- 學位論文
非等向性材料的Goos-Hanchen位移
The Goos–Hanchen shift of the oriented anisotropic materials
摘要
近年來，隨著微小化尺度科技與實驗儀器的進步，Goos-Hanchen shift(GH位移)又開始成為熱門的話題。GH位移為反射光束在介質介面上有一段橫向的位移。GH位移在天然材料下就存在的物理特性，像是在介電材料下，接近臨界角有明顯正的GH位移(與波向量在介質介面的分量方向同向);在金屬中的低吸收介質，接近布魯斯特角有明顯負的GH位移。GH位移可用來作為電漿子共振的感測器、溫度感測器，或是光學路徑的設計等等。伴隨著各式各樣的超常材料的研發像是左手材料、對掌性材料等等，很多自然界不存在的物理現象也跟著被發現。然而，在不同超常材料下的GH位移發生的機制也會有所不同。超常材料中的非等向性材料可利用金屬或介電材料平板以週期排列後，並等效達到材料參數為矩陣的效果。在了解發生明顯GH位移的機制後，我們更容易設計材料參數來達到產生明顯GH位移的目的。 本論文探討非等向性材料的Goos-Hanchen (GH)位移。利用介電矩陣只有對角線元素的非等向性材料旋轉主軸產生介電矩陣含有非對角線元素的非等向性材料。首先在對稱非等向性材料中，以馬克士威爾波動方程式搭配適當的邊界條件進行計算，得到此材料TM偏振的色散關係、阻抗以及反射係數與穿透係數，並由色散關係將情況分成橢圓曲線與雙曲線兩種情況，並討論旋轉主軸對於色散曲線的影響，進而探討轉角對於臨界角與布魯斯特角的關係；分成三種入射角：臨界角、布魯斯特角、與掠射角，分別觀察GH位移的大小與正負，再對材料的主軸旋轉，討論轉角與GH位移的變化。最後以有限元素法模擬高斯光束，並觀察場圖來討論在介質介面上的GH位移。
並列摘要
Metamaterails already played a very important role in the tools uesd by people. Humans usually obtain some special properties from designing artificial structure rather than composition, using small inhomogeneities to achieve effective macroscopic behavior. Due to the advancement of the nanotechnology, the study of the Goos-Hanchen shift becomes popular disquisition. The Goos-Hanchen shift of reflection of a electromagnetic beam wave from an interface between two media, where the reflection coefficient’s phase changes with the change of incident angle is known to be accompanie by a small lateral shift in the plane of incidence. The phenomena has also been interpreted as a proof of the existence of such a flux of engery parallel to the surface inside the incident media. The direction of the GH shift is equal to the direction of a flux of engery on the interface. The phoenomena can be applied to the Goos-Hanchen shift surface plasmon resonance sensor, Optical temperature sensing based on the Goos-Hanchen effect…etc. This thesis mainly investigates the apparent GH shift in the Metamaterails. In the first , we can use the anistropic medium rotating an angle to bring out the sysmmetrically oriented medium. By applying Finite Element Method(FEM) and appropriate Boundary Conditions (BCs), we can simulate Maxwell wave equation to get the dispersion relation.It can classify this metamaterails as two conditions. One is the discriminant of the dispersion relation is greater than zero,which the dispersion curve is an ellipse ,and the GH shift will be obvious at the incident angle near critical angle.The other is the discriminant of the dispersion relation is less than zero, which the dispersion curve is a hyperbola ,and the GH shift is obvious at the incident angle near critical angle. And then ,the GH shift of reflected beam wave at the incident angle near Brewster angle is also obvious ,and there are postive and negative shift. In the last, by applying FEM ,we can simulate the Gaussian Beam Wave to proof the Goos-Hanchen shift at the incident angle near critical angle and brewster angle in the sysmmetrically oriented medium.