional volume fv: comparison between QCA and QCA-CP. e=2 and εs=3.2.

Fig. 3
Fig. 3

Effective permittivity as a function of elongation ratio e=b/a: comparison between QCA and QCA-CP. fv=0.2 and εs=3.2.

Fig. 4
Fig. 4

Normalized extinction coefficient κe/k as a function of fractional volume fv: comparison between different methods. MC stands for Monte Carlo simulation, and ind stands for independent scattering approximation. ka=0.2, e=2, and εs=3.2.

Fig. 5
Fig. 5

Normalized extinction coefficient κe/k as a function of fractional volume fv: comparison between different methods. ka=0.1, e=2, and εs=3.2.

Fig. 6
Fig. 6

Normalized extinction coefficient κe/k as a function of fractional volume fv for lossy particles: comparison between different methods. ka=0.2, e=2, and εs=3.2+i0.01.

Fig. 7
Fig. 7

Normalized extinction coefficient κe/k as a function of elongation ratio e=b/a: comparison between different methods. ka=0.2, e=2, and εs=3.2.

Equations (108)

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Gs(r, r)=Go(r, r)+drGo(r, r)×U(r-rj)Gs(r, r),
U(r-rj)=ks2-k2 forPj<1(insidespheroid)0forPj>1(outsidespheroid),
Gs=Go+GoUjGs,
Gs=Go+GoTjGo,
Tj=Uj+UjGoTj.
Tj=(I-UjGo)-1Uj.
G=Go+Goj=1NUjG.
G=Go+Goj=1NQjGo,
Qj=Tj+TjGol=1,ljNQl.
E(G)=Go+NGoE(Ej(Qj))Go,
Ej(Qj)=Tj+(N-1)TjGoEj(Ejl(Ql))(jl).
Ejl(Ql)El(Ql).
Ej(Qj)=Tj+(N-1)TjGoEj(El(Ql))(jl),
p|Ej(Qj)|p=Q(p, p)exp[-i(p-p)  rj],
p|Tj|p=T(p, p)exp[-i(p-p)  rj],
C(p, p)=T(p, p)+nodp(2π)3 H(p-p)×T(p, p)Go(p)C(p, p),
C(p, p)Q(p, p)[I+noGo(p)Q(p, p)]-1.
G(p)=[Go-1(p)-noC(p, p)]-1.
det[Go-1(p)-noC(p, p)]=0.
Go-1-j=1NUjG=I.
G^o-1=Go-1-now,
U^j=Uj-1Vw.
G^o-1-j=1NU^jG=I,
E(G)=G^o.
G(p)=[Go-1(p)-noCˆ(p, p)]-1,
Cˆ(p, p)=t^j(p, p)+nodp(2π)3 H(p-p)×tˆ(p, p)G(p)Cˆ(p, p).
t^j=Uj+UjE(G)t^j.
Tm(r, p)=r|T|p.
Tm(r)=U(r)I+U(r)drGo(r, r)Tm(r).
Go(r, r)=-Lk2 δ(r-r)+ik6πI,
Lc=-1-e˜2e˜21+12e˜ln1-e˜1+e˜,
La=12 (1-Lc)
Tm(r)=Tor insidespheroid0,r outsidespheroid,
To=1ks2-k2I+1k2L-ikv6πI-1.
To=3k2ηI+ik3v2πη,
η=13 (ks2-k2)[k2I+(ks2-k2)L]-1.
T(p, p)=drexp(-ip  r)Tm(r, p)vTo.
C(p, p)=vTo+fvTodp(2π)3 H(p-p)×Go(p)C(p, p),
C(p, p)=Co,
Co=I-fvTodp(2π)3 H(p)Go(p)-1vTo.
dp(2π)3 H(p)Go(p)=1k2L+1k6π HoI,
Co=I-fvToLk2+Iik6π Ho-1vTo.
Co=3k2vDη1+iDηk3v2π So,
D=(1-3fvηL)-1.
G-1(p)=(p2-k2)I-pp-noCo.
Gua-1(p)=p2I-pp-k2ε,
ε(eff)=I+1k2 noCo
=(I+3fvDη)+i(Dη)23fvk3v2π So.
εμ(eff)=1+fv(εs-1)1+(1-fv)(εs-1)Lμ,
εμ(eff)=k3v6π Sofv(εs-1)2[1+(1-fv)(εs-1)Lμ]2,
1εa K2=k2,
1εc (Kx2+Ky2)+1εa Kz2=k2,
tˆ=U+UE(G)tˆ,
G-1(p)=p2I-pp-k2ε(eff),
G(r, r)=-K-2Nδ(r-r)+i6πKM,
α=εcεa.
tˆ(p, p)=vt^o,
t^o=1ks2-k2I+K-2N-iv6πKM-1.
t^o=3K2ηˆI+iv2πK3ηˆ,
ηˆ=13 (ks2-k2)[K2+(ks2-k2)N]-1.
C^o=I-fvt^oK-2N+KMi6π Ho-1vt^o.
C^o=3vK2DˆηˆI+iDˆηˆMK3v2π So,
Dˆ=(I-3fvηˆN)-1.
ε(eff)=I+1k2 noC^o=[I+3fvε(eff)Dˆηˆ]+i 3fvk3v2π [ε(eff)]5/2(Dˆηˆ)2MSo.
εμ(eff)=1+εμ(eff)fv(εs-1)εμ(eff)+(1-fv)(εs-1)Nμ,
εμ(eff)=k3v6π SoMμ[εμ(eff)]5/2×fv(εs-1)2[εμ(eff)+(1-fv)(εs-1)Nμ]2,
εμ(eff)=1+εμ(eff)fv(εs-1)εμ(eff)+(1-fv)(εs-1)Nμ,
εμ(eff)=k3v6π SoMμ[εμ(eff)]5/2×fv(εs-1)2[εμ(eff)+(1-fv)(εs-1)Nμ]2,
εμ(eff)(MG)=1+fv(εs-1)1+(1-fv)(εs-1)Lμ,
g(r1, r2)=N-1N V2p(r1, r2)=N-1N Vp(r1|r2),
h(r)=g(r)-1.
h(r)=c(r)+nodrc(r)h(r-r),
u(r)=forP<10forP>1,
R=Ar,R=Ar.
h(R)=c(R)+34π fvdRc(R)h(R-R),
u(R)=forR<10forR>1.
S(p)=1+noH(p),
H(p)=drexp(-ip  r)h(r)
SoS(0)=(1-fv)4(1+2 fv)2.
= diag[εa, εa, εc].
××G(r, r)-k2εG(r, r)=Iδ(r-r),
G(r, r)=dp(2π)3exp[ip  (r-r)]G(p).
G-1(p)=p2(I-pˆpˆ)-k2ε.
Go-1(p)=(p2-k2)I-pp.
G-1(p)
=p2-px2-k2εa-pxpy-pxpz-pypxp2-py2-k2εa-pypz-pzpx-pzpyp2-pz2-k2εc.
 
det G-1(p)=0,
1εa p2=k2,
1εc (px2+py2)+1εa pz2=k2.
G(r, r)=14πεaA+1k2 exp(ikRe)Re+F1(R)+F2(R),
F1(R)=εaexp(ikRo)Ro-εcexp(ikRe)Re(R×zˆ)(R×zˆ)|R×zˆ|2,
F2(R)=exp(ikRo)-exp(ikRe)ik|R×zˆ|2×I-zˆzˆ-2 (R×zˆ)(R×zˆ)|R×zˆ|2,
Ro=εaR,
Re=(RtAR)1/2,
A=diag[εc, εc, εa].
14πεa  exp(ikRe)Re.
ge(Re)=14πRe,
K=k2ε,
B=εadiag[1, 1, α],
α=εcεa.
Re G(r, r)-K-2Nδ(r-r),
N=-BdSnˆge(Re)
e˜˜=1-α a2c21/2.
Nc=-1-e˜˜2e˜˜21+12e˜˜ln1-e˜˜1+e˜˜,
Na=12(1-Lc).
Im G(r, r)i6πKM,
M=diag34+α4, 34+α4, 1α.

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