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 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 of the order , where is the period of the medium. We determine the asymptotic behaviour of the electromagnetic response of such a medium in the “homogenization limit”, as , and derive the limit system of Maxwell equations in . 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.