超穎材料傳輸線模型與光子晶體之計算

Abstract

本文著筆研究於超潁材料所組成的一維光子晶體，此光子晶體所產生的能隙現象在本文有做深入的探討與研究，我們所謂的超穎材料是指材料參數中介電常數和導磁常數之其一常數為負值，而另一個常數為正值的材料，此單一材料參數為負值所組成的光子晶體我們簡稱SNG，接著我們考慮材料的厚度比例對於能隙的邊界和禁帶的頻寬所產生之影響，我們簡單的結合左手傳輸線理論，利用近似的方式，有效的利用厚度變化來描述能隙邊界與寬度變化的趨勢，並且討論加入損耗後所造成的影響。 除此之外，我們也利用阻抗匹配的理論去討論不同角度入射對於能隙的寬度所產生的影響，並做理論上的分析，然而一樣是用單一負值的材料參數所組成的光子晶體，我們討論這兩種極化模態的穿透光譜，當然主要的討論方向為不同的角度和不同的極化模態所產生的能隙禁帶大小變化，接著我們成功的利用(k2/k1)參數去討論厚度和角度的變化與能隙的關係，在此篇論文中我們有清楚的定義，此參數是利用不同角度在阻抗匹配狀態下所計算出的波向量比例關係，利用這個比例關係我們可以清楚的解釋在不同模態下，角度改變造成光子晶體能隙的禁帶大小跟著改變的傾向，而這個比例關係也可以用於解釋厚度變化所導致禁帶大小和能隙邊界的變化情形，此研究結果對於研究單一負值的材料所組成的光子晶體具有相當幫助。

In this thesis, the thickness-dependent photonic bandgap for a one-dimensional photonic crystal consisting of two different single-negative materials is theoretically investigated. The two single-negative (SNG) materials include one with a single-negative permittivity and the other having a single-negative permeability. It is found that the size of the bandgap and the positions of the bandedges are strongly dependent on the thickness ratio of the two constituent SNG layers. Then, we also consider about in loss case effective for bandgap. Moreover, the angular dependence of the photonic band structure of a single-negative one-dimensional photonic crystal is theoretically investigated. To use the same photonic crystal structure, we discussed two propagation mode, which are TE mode and TM mode, for different incident angle. We use the concept of impedance matching to discuss the bandgap shift, thus the gap size with incident angle had been described clearly. Additionally, the characteristic frequency determined by the condition of impedance match is closely related to the center frequency of the bandgap in TE mode and TM mode. We used the parameter by ratio of the wavenumber on two medium, which is the wavenumber ratio of the two materials, to successfully explain angle varition and thickness-dependent bandgap and the bandedges for two polarization modes.