The Numerical Study The Transmission Characteristics Of The Photonic Crystals Containing Metamaterials

Thanks to the intriguing electromagnetic properties of specific materials, introducing specific materials into photonic crystals will surely bring about lots of new phenomena and new rules. Take advantage of these new features can create new optical devices. By means of numerical stimulations and theoretical analysis, the transmission properties of photonic crystals containing specific materials were investigated. The major contents and most important results are given as follows:(1) Based on Maxwell equations, the transfer matrix and dispersion relation, which suitable for one-dimensional photonic crystal containing negative refractive index materials or single negative materials, was derived. The ordinary one-dimensional photonic crystal dispersion properties and band gap characteristics were analyzed by numeral simulated calculation.(2) Nonlinear kerr defect physical model was set up and the nonlinear part was stratified. Sub-layer recursive reverse transfer matrix method and sub-layer differential reverse iteration algorithm were put forward for this physical model.Both of them were described respectively, and then were compared and the accuracy of two methods was verified. And the various parameters affect the characteristics of optical bistability were studied, a deep-level discussion about the reasons for the emergence the optical bistability was discussed.(3) The band gap structure and defect mode of one-dimensional photonic crystals constituted by alternate layers of negative refraction and positive refraction materials were studied by means of transfer matrix. It's shown that, on normal incidence, the photonic crystals containing negative refraction material have wider photonic band gaps which is different from the case of traditional photonic crystals with narrow transmission bands. This kind of photonic crystal can be made narrow band filter. At the same time, we found that has a better angle perspective, it can be used to make high quality omni-directional reflector. Defects were introducted into this photonic crystal, found that the number of the defect modes increase with the width of the defect layer added. The defect modes distribute at the center frequency of the mirror symmetry. The number of defect modes must have the relationship of the thickness of the defect. This feature of the design of ultra-narrow filter has important reference value.(4) The photonic crystal with dispersive double-negative medium was studied in details. We find there are two photonic band gaps: the lower forbidden band which is called omni-directional photonic band gap remains nearly invariant under a various incident angle, while the higher one which is called Bragg gap changes ceaselessly with the increasing incident angle. There are two methods: insertion and substitution to introduce defects into the arranged photonic crystal,will have defect modes。The defect modes resulted from negative defect often appears in the omni-directional photonic band gap, while those resulted from positive defect usually appears in the Bragg gap.(5) The optical properties of one-dimensional photonic crystal with single-negative medium were studied in this chaper. Firstly, Transmission and dispersion were studied for multiple heterostructures consisting of two kinds of single-negative materials. Its also has omni-directional photonic band gap. Then introducted defect with positive refraction index. The omni-directional photonic band gap in the state will be with the local angle, unit scaling media thickness changes with relatively stable。When introduced a defect of single-negative material, found that the negative dielectric constant material impact on the band gap, but the negative magnetic permeability of the material not. The resonant tunneling modes in the construction of anegative magnetic permeability material and positive refraction index of materials were studied, and found that the location is mainly due to positive refraction index layer. The last study was conducted by two single-negative material composition of the photonic crystal heterostructure transmission characteristics; its mode of resonant tunneling is analyzed.