École Nationale Supérieure de
Techniques Avancées

Abstract

Metamaterials are composite synthetic materials which exhibit particular properties. They have gain a lot of interest over the past decade, as they enable to design new useful tools in a wide range of domains, from aerospace to medicine. In particular, the mathematical study of metamaterial is crucial as it allows to understand the properties of the materials, and thus allows to design new metamaterials whose prop- erties meet a certain need. In this work, we focus an a type of metamaterials called photonic crystals. It consists in a three dimensional periodic structure which is made of two materials with different dielectric constants. Such crystals modify the propagation of electromagnetic waves and in particular, they present band gaps i.e. ranges of frequencies which can not propagate in the crystal. This peculiar property makes photonic crystals very useful, as they can be used to create waveguides, filters, microcavities and more.