Wideband analysis of periodic electromagnetic elements

This paper describes the application of an efficient implicit finite-difference time-domain method (FDTD) based on the locally one-dimensional (LOD) scheme to the analysis of periodic band-gap structures. In particular, the technique of oblique incidence is introduced into the periodic LOD-FDTD method. To maintain a tridiagonal system of linear equations, we newly develop a three-step algorithm consistent with the LOD procedure. In addition, the Sherman-Morrison formula is used to solve a cyclic matrix problem resulting from the application of the implicit scheme to the periodic boundary condition. The effectiveness of the present method is investigated through the analysis of periodic band-gap structures at oblique incidence. It is shown that the method efficiently provides the transmission spectrum, compared with the traditional explicit periodic FDTD method.