准周期结构一维光子晶体的多重分形特性

准周期结构一维光子晶体的多重分形特性 The Multifractal Properties of the One-Dimensional Quasi-Period Photonic Crystal 赵江南 ZHAO Jiangnan1 1 first-author 张援农 ZHANG Yuannong1 1 黄盛达 HUANG Shengda2 2 武汉大学电子信息学院 武汉大学电子信息学院 School of Electronic Information,Wuhan University School of Electronic Information,Wuhan University 北京大学物理学院 北京大学物理学院 School of Physics,Peking University School of Physics,Peking University 利用传输矩阵理论分析了Fibonacci准周期结构的光子晶体的带隙特性,并讨论了当介质层中含有负折射率介质时光子带隙的特性,分析了该准周期结构频谱的多重分形.研究结果表明,Fibonacci准周期结构的分层介质的光子带隙（PBG）特性,不论其为普通介质还是含负折射率介质,其透射谱具有相似性,且随阶数的增大其不均匀性增加.对广义Fibonacci准周期结构——GF（1,n）和GF（m,1）,其透射谱的不均匀性随n和m的增加而增大. Using transfer-matrix method and multi-fractal theory,we have studied the transmission properties of the one-dimensional Fibonacci structures Fc（l） and the generalized Fibonacci structures GF（m,n）,in which m,n different intervals are integer according to a substitution rule.By using a transfer-matrix method,the optical transmission through GF（1,n） and GF（m,1） is obtained.Multi-fractal analysis is employed to characterize the transmission spectra.The transmission spectra of Fibonacci structures have self-similarity and inhomogeneity with the increase of the order.It is demonstrated that the transmission coefficient has a rich structure,which depends on the wavelength of light and the number of different integer m and n. 光子带隙 准周期结构 传输矩阵 多重分形 photonic bandgap quasi-periodic structures transfer matrix multifractal analysis 10.14188/j.1671-8836.2011.03.001 O734 国家自然科学基金资助项目（10904118） 2011-03-01 2021-04-01 3 57