Chapter one - Periodic arrays of dielectric resonators as metamaterials and photonic crystals

Abstract

This chapter introduces dielectric metamaterials (MMs) composed of periodic arrays of dielectric resonators and discusses as the nature of resonances in array “atoms,” the effects of periodicity, defining similarities between these arrays, and strongly modulated photonic crystals (PhCs). To highlight the specifics of dielectric MMs, conventional MMs composed of metal split-ring resonators (SRRs) and cut wires are described first. It is shown how the responses of SRRs can be characterized by Lorentz-type resonances and responses of cut wires by the relations obtained from the Drude model, and how the properties of MMs are explained in frames of the effective medium approximation. Then, the first realizations of MM properties in arrays of dielectric resonators are described. This is followed by the discussion of such unusual phenomena as negative refraction and wave propagation with superluminal phase velocity, which were found to be characteristic for both MMs and PhCs. Dualism of the properties expected from dielectric MMs is stressed out.