Study Of The Structures And Properties Of A Linear Gradient Photonic Crystals

Photonic crystals are a sort of new functional materials whose dielectric constant is periodic in three-dimensional space. Bandgap properties of photonic crystals can overcome the disadvantage of electronic crystals in several aspects, so Photonic Crystals have been researched in many field. Many great progresses have been made in theoretical studies, preparation techniques and practical applications. However, practical applications of photonic crystal in electronic engineering still faces many challenges, e.g. the bandgap depth and width can not meet the needs of practical engineering applications. Hence some useful exploration and study on Photonic Crystal with a novel structure were made in this thesis.In this thesis, a waveguide model was used for the systematic study of a linear gradient photonic crystal on the basis of finite element method analysis. By calculating the parameters S21, the forbidden band width of the structure were analyzed. The main topics and conclusions of our work are as follows:Firstly, two-dimensional photonic crystal structure with conventional square lattice structure, are made up of silicon and polyethylene. The radius of the dielectric cylinder are 0.12 a, 0.15 a, 0.2a, and 0.225 a. Studies of the relative width of the band gap indicates that when the cylinder radius is 0.15 a the relative width of the band gap reaches the maximum and the cylinder radius is adjustable to some extent, and the width of the band gap is stable. Photonic Crystals with point defects induced by dielectric constant and cylinder radius, have similar effect on the bandgap characteristics. It was found that changing the dielectric cylinder or the ratio of the dielectric constant can not enhance the relative band gap width to a certain level, which would restraint its practical value.Secondly, in order to obtain a larger bandgap width and better performance of the photonic crystal, we proposed a linear gradient structure which cylinder radius are grading in a linear way in direction of propagation of electromagnetic waves, i.e. the cylinder radius are rn=r0+n?, here r0 is base radius. It was shown that the gradient structure can promote relative bandgap width up to nearly 100 percent compared with the traditional lattice. ? is closely related to the width of the band gap. When delta is 0.05 the relative width of the bandgap will get to maximum. At some value of delta, there are some small resonant peaks in the range of bandgap.Finally, changing the ratio of the dielectric constant of gradient structure, it was found that the gradient structure can still significantly increase the relative bandgap width and its property is very stable. The results show that the gradient structure can universally increase the relative width of the bandgap, so this conclusion is helpful for the further research.In conclusion, this thesis covered the topics of the relative bandgap width and stability of photonic crystals. Through study on stability and relative bandgap of a linear gradient structure models, many good results have been obtained. All these conclusions are helpful for the further research and practical applications of photonic crystals in the future.