Analytical expressions for reflection coefficients of dielectric slab loaded with a periodic array of strips over a ground plane

Artificial soft and hard surfaces are intensively applied for antenna engineering. The importance of this kind of surface in antenna and propagation studies makes accurate and simple electromagnetic expressions necessary. The purpose of the present paper is to analyze the reflection coefficients of the strip gratings on a dielectric slab over a ground plane and by using the low frequency assumption, the simple closed form expressions of reflection coefficients are derived. These are based upon the singular integral equations approach developed for the analyses of gratings. We can use the simple expressions to design hard and soft surfaces artificially.