含超穎材料光子晶體之散射

Abstract

本文主要討論含超穎材料平板波導結構與週期性結構的特性及現象。首先於平板波導結構方面，我們探討光散射與色散關係，並利用穿透係數以及色散方程式分析含超穎材料平板波導結構的特性。結果顯示含超穎材料平板波導結構在同一折射率之下會有多種的穿透頻譜，其色散曲線會有表面模態的存在，這些現象都是傳統平板波導結構所不會發生的。此外於週期性結構的部份，我們利用帶隙邊緣方程式，分別對於不同結構參數的週期性結構之特性進行分析，最後針對帶隙結構的變化和超穎材料特有的性質來討論。由分析結果顯示含超穎材料週期性結構的帶隙結構比傳統週期性結構複雜許多，也可以產生同傳統週期性結構所具有的全反射特性。

In this thesis, properties of planar waveguides and periodic structures containing metamaterials are investigated. Firstly, for planar waveguides, we employ the transmission coefficient and dispersion equation to analyze the characteristics of the scattering and dispersion relation for planar waveguides containing metamaterials. The results show that the transmission spectra of planar waveguides containing metamaterials are various at same refractive index. Moreover, surface modes exist in planar waveguides containing metamaterials which are different in conventional materials. For periodic structures, we employ the band-edge equations and then discuss the characteristics of band structures by changing the parameters of periodic structures. The results show that the band structures containing metamaterials are more complicated than conventional materials and properties of total omnidirectional reflection can also be produced.