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