Finite element modeling of periodic structures

Periodic structures have a variety of important applications in modern technologies and engineering due to their unique electromagnetic properties. Commonly used periodic structures include frequency selective surfaces, optical gratings, phased array antennas, photonic bandgap materials, and various metamaterials. The analysis of periodic structures has always been an important topic in computational electromagnetics. In this chapter, we describe an accurate and efficient numerical analysis, based on a higher-order finite element method (FEM), for characterizing the electromagnetic properties of periodic structures. Based on the Floquet theory, periodic boundary conditions and radiation conditions are first derived for the unit cell of a periodic structure. The FEM is then applied to solve Maxwell’s equations in the unit cell. To enhance the accuracy and efficiency of the FEM, curvilinear elements are employed to discretize the unit cell and higher-order vector basis functions are used to expand the electric field. The asymptotic waveform evaluation (AWE) is implemented to perform fast frequency and angular sweeps. To demonstrate the capability of the proposed FEM, we apply it to the analysis of periodic absorbers, frequency selective structures, and phased array antennas. For the antenna analysis, a rigorous waveguide port condition is developed to accurately model the antenna feed structures. In all the cases studied, satisfactory results are obtained.