摘要：本文設計了一個一維的準周期Thue-Morse（ThM）序列結構，利用傳輸矩陣理論研究該結構的透射譜、模密度和光強分布。研究發現，ThM序列結構的透射譜和模密度分布都是以=2為周期的；且結構呈現出自相似分布：隨著階數n的增大，除了出現前一階ThM系列的共振模外，還在它們的兩共振模之間出現一個新的共振模。在共振模處，模密度出現極值。電磁波在ThMn序列結構中的光強分布也具有自相似特性。可見，光在ThMn序列結構中傳輸時具有兩大特性：周期性和自相似性。

關鍵字：Thue-Morse序列，傳輸矩陣，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