Abstract
Applications of photonic crystal are numerous. The key point to the application of photonic crystals is the photonic band gap, a range of forbidden frequencies for electro-magnetic waves which propagate in the crystal. In order to find photonic crystals with large photonic band gap, we need to calculate band structures of photonic crystals. For this reason, calculation of band structure with high efficiency is an important topic. Our lab has constructed an 1D effective model to calculate the band structure of 2D photonic crystals. With the inclusion of degenerate perturbation, the approximation of the effective model works well in the case of 2D photonic crystal band structure calculated along any direction. We extend this method to 3D photonic crystal calculation with modification specifically made to take into account the 3D nature of the crystal. We make error/accuracy analysis of different approximations, to achieve a solution with high efficiency.