Analytical expressions for reflection coefficients of artificially soft and hard surfaces: dielectric slab loaded with a periodic array of strips over a ground plane

Simple and closed form expressions for plane wave reflection coefficients of a dielectric slab loaded with a periodic array of strips over a ground plane are presented for use in antenna applications. In the analysis, a set of integral equations for the fields between the strips and dielectric slab are derived from the three-dimensional boundary value problem. Using the low frequency approximation, closed form expressions were obtained for the reflection coefficients. Numerical comparison with the point matching method shows that the accuracy is excellent in practical uses. The frequency bandwidth of the surfaces at the artificially soft and hard boundaries is discussed