HOMOGENIZATION OF THE SYSTEM OF HIGH-CONTRAST MAXWELL EQUATIONS

We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities is an element of 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 is an element of is of the order eta(2), where eta > 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 eta -> 0, and derive the limit system of Maxwell equations in R-3. 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.