HOMOGENIZATION OF THE SYSTEM OF HIGH-CONTRAST MAXWELL EQUATIONS. Issue 2 (27th February 2015) - Cherednichenko, Kirill
Abstract : We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities ${\it\epsilon}$ 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 ${\it\epsilon}$ is of the order ${\it\eta}^{2}$, where ${\it\eta}>0$ is the period of the medium. We determine the asymptotic behaviour of the electromagnetic response of such a medium in the "homogenization limit", as ${\it\eta}\rightarrow 0$, and derive the limit system of Maxwell equations in $\mathbb{R}^{3}$ . 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.