Two-dimensional Photonic Crystal Band-gap Defect Model Of Fdtd Numerical Study

In this paper we simulated two-dimensional photonic crystals by using the Finite Difference Time Domain method(FDTD). The main topics of this thesis are listed as follows:1. We introduced the conception and character of the photonic crystals, and summarized the research on photonic crystals in theory, experiment and application. The general principle of FDTD method was introduced, and special care is given to the application of FDTD on the simulation of two-dimensional photonic crystals.2. Two-dimensional photonic crystals was simulated by using the Finite Difference Time Domain method. The program code was written in both Fortran and Matlab. Our FDTD simulator and the associated FFT postprocessing program were validated by the comparison of others' results and ours. Two-dimensional photonic crystals with heterostructure was proposed. Our numerical analysis showed that a larger band gap was found. Its band gap is the sum of all the fractions. When the packing ratio equals to the best value,the band gap is maximal,and the central frequency of the band gap become smaller while the packing ratio becoming larger.The shape of the cross-section of the medium rod is also one of factors that affect the position and width of the band gap,that is if the packing ratio is same, the shape of the cross-section is different ,its band gap are also different.3. The localized mode was found in the point defect of Two-dimensional photonic crystals, the frequency of the defect mode is concerned its dielectric constant. Its magnitude is diminished if the dielectric constant increased and the central frequency of the Defect Mode is linear to the dielectric index of the defect approximately. The distribution of the energy was listed by the graph. The amplitude of the defect mode is at the most in the centre, the farther from thecentre the amplitude is diminished.4. The transmission of the light waves in empty space and photonic crystals was visualized by matlab in order to understand the its rule. The wave is controlled by the photonic crystals. Some of energy exists in medium rod.