Analytical and highly efficient numerical modeling of electromagnetic periodic structures

Periodic printed metallodielectric structures have been used for a long time to control the transmission, absorption and polarization of electromagnetic waves from the RF / microwave domains up to the optical range. During the last two decades, the modeling of these structures has become a popular research topic due several incentives. Such incentives are both of technical (frequency selective surfaces, reflectarrays, planar lenses, etc.) and scientific (extraordinary transmission, exotic diffraction effects, etc.) nature. In this contribution we present some recent advances carried out by our research group along two directions: (i) approximate analytical circuit-like models, and (ii) highly efficient computational methods. The goal is to develop fast and accurate tools to be used in conjunction with optimizers to design antennas, filters and other devices. These techniques also provide simple models to explain the exotic behavior of some periodic structures.