Abstract : The first part of this document is dedicated to the obtention of the effective properties of monodimensional photonic crystals. The procedure consists in identifying the dispersive and reflective properties of some crystal with the ones from a medium both homogeneous and anisotropic. This novel approach permits one to express the effective permittivity and permeability of a crystal by two tensors. Their expression gives a necessary criterion to observe impedance matching between one crystal and the environment. Such a criterion is adapted and then applied to bidimensional crystals.
The second part of the study is about the guiding of uniform quasi-TEM modes in a metallic waveguide via structured walls. The structures are the so-called hard surfaces. While the modal method is used to handle such surfaces, we use the fictitious sources method to model the associated waveguides. Map fields and dispersion curves reveal the behavior of the involved structures.