Method of moments simulation of infinite and finite periodic structures and application to high-gain metamaterial antennas

Recent years have seen a growing interest in a new kind of periodic structures called ``metamaterials'. These new artificial materials exhibit many new appealing properties, not found in nature, and open many new possibilities in the domain of antenna design. This thesis describes efficient numerical tools and methods for the analysis of infinite and finite periodic structures. A numerical simulation code based on the Method of Moments has been developed for the study of both large phased arrays and periodic metamaterials made of metal and/or dielectrics. It is shown how fast infinite-array simulations can be used in a first instance to approximately describe the fields radiated by large antenna arrays or compute transmission and reflection properties of metamaterials. These infinite-array simulations rely on efficient computation schemes of the doubly periodic Green's function and of its gradient. A technique based on eigenmode analysis is also described, that allows to efficiently compute the dispersion curves of periodic structures. Accounting for the finiteness of real structures is possible in good approximation thanks to a finite-by-infinite array approach. Moreover, the excitation of large finite periodic structures by a single (non periodic) source can be studied by using a combination of the Array Scanning Method with a windowing technique. All these techniques were validated numerically on several examples and it is finally shown how they can be combined to design high gain antennas, based on metamaterial superstrates excited by a slotted waveguide. The proposed design method relies on the separation of the whole structure in two different problems. An interior problem is used to optimize the input impedance of the antenna, while the radiation pattern can be optimized in the exterior problem.