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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 23, Iss. 16 — Aug. 15, 1984
  • pp: 2718–2728

Frequency dependent dielectric constant and conductivity for a medium containing impurities

Donald G. Burkhard  »View Author Affiliations


Applied Optics, Vol. 23, Issue 16, pp. 2718-2728 (1984)
http://dx.doi.org/10.1364/AO.23.002718


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Abstract

A formula is derived for the effective complex dielectric constant of a dielectric medium containing a cubical array of dielectric or metallic impurities. The formula is given to two levels of approximation; one based on the Clausius-Mosotti equation which assumes zero contribution to the polarization from dipoles within the Lorentz sphere. The second is a generalization of a more accurate calculation of Rayleigh. Specific expressions are given for the real dielectric constant and the effective conductivity (and loss tangent) both as a function of frequency and impurity content. Formulas are valid for wavelengths large compared with the dimensions of the impurities. Results are compared with experimental values of Kharadly and Jackson. The complex dielectric constant is also obtained from the more accurate dc formula for a uniform array of spheres embedded in a uniform dielectric as derived by Zuzovsky and Brenner and again from the dc formula of a random array as derived by Felderhof.

© 1984 Optical Society of America

History
Original Manuscript: March 23, 1984
Published: August 15, 1984

Citation
Donald G. Burkhard, "Frequency dependent dielectric constant and conductivity for a medium containing impurities," Appl. Opt. 23, 2718-2728 (1984)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-23-16-2718


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References

  1. J. W. Rayleigh, “On the Influence of Obstacles Arranged in Rectangular Order upon the Properties of a Medium,” Philos. Mag. 34, 481 (1982).
  2. W. K. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1955), p. 33.
  3. J. R. Reitz, F. J. Milford, R. W. Christy, Foundations of Electromagnetic Theory (Addison-Wesley, Reading, Mass., 1980).
  4. M. M. Z. Kharadly, W. Jackson, “The Properties of Artificial Dielectrics Comprising Arrays of Conducting Elements,” Proc. Inst. Elec. Engrs. 100, 199 (1953).
  5. M. Zuzovsky, H. Brenner, “Effective Conductivities of Composite Materials Composed of Cubic Arrangements of Spherical Particles Embedded in an Isotropic Matrix,” Z. Angew. Math. Phys. 28, 979 (1977). [CrossRef]
  6. B. U. Felderhof, “Bounds for the Effective Dielectric Constant of a Suspension of Uniform Spheres,” J. Phys. 15, 1731 (1982).
  7. H. Frohlich, Theory of Dielectrics (Oxford U.P., London, 1949).
  8. C. J. F. Böttcher, P. Bordewijk, Theory of Elec. Polarization (Elsevier, New York, 1978).
  9. I. Runge, “On the Electrical Conductivity of Metallic Aggregates,” Z. Tech. Phys. 6, 61 (1925).
  10. D. A. DeVries, “Het Warmtegeleidingsvermogen van grond,” Meded. Landbouwhogesch. Wageningen 52, 1 (1952).
  11. A. S. Sangani, A. Acrivos, “The Effective Conductivity of a Periodic Array of Spheres,” Proc. R. Soc. London Ser A 386, 263 (1983). [CrossRef]
  12. J. G. Kirkwood, “On the Theory of Dielectric Polarization,” J. Chem. Phys. 4, 592 (1936). [CrossRef]
  13. J. Yvon, Recherches sur la Theorie Cinetique des Liquides (Hermann, Paris, 19).
  14. D. A. G. Bruggeman, “Calculations of Various Physical Constants of Heterogeneous Substances: Part I. Dielectric Constants and Conductivity of Mixtures of Isotropic Substances,” Ann. Phys. 24, 636 (1935). [CrossRef]

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