Analysis of Nonsquare Artificial Dielectric Layers and Application to the Design of Anisotropic Slabs

We present a general analysis to describe nonsquare artificial dielectric layers (ADLs). Closed-form expressions for the equivalent layer impedance are given for generic plane-wave incidence, assuming that the ADLs have different geometrical parameters in the
${x}$
- and
${y}$
-directions. The analytical expressions account for the interaction between the layers due to higher order Floquet modes, thus remain valid for arbitrarily small electrical distance between layers. Such nonsquare geometries allow the design of artificial anisotropic slabs with azimuth-dependent effective refractive index. As an example for an application, the equivalent model is used to design the superstrate of a double-slot antenna, with independent pattern shaping in the two main planes.