Projects per year
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), 719773] to the case of the full system of Maxwell equations.
Original language  English 

Pages (fromto)  475500 
Number of pages  26 
Journal  Mathematika 
Volume  61 
Issue number  2 
Early online date  27 Feb 2015 
DOIs  
Publication status  Published  May 2015 
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Projects
 1 Finished

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council