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.
Grating based integrated waveguide demultiplexer is one of the most promising types of planar waveguide DWDM devices. In order to reduce reflection loss of the grating, the grating facets need metallic coating for high efficiency. The analysis of retro-diffraction efficiency for echelle grating with metallic coating is given in the present paper by using a Finite-Difference Time-Domain (FDTD) method. This numerical method is more accurate and reliable than other methods such as the ray approximation method. Numerical simulation is given for S-polarized lights and the numerical results show that the loss is about 1dB.