基于Sierpinski地毯结构的类分形光子晶体特性研究

Study on Characteristics of Quasi-Fractal Photonic Crystal Based on Sierpinski Gasket Structure

将谢尔宾斯基(Sierpinski)地毯结构引入二维光子晶体,设计了一种具有规则分形结构特征的光子晶体——Sierpinski类分形光子晶体。采用时域有限差分法仿真分析了空气背景介质柱和介质背景空气孔结构Sierpinski类分形光子晶体的透射谱。结果表明,只有当TM波入射空气背景介质柱结构时,Sierpinski类分形光子晶体存在禁带,其它情况均不存在禁带。分析了圆柱形Sierpinski类分形光子晶体的禁带宽度、禁带中心频率以及禁带中所出现的通带的特性随介质柱介电常数、介质柱填充因子的变化规律;仿真了不同分形级数以及不同介质柱形状对Sierpinski类分形光子晶体透射谱和带隙特性的影响。

The Sierpinski gasket structure is introduced into two-dimensional photonic crystal to design a new kind of photonic crystal——the Sierpinski quasi-fractal photonic crystal.By using finite-difference time-domain method,the transmission spectra of Sierpinski quasi-fractal photonic crystal with dielectric rods and air holes are calculated and analyzed respectively.The results show that the band gap exists on the condition of dielectric rods and incidence of TM wave only.The band gap property（bandwidth and central frequency） and characteristics of the pass-bands which exist in the band gap of Sierpinski circular-rods quasi-fractal photonic crystal with different dielectric constant and fill ratio are analyzed.Further more,the effects of different fractal series and dielectric-rod shapes on the transmission spectra and band-gap characterishis are simulated.