The contribution corresponds to the electromagnetic modeling of fiber-reinforced periodically organized composites. The final goal is to gain a good understanding of their electromagnetic behavior as well as to acquire images that should exhibit the location of possibly damaged zones, and provide some quantification of these zones. The thesis focuses on the scattering of well-organized periodic structures and building up an efficient full-wave computational model for multilayered composites, wherein each layer is reinforced by a periodic array of fibers, which is the first step for further study of the disorganized one.

The work firstly considered the scattering problem of a slab in which infinite circular fibers, with the same radius, are periodically embedded with the same orientation of their axes and the same center-to-center distance. A 2-dimensional problem with normally and obliquely incident E- and H-polarized plane waves as well as Gaussian beams is firstly considered for understanding the principles and philosophies of the used mode-matching method and multipole expansion. Then the work is extended to the investigation of the scattering of the slab to a conically incident 3-dimensional electromagnetic wave, which shows the potential of the work for obtaining the response of the structure to a point source.

A more practical but complicated multilayered composite, constructed by stacking up the slabs one over the other, is further investigated. Two different composites are taken into account. To study the first composite, with fibers in different layers having the same orientations, T-matrix- and S-matrix-based methods are introduced into the work for solving the linear system produced by mode-matching at the boundaries between two adjacent layers. Then, further investigation of the second kind of composite, wherein the fibers within different layers are orientated into different directions, is carried out by extending the approach properly.

Some attention is also given to homogenization issues, so as to link small-scale approaches as developed in the thesis with large-scale ones as often considered in non-destructive testing of composite laminates.

Extensive numerical simulations are proposed, validated with results existing in the literature (notably the ones of photonic crystals) and by using brute-force solvers. Emphasis is also on special cases of composites (glass-fiber- and graphite-fiber-based ones) as most often faced in practical applications, with appropriate frequency bands chosen in harmony with the dielectric or conductive aspect of the reinforcing fibers.

**Composition du jury :**

O. Dazel, Professeur, Université du Maine, Le Mans, rapporteur,

A. Nicolet, Professeur, Aix-Marseille Université, Marseille, rapporteur,

J.-J. Greffet, Professeur, Laboratoire Charles Fabry de l'Institut d'Optique, Palaiseau, examinateur,

P. Joly, Directeur de recherche INRIA, Palaiseau, examinateur,

C. Reboud, Ingénieur-chercheur, CEA LIST, Département Imagerie Simulation pour le Contrôle, Saclay, examinateur,

D. Lesselier, Directeur de recherche CNRS, L2S, Gif-sur-Yvette, Directeur de thèse.