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

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

doi:10.1117/12.824619

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 proceeding › Conference contribution

1 Scopus citations

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 language	English (US)
Title of host publication	Nanostructured Thin Films II
DOIs	https://doi.org/10.1117/12.824619
State	Published - 2009
Event	Nanostructured Thin Films II - San Diego, CA, United States Duration: Aug 5 2009 → Aug 6 2009

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	7404
ISSN (Print)	0277-786X

Other

Other	Nanostructured Thin Films II
Country/Territory	United States
City	San Diego, CA
Period	8/5/09 → 8/6/09

All Science Journal Classification (ASJC) codes

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

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10.1117/12.824619

Cite this

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title = "On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials",

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.",

author = "Mackay, {Tom G.} and Akhlesh Lakhtakia and Duncana, {Andrew J.}",

year = "2009",

doi = "10.1117/12.824619",

language = "English (US)",

isbn = "9780819476944",

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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 proceeding › Conference contribution

TY - GEN

T1 - On limitations of conventional approaches to homogenization applied to uniaxial dielectric composite materials

AU - Mackay, Tom G.

AU - Lakhtakia, Akhlesh

AU - Duncana, Andrew J.

PY - 2009

Y1 - 2009

N2 - 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.

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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M3 - Conference contribution

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T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - Nanostructured Thin Films II

T2 - Nanostructured Thin Films II

Y2 - 5 August 2009 through 6 August 2009

ER -

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

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