Photonic crystal is a kind of new-style artificial crystal, which is composed of periodically structured electromagnetic mediums. Because of the unique performance and potential huge application, the people have enormous interest to the theoretical analysis and laboratorial research on photonic crystals. Presently, the complete band gap and defect characteristics are still the important research directions in this domain. The relation between complete bandgap and three main influence factors, lattice structure, fill ratio, dielectric constant ratio of two dimensional dielectric column and air column photonic crystal based on Al2O3, Si and Ge is studied.According to the computed result, we mainly aim at three kinds of structures which are easily to get complete bandgap to carry on the key computation. The dielectric constant ratio is changed from 8-40, and the fill ratio is changed simultaneously to seek for the design parameters of biggest complete bandgap and the change rule of the bandgap.The band structure of two dimensional square lattice photonic crystal with point defect is computed. The band structure and localized modes of two dimensional photonic crystal straight waveguide and L-shape curving waveguide is calculated, and it's transmission characteristic is also simulated.
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