In the framework of this MSc thesis the analysis of core-shell leaky-wave lens antennas is presented, based on a combination of asymptotic and Physical Optics techniques. This study aims to develop an analysis approach which can be subsequently used for the optimization of the Fly’s Eye antenna concept, through enabling the investigation of shaped variations of the core lens. The main difficulty of this prospect refers to the surface of the core lens being in the near field of the leaky wave feeding structure, since the evaluation of the near field is in general a computationally inefficient process. Adhering to this conclusion, a big part of this thesis elaborates on a very fast approach for the derivation of the near field, through asymptotically approximating the involved integral expressions. More specifically, the presented method exploits the nature of the near field in the examined stratification through introducing an approximation in the integral expressions, which in turn enables their asymptotic evaluation in a straightforward manner. Subsequently, the near field on the core lens is combined with a set of Physical Optics techniques in order to develop a model for the integrated lens architecture of the Fly’s Eye antenna. Modelling the core-shell structure in such a manner enables its study in a much more computationally efficient fashion compared to the use of a full-wave simulator. In addition, it facilitates the investigation of structural alterations in the antenna concept, like shaped variations of the core lens. The derived model presented in this thesis also contributed to the measurement campaign of the Fly’s Eye antenna prototype, through identifying a problematic component in the assembled prototype.