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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 6 — Jun. 1, 2002
  • pp: 1145–1156

Analytical approximations in multiple scattering of electromagnetic waves by aligned dielectric spheroids

Chi O. Ao and Jin A. Kong  »View Author Affiliations

JOSA A, Vol. 19, Issue 6, pp. 1145-1156 (2002)

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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

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(290.0290) Scattering : Scattering
(290.2200) Scattering : Extinction
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles

Original Manuscript: June 7, 2001
Revised Manuscript: December 18, 2001
Manuscript Accepted: December 18, 2001
Published: June 1, 2002

Chi O. Ao and Jin A. Kong, "Analytical approximations in multiple scattering of electromagnetic waves by aligned dielectric spheroids," J. Opt. Soc. Am. A 19, 1145-1156 (2002)

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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]
  6. 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).
  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]
  10. 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]
  11. V. Twersky, “Coherent scalar field in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 18, 2468–2486 (1977). [CrossRef]
  12. V. Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978). [CrossRef]
  13. L. Tsang, “Scattering of electromagnetic waves from a half space of nonspherical particles,” Radio Sci. 19, 1450–1460 (1984). [CrossRef]
  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). [CrossRef]
  16. 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]
  17. J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958). [CrossRef]
  18. M. S. Wertheim, “Exact solution of the Percus–Yevick integral equation for hard spheres,” Phys. Rev. Lett. 20, 321–323 (1963). [CrossRef]
  19. E. Thiele, “Equation of state for hard spheres,” J. Comput. Phys. 39, 474–479 (1963).
  20. M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids (Oxford U. Press, New York, 1989).
  21. J. P. Hansen, I. R. McDonald, Theory of Simple Liquids (Academic, New York, 1986).
  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).
  31. L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, UK, 1984).
  32. N. Harfield, “Conductivity calculation for a two-phase composite with spheroidal inclusions,” J. Phys. D 32, 1104–1113 (1999). [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]
  35. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [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).

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