Analysis of FSS with symmetrical periodic unit by ADI-FDTD combined with even-odd mode method

A hybrid method of alternating-direction implicit-finite-difference time-domain (ADI-FDTD) and even-odd mode method is proposed for the analysis of frequency selective surfaces (FSS) with symmetrical periodic unit. When a FSS is analyzed by conventional ADI-FDTD, the coefficient matrix of the linear equations derived from the implicit formulation is not a tri-diagonal matrix, then the equations can not be solved with the efficient forward-elimination and backward-substitution method. Thereby the computational efficiency decreases. In this paper, the time-domain periodic boundary conditions at the odd and even mode incidence are derived, respectively. When the periodic unit of FSS is symmetrical and these conditions are implemented, the coefficient matrix of the linear equations is still a tri-diagonal matrix. The scattered field of a 2D FSS, which is excited by the single-frequency obliquely incident TM-wave, is simulated by the proposed method. Compared with the computational results of regular FDTD and ADI-FDTD, perfect agreement of numerical results is achieved. High computational efficiency of the proposed method is demonstrated.