Closed-form analysis of the decoupling properties of artificial dielectric layers

We present an analytical formulation to model artificial dielectric layers (ADLs), for arbitrary field incidence. We first derive the solution for the magnetic current distribution on a single layer, under generic plane-wave illumination. This solution is found in closed-form by expanding the total current with proper entire-domain basis functions. Simple analytical expressions are also derived for the scattered field and the equivalent sheet impedance of the layer. The formulation is then extended to the multi-layer case, by including the higher-order interaction between parallel layers in analytical form. The method can be used, for example, to describe the radiation of a source located in the close proximity of the ADL. The theoretical analysis agrees well with simulations from commercial electromagnetic solvers and measurements from a X-band prototype.