Effective properties of a photonic crystal with air hole in multilayer dielectric structure

Photonic Crystals (PhCs) have been found to have exotic properties, such as the high dispersion and the slow group velocity, at different frequency range. It has also been reported that the photonic crystal can behave like a negative index material that is similar to the metallization based metamaterials composed of ring resonators and wires. It is essential to have knowledge about the effective properties of a photonic crystal to evaluate its performance. Here, we discuss a photonic crystal with air holes etched in a multilayer dielectric material. This structure can be cascaded to a three dimensional photonic crystal by simply stacking the porous multilayer film. Light is propagating perpendicularly through the multilayer film, and the transmission and reflection including both the magnitudes and the phases are obtained through numerical simulation. Effective properties along this direction, including the permittivity, the permeability and the effective refractive index, are calculated. From these basic and essential properties, other features such as dispersion, group velocity can be derived.