Homogenization of the system of high-contrast Maxwell equations

Kirill Cherednichenko, Shane Cooper

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Abstract

We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities &epsilon have a high degree of contrast between each other. We assume that the ratio between the permittivities of the components with low and high values of &epsilon is of the order η<sup>2</sup>, where η>0 is the period of the medium. We determine the asymptotic behaviour of the electromagnetic response of such a medium in the homogenization limit, as η 0, and derive the limit system of Maxwell equations in R<sup>3</sup>. Our results extend a number of conclusions of a paper by Zhikov [On gaps in the spectrum of some divergent elliptic operators with periodic coefficients. St. Petersburg Math. J. 16(5) (2004), 719-773] to the case of the full system of Maxwell equations.

LanguageEnglish
Pages475-500
Number of pages26
JournalMathematika
Volume61
Issue number2
Early online date27 Feb 2015
DOIs
StatusPublished - May 2015

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Maxwell's equations
Homogenization
Permittivity
Periodic Coefficients
Elliptic Operator
Asymptotic Behavior
Composite

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Homogenization of the system of high-contrast Maxwell equations. / Cherednichenko, Kirill; Cooper, Shane.

In: Mathematika, Vol. 61, No. 2, 05.2015, p. 475-500.

Research output: Contribution to journalArticle

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