Determination of Effective Index of Refraction of Structured Materials (Photonic Crystals)

Photonic crystals have been widely studied by researchers due to their ability to control light propagation in all spatial directions. For example, 2D photonic crystals can be made of dielectric rods arranged in a square lattice. When light propagates through 2D photonic crystals, it experiences multiple scatterings by the crystal centers. The superposition of all scattered waves forms the transmitted field largely dependent upon the effective index of refraction of the structured material. We propose a method to determine the effective index of refraction through such materials with the Finite-Difference Time-Domain (FDTD) model. We set up the interface of two media, such as air and photonic crystal, modeled the refraction of the EM waves at the interface, collected the data from FDTD and analyzed the data in MATLAB using FFT2. The proposed method promises to be a simple tool for determining the effective index of refraction of structured materials