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IEEE Transactions on Antennas and Propagation
Volume 48 Number 2, February 2000

Table of Contents for this issue

Complete paper in PDF format

T-Matrix Determination of Effective Permittivity for Three-Dimensional Dense Random Media

Paul R. Siqueira, Member, IEEE and Kamal Sarabandi Senior Member, IEEE

Page 317.

Abstract:

In this paper, we present a full wave method for determining the effective permittivity for random media in three dimensions. The type of media addressed is composed of spherical dielectric particles in a homogeneous dielectric background. The particle volume fraction ranges from 0 to 40% and dielectric contrast may be significantly different from the background medium. The method described relies on the T-matrix approach for solving Maxwell's equations using a spherical wave expansion in conjunction with a Monte-Carlo simulation for calculating the mean scattered field confined within a prescribed fictitious boundary. To find the effective permittivity, the mean scattered field is compared with that of a homogeneous scatterer whose shape is defined by the fictitious boundary and its dielectric constant is varied until the scattered fields are matched. A complete description of the T-matrix approach is given along with an explanation of why the recursive form of this technique (RATMA ) cannot be used for addressing this problem. After the method development is completed,the results of our numerical technique are compared against the theoretical methods of the quasi-crystalline approximation and the effective field approximation to demonstrate the region of validity of the theoretical methods. The examples contained within the paper use between 30 and 120 included spheres (with radii ranging from from ka = 0.6 to 0.8) within a larger, fictitious sphere of diameter kD = 8.4.

References

  1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, New York: Dover, 1965, p.  1046. 
  2. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles , New York: Wiley, 1983, p.  519. 
  3. W. C. Chew, Waves and Fields in Inhomogeneous Media, New York: IEEE Press, 1990, p.  608. 
  4. W. C. Chew, "Recurrence relations for three-dimensional scalar addition theorem", J. Electromagn. Waves Applicat., vol. 6, no.  2, pp.  133-142, 1992.
  5. W. C. Chew, Y. M. Wang and L. Gurel, "Recursive algorithm for wave-scattering solutions using windowed addition theorem", J. Electromagn. Waves Applicat., vol. 6, no. 11, pp.  1537-1560, 1992.
  6. W. C. Chew and C. C. Lu, "The resurive aggregate interaction matrix algorithm for multiple scatterers", IEEE Trans. Antennas Propagat., vol. 43, pp.  1483-1486,  Feb.  1995.
  7. A. Nashashibi and K. Sarabandi, "A technique for measuring the effective propagation constant of dense random media", IEEE AP-S Int. Symp., Newport BeachCA 748751 June1995
  8. J. Percus and G. Yevick, "Analysis of classical statistical mechanics by means of collective coordinates", Phys. Rev., vol. 110, pp.  1-113,  1958.
  9. B. Peterson and S. Storm, "T-matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3)", Phys. Rev. D, vol. 8, no. 10, pp.  3661-3678, 1973.
  10. D. Polder and J. H. VanSanten, "The effective permeability of mixtures of solids", Physica, vol. 12, no. 5, pp.  1257-1271, 1946.
  11. K. Sarabandi and P. R. Siqueira, "Numerical scattering analysis for two-dimensional dense random media", in IEEE Antennas Propagat. Conf. Proc., Seattle, WA, May 1994, pp.  858-867. 
  12. K. Sarabandi and P. R. Siqueira, "Numerical scattering analysis for two-dimensional dense random media: Characterization of effective permittivity", IEEE Trans. Antennas Propagat., vol. 45, pp.  858-867, May  1997.
  13. P. R. Siqueira, K. Sarabandi and F. T. Ulaby, "Numerical simulation of scatterer positions in a very dense media with an application to the two-dimensional born approximation", Radio Sci., vol. 30, no. 5, pp.  1325 -1339, Sept./Oct.  1995.
  14. P. Siqueira and K. Sarabandi, "Method of moments evaluation of the two-dimensional quasicrystalline approximation", IEEE Trans. Antennas Propagat., vol. 44, pp.  1067-1077, Aug.  1996.
  15. L. Tsang, J. Kong and R. Shin, Theory of Microwave Remote Sensing, New York: Wiley, 1985.
  16. 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., vol. 17, no. 5, pp.  314-316, 1992.
  17. Y. M. Wang and W. C. Chew, "A recursive T-matrix approach for the solution of electromagnetic scattering by many spheres", IEEE Trans. Antennas Propagat., vol. 14, pp.  1633-1639, Dec.  1993.
  18. P. C. Waterman, "Matrix formulation of electromagnetic scattering", in IEEE Proc., vol. 53, Aug. 1965, pp.  805- 812. 
  19. 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. Amer. A, vol. 12, pp.  1772-1781, 1995.
  20. L. M. Zurk, L. Tsang and D. P. Winebrenner, "Scattering properties of dense media from Monte Carlo simulations with the application to active remote sensing of snow", Radio Sci., vol. 31, pp.  803-819, 1996.