This paper investigates an FDTD modeling method for precisely calculating the characteristics of a single, that is, a nonperiodic antenna located above a metasurface that consists of an infinite periodic conducting element on a flat dielectric substrate. The original FDTD method requires enormous computational resources to analyze such structures because an appropriate periodic boundary condition (PBC) is not supported, and a brute force approach has to be used for this reason. Another option is to use the array scanning method in which a single source is synthesized from a superposition of infinite phased array of point sources. In this method, some problems such as a mutual coupling between the single antenna and the metasurface, a computational error contained in a numerical integration over the Brillouin zone and so on have not been resolved yet. In order to resolve these difficulties and to reduce computational resources, a surface impedance boundary condition (SIBC) is incorporated into the FDTD method in this paper. The validity of the method is numerically confirmed by calculating an input impedance and a radiation pattern of a horizontal dipole antenna located above the metasurface.
Surface Impedance Boundary Condition With Circuit Coupling for the 3-D Finite-Element Modeling of Wireless Power Transfer