Analysis of a photonic crystal band-edge resonator embedded in a negative electric permittivity medium

Abstract

In recent years, artificial structures with characteristic dimensions much smaller than a wavelength, the so-called metamaterials, have been demonstrated experimentally. Some of these materials have interesting properties, such as negative electric permittivity and/or magnetic permeability. Although metamaterials are often based on metallic structures, they can also be created with nonmetallic structures. Photonic crystals (PhCs) may be considered as being a specific type of metamaterial with (ideally) a purely dielectric combination of at least two separate characteristic materials and periodic structuring. (Metamaterial PhCs will have effective negative electric permittivities.) In solid state physics, the solution of the Dirac equation for two distinct regions of positive and negative masses is a bound state at the interface between the two regions. In an analogy with solid state physics, we study the propagation of electromagnetic waves emerging from a band-edge resonator (with positive refractive index) into a region of negative refractive index; we show that an evanescent wave can be created in the negative index region, the properties of which are strongly dependent on the filling factor of the PhC medium.