Analytical Formulas for Artificial Dielectrics with Nonaligned Layers

In this paper, we present analytical models to describe artificial dielectric layers (ADLs), when a lateral shift between layers is present. The alternate lateral displacement between layers is an important parameter to engineer the desired effective electromagnetic properties of the equivalent homogeneous material realized with the ADLs. More specifically, the equivalent dielectric constants that can be realized by alternatively shifting the layers are higher compared with the aligned case. Closed-form expressions are derived for the equivalent layer reactance that includes the higher order interaction between shifted layers. The given analytical formulas can be used to derive an equivalent circuit model that describes the scattering parameters of a plane wave impinging on a slab composed by an arbitrary finite number of metal layers. To aid the design of artificial dielectric slabs, the effective permittivity and permeability tensors are also retrieved from the scattering parameters.