A hybrid spectral-FDTD/ARMA method for periodic structure analysis

Periodic structures are widely used in microwaves and antennas, such as waveguides, frequency selective surfaces (FSS), and novel metamaterials. The finite-difference time-domain (FDTD) method has been used to analyze these structures, and various periodic boundary conditions (PBC) have been developed to enclose the computational domain. Among various techniques, a spectral FDTD approach was first proposed to solve guided wave property in periodic structures and later expanded to calculate the plane wave reflection and transmission. An advantage of the spectral FDTD method is its capability to analyze the plane wave and guided wave properties in a unified manner. When both plane wave and guided wave are computed simultaneously using the spectral FDTD method, the resonant behavior of a periodic structure such as surface wave modes will deteriorate the simulation results. In this paper, an auto-regressive moving-average (ARMA) estimator is combined with the spectral FDTD method to solve the resonance problem. This new hybrid technique not only characterizes the periodic structures with resonance but also identifies the eigen-frequencies of guided wave modes automatically. The efficiency and accuracy of the proposed method is demonstrated through numerical examples.