Analysis of truncated gratings and a novel technique for extrapolating their characteristics to those of infinite gratings

Periodic gratings, such as Frequency Selective Surfaces (FSSs) and EBG (electromagnetic band gap) structures, are used in a wide variety of electromagnetic applications and are typically analyzed under the assumption that they are infinite periodic. Since the real-word structures are necessarily finite, and are derived by truncating the corresponding infinite structures, it is of interest to determine how large the finite structure needs to be so that it mimics its infinite counterpart. A related question is how to extrapolate the simulation results of a finite structure to predict the performance of the corresponding infinite structure in a computationally efficient manner. The objectives of this work are to address both of these questions and to present a novel computational technique which hybridizes analytical and numerical techniques to provide the answers. We illustrate the application of the proposed technique by considering the test case of plane wave scattering by a strip grating and investigate the asymptotic behavior of the solution for the current on a truncated periodic grating as we increase its size. The proportionality constant, relating the current distribution on the unit cell of the infinite grating to the corresponding distribution in the truncated grating, is computed, and its asymptotic value is accurately predicted by using an extrapolation algorithm presented in the paper. The required number of strips is estimated such that the current on the finite structure is sufficiently close to that on the infinite one. The results obtained for the current are found to be in excellent agreement with those derived from full-wave simulations