Effective medium properties of finely periodic substrates

This work aims to create high-Q bandgap resonators and filters by making fine periodic structures inside an otherwise homogeneous material. The result is to create local control of the dielectric constant and loss tangent. The analytical evaluation of the effective medium is done by both quasi-static and full wave simulations. The focus of the analysis is mainly on three types of periodicities, the so called window pane periodicity, the stratified periodicity, and the cross-hatched periodic media. It is found that the type of small scale periodicity controls the effective dielectric constant to a great extent, with a stratified medium reducing the dielectric constant significantly more for a given amount of substrate removal than the window pane periodicity. Accurate characterization was achieved to within 0.5 % between the different analysis methods. Low-loss materials with loss properties that are better than that found in nature are determined, and therefore is a form of metamaterial in itself. In addition, the local control of the dielectric constant is an enabling step in creating bandgap metamaterials from a single constituent substrate.