Fdtd Method On The Transmission Characteristics Of The Two-dimensional Photonic Crystal

Photonic crystal is a new type of optical and periodic structure that has refractive index periodicity in space with characteristic of photonic band gap. The application of the one-dimensional photonic crystal is restricted due to the simple structure. To the three-dimensional photonic crystal, the higher technologies must be required. Comparably, the two-dimensional photonic crystal has been shown to have a promising future because of many adjustable factors. So, the theoretical and applied study of two-dimensional photonic crystal has been one of the hottest topics in several areas such as physics, materials science and optical electronics.In this paper, the transmission characteristics of two-dimensional photonic crystal with triangular lattices are studied by using the Finite Difference Time Domain method (FDTD). The contents are presented as following:1. The background and the main properties of photonic crystal are introduced systematically. The main theoretical research methods and the fabricated methods are also discussed.2. The possible applications and the development of FDTD are introduced. The FDTD equations are derived in Cartesian coordinate system from Maxwell's equations. So, the value of electromagnetic field of every discretized lattice at any time can be obtained with the value of permittivity.3. The factors to affect the transmission characteristics are discussed. The results show that lattice structure, the sectional area and azimuth angle of dielectric rod affect the width of forbidden band. The transmission characteristics of different incident direction are further studied. It has no changes in the range of the low frequency, but the transmission coefficient decrease in the high frequency band near the original forbidden band with the increasing of incident angle, even new wider band gap appears.4. The transmission characteristics for line defects, compound defects and dope effects are studied, respectively. The effect of the compound defects combined with the dopes on transmission characteristic is further investigated. The results show that the thinner and the smaller of the refractive index of the embedded concentric triangular rod is, the wider the band gap is.5. The refraction for Gaussian beam through 2-D triangular lattice photonic crystal slab is simulated, and the imaging properties are studied. The results prove that the Gaussian beam undergoes a negative refraction in the interface of photonic crystal slab and air. This work will be of significance in further understanding of negative refraction.