The primary interest of the electromagnetic behavior of a periodic structure is in its near field and far field. However, it is still numerically difficult to analyze either one in the time domain. The primary goal of this dissertation is to develop corresponding time domain technique to analyze two topics. The first one is to evaluate the far field of a realistic, large antenna array using an efficient method. The second one is to evaluate the propagation characteristic of a commercially available printed circuit board (PCB) with intentional roughness. Both of which are hot topics in the antenna and signal integrity (SI) society respectively; however, none of them have ever been solved in the time domain.

To efficiently evaluate the far field pattern of a realistically large antenna array, the spectral domain method and the reciprocity theorem are implemented in the finite difference time domain (FDTD) technique to avoid the simulation of the near field. By taking advantage of the periodic boundary condition (PBC), the proposed method demonstrates its capability to speed up far field evaluation from hours to minutes. Good agreement of the results is provided for various cases: circular antenna array, arbitrary feeding array, and highly directional leaky wave antenna, etc.

Periodic structure modeling with finite sized feedings is developed by the array scanning method (ASM) implemented in the FDTD technique. The minimally coupled electric and magnetic co-mingled antenna array is evaluated by the method. Moreover, a commercially available PCB with very small roughness is modeled by the ASM-FDTD and the propagation characteristic is evaluated. Both are evaluated by time domain method for the first time. Efficiency in terms of memory and computing time is shown for this method and parallelization in the future is proposed.