Closed-Form Analysis of Artificial Dielectric Layers—Part I: Properties of a Single Layer Under Plane-Wave Incidence

This two-part sequence of papers deals with the analysis of artificial dielectric layers (ADLs). ADLs consist of a cascade of planar periodic surfaces designed to realize dielectric slabs with a desired equivalent permittivity. A single layer is typically composed of an array of electrically small patches periodically arranged in a rectangular lattice. In this paper we present an analytical formulation to model a single layer for arbitrary plane-wave incidence, highlighting the characteristic properties and their frequency range of validity. We derive a closed-form solution for the magnetic current distribution, including the reactive near field on the crossing slots, by expanding the total current with ad-hoc entire-domain basis functions. Simple analytical expressions are also derived for the equivalent sheet impedance of the layer. The second part of the paper extends the analysis to finite ADL slabs and nonplane wave sources.