Homogenization of the system of high-contrast Maxwell equations

Cherednichenko, Kirill; Cooper, Shane

Abstract

We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities ε 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 ε is of the order η2, 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 R3. 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.

Citation

Cherednichenko, K., & Cooper, S. (2015). Homogenization of the system of high-contrast Maxwell equations. Mathematika, 61(02), 475-500. https://doi.org/10.1112/s0025579314000424

• Journal Article Type: Article
• Online Publication Date: Feb 27, 2015
• Publication Date: May 1, 2015
• Deposit Date: Oct 31, 2017
• Publicly Available Date: Apr 23, 2018
• Journal: Mathematika
• Print ISSN: 0025-5793
• Electronic ISSN: 2041-7942
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 61
• Issue: 02
• Pages: 475-500
• DOI: https://doi.org/10.1112/s0025579314000424
• Public URL: https://durham-repository.worktribe.com/output/1372704