Numerical analysis of semi-infinite frequency selective surfaces

Metamaterials are defined as synthetic structures which usually possess periodic symmetries and exhibit very promising electromagnetic properties. Some very wellknown examples are planar bulk metamaterials made of frequency selective surfaces (FSS) with double split ring resonator [1] or thin wires [2] as the patch unit cell. It is shown that an electromagnetic wave propagating within these structures experiences negative dielectric and magnetic constants in a certain frequency band. To explore the device performance, a very useful approach is analyzing the reflection and transmission of an incident field when hitting the surface of either a thick or semi-infinite slab of the bulk metamaterial. Like in the classical electromagnetics, analysis of the electromagnetic interaction at the boundary of a half-space metamaterial offers one an intuition of the field behavior within the material. However, development of an efficient method to fulfill this task is challenging. Recently, an impedance boundary condition is developed for the analysis of general semi-infinite structures [3]. The concept can be used for the analysis of semi-infinite FSS as well. By semi-infinite FSS, we mean a structure which comprises analogous layers of patches and substrates stacked on each other towards infinity in one direction. Each layer consists of a 2D periodic patch layer which may be either freestanding or printed on a substrate. This paper reports the way to utilize this boundary condition for a full-vector analysis of metallic metamaterials.