On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials

Tom G. Mackay, Akhlesh Lakhtakia, Andrew J. Duncana

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Under certain conditions, the Bruggeman formalism yields estimates of the effective constitutive parameters of homogenized composite materials (HCMs) which are physically implausible. Furthermore, under these conditions, the generalized Hashin-Shtrikman bounds (which are equivalent to the estimates of the effective constitutive parameters of the HCMs provided by the Maxwell Garnett formalism) exhibit strong resonances. The conditions are that (i) the real parts of the constitutive parameters of the constituent materials have opposite signs; and (ii) the constituent materials are weakly dissipative. These limitations - which we had previously established for isotropic dielectric HCMs - Are shown to afflict uniaxial dielectric HCMs.

Original languageEnglish (US)
Title of host publicationNanostructured Thin Films II
DOIs
StatePublished - Nov 23 2009
EventNanostructured Thin Films II - San Diego, CA, United States
Duration: Aug 5 2009Aug 6 2009

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume7404
ISSN (Print)0277-786X

Other

OtherNanostructured Thin Films II
CountryUnited States
CitySan Diego, CA
Period8/5/098/6/09

Fingerprint

homogenizing
Composite Materials
Homogenization
composite materials
Composite materials
Strong Resonance
formalism
estimates
Estimate

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Mackay, T. G., Lakhtakia, A., & Duncana, A. J. (2009). On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials. In Nanostructured Thin Films II [740406] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 7404). https://doi.org/10.1117/12.824619
Mackay, Tom G. ; Lakhtakia, Akhlesh ; Duncana, Andrew J. / On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials. Nanostructured Thin Films II. 2009. (Proceedings of SPIE - The International Society for Optical Engineering).
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Mackay, TG, Lakhtakia, A & Duncana, AJ 2009, On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials. in Nanostructured Thin Films II., 740406, Proceedings of SPIE - The International Society for Optical Engineering, vol. 7404, Nanostructured Thin Films II, San Diego, CA, United States, 8/5/09. https://doi.org/10.1117/12.824619

On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials. / Mackay, Tom G.; Lakhtakia, Akhlesh; Duncana, Andrew J.

Nanostructured Thin Films II. 2009. 740406 (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 7404).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - Under certain conditions, the Bruggeman formalism yields estimates of the effective constitutive parameters of homogenized composite materials (HCMs) which are physically implausible. Furthermore, under these conditions, the generalized Hashin-Shtrikman bounds (which are equivalent to the estimates of the effective constitutive parameters of the HCMs provided by the Maxwell Garnett formalism) exhibit strong resonances. The conditions are that (i) the real parts of the constitutive parameters of the constituent materials have opposite signs; and (ii) the constituent materials are weakly dissipative. These limitations - which we had previously established for isotropic dielectric HCMs - Are shown to afflict uniaxial dielectric HCMs.

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Mackay TG, Lakhtakia A, Duncana AJ. On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials. In Nanostructured Thin Films II. 2009. 740406. (Proceedings of SPIE - The International Society for Optical Engineering). https://doi.org/10.1117/12.824619