摘要：本文设计了一个一维的准周期Thue-Morse（ThM）序列结构，利用传输矩阵理论研究该结构的透射谱、模密度和光强分布。研究发现，ThM序列结构的透射谱和模密度分布都是以=2为周期的；且结构呈现出自相似分布：随着阶数n的增大，除了出现前一阶ThM系列的共振模外，还在它们的两共振模之间出现一个新的共振模。在共振模处，模密度出现极值。电磁波在ThMn序列结构中的光强分布也具有自相似特性。可见，光在ThMn序列结构中传输时具有两大特性：周期性和自相似性。

关键字：Thue-Morse序列，传输矩阵，模密度，自相似

Abstract: In this paper we design an one dimensional sequence structure of Thue-Morse,we researched it's transmission spectrum,mode density and intensity distribution by Transmission matrix.We find that the cycle of transmission spectrum and mode density of Thue-Morse sequence structure is =2;And the structure exhibiting with self similarity:with the growing of generation n,but for the appearing of resonance mode of the front Thue-Morse sequence,a new resonant was appeared between the two resonant mode.At the resonant mode,the mode density becomes a maximum.Also the light intensity of electromagnetic wave in Thue-Morse sequence structure have the characteristic of self similarity.In general,the transmission characteristics of light in Thue-Morse sequence structure is self similarity and periodic.

Keywords: Thue-Morse sequence,Transmission matrix, Mode density,Self similarity