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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.

Original language | English |
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Pages (from-to) | 475-500 |

Number of pages | 26 |

Journal | Mathematika |

Volume | 61 |

Issue number | 2 |

Early online date | 27 Feb 2015 |

DOIs | |

Publication status | Published - May 2015 |

## Fingerprint Dive into the research topics of 'Homogenization of the system of high-contrast Maxwell equations'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Engineering and Physical Sciences Research Council

23/07/14 → 22/06/19

Project: Research council

## Cite this

*Mathematika*,

*61*(2), 475-500. https://doi.org/10.1112/S0025579314000424