### Reference:

Cherednichenko, K. and Cooper, S., 2015. Homogenization of the system of high-contrast Maxwell equations. *Mathematika*, 61 (2), pp. 475-500.

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### Official URL:

http://dx.doi.org/10.1112/S0025579314000424

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### 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 η<sup>2</sup>, 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 R<sup>3</sup>. 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.

Item Type | Articles |

Creators | Cherednichenko, K.and Cooper, S. |

DOI | 10.1112/S0025579314000424 |

Related URLs | |

Departments | Faculty of Science > Mathematical Sciences |

Refereed | Yes |

Status | Published |

ID Code | 42125 |

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