Comparison of FT-FDTD and Spectral Domain FDTD for Periodic Structures

In recent years, the metamaterials and its applications to antenna and other fields have been widely investigated theoretically and experimentally. The metamaterials are usually realized by some periodic structures composed of a conductor and/or dielectric/magnetic materials. In order to design the characteristics of metamaterial properly, some theoretical and/or numerical techniques are required. The FDTD method is recognized as a powerful analyzing method for the metamaterials, because considerably, complicated phenomena can be analyzed easily. Furthermore, some techniques have been proposed to analyze the periodic structures using the FDTD method. One of which is the Spectral Domain FDTD method. This method has a very simple algorithm, and gives stable results, but this method can be applied only for a single frequency in general. The another one is called Field-Transformation (FT-FDTD)method proposed. This technique can be applied to a pulse response, but, requires some additional variables to realize a periodic boundary condition, The Mur´s absorbing boundary condition is usually used in this method, for the simplicity. The application to the PML absorbing boundary is quite difficult because the more auxiliary variables are required. Furthermore, it has been found that some instability occurs when analyzing an oblique incident wave. In the first half, the spectral domain and FT-FDTD methods are briefly reviewed. In the second half, we analyze some periodic structures and we compare FT-FDTD method and spectral domain FDTD.