Métamatériaux Electromagnétiques - Des Cristaux Photoniques aux Composites à Indice Négatif

Composite metamaterials are periodic metal-dielectric structures operating at wavelengths larger than the structure period. If properly designed these structures behave as homogeneous media described by effective permittivity and permeability parameters. These effective parameters can be designed to take values in domains that are not available in naturally occurring media; notably it is possible to design composite metamaterials with simultaneously negative permittivity and permeability, or, in other words, with a negative refractive index. However, in many experimental or numerical studies it is far from obvious that the use of a homogeneous model is justified for a given structure at a given wavelength. This issue is often glossed over in the literature. In this work I take a detailed look at the fundamental assumptions on which effective medium models rely and put forward a method for determining frequency domains where a given structure may or may not be accurately described by homogeneous effective medium parameters. This work opens the door to a more detailed understanding of the transition between homogeneous and inhomogeneous behavior in composite metamaterials, in particular by introducing the novel notions of custom made effective medium model, and of meta-photonic crystal