Homogenization of the system of high-contrast Maxwell equations

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 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.