本篇論文中，我們研究隱形斗篷介質參數的選擇與簡化，以設計出實驗上較可行的隱形斗篷。由變換光學出發，透過座標變換，我們可以得到介質參數與空間座標函數的對應關係，再由二維系統中圓柱座標下的波動方程式得知，假若我們選用TM波(磁場在Z方向)，即可在幾何光學極限下簡化成磁導率為1，避免了磁性材料的需要。此時，更可以由簡化過的非磁性介質參數看出我們所選用的座標變換函數影響甚大。所以，適當設計空間座標變換函數，就可以得到適當的介質參數，再注意一些阻抗匹配、空間奇異點的問題，我們就可以大幅降低散射，改善非磁性隱形斗篷的效果。另外我們也討論了任意形狀的隱形斗篷結構。藉由有限元素法(Finite Element Method, 簡稱FEM)進行數值模擬，可以驗證我們的設計與理論。 In this thesis, we focus on the material parameters design of an invisibility cloak.Through a parameter-simplifying procedure, we could make the experiment of cloaking device more practical. Starting with a set of properly choosing coordinate transformation functions, we can get the relations between the material parameters and these functions. From the wave equation in two-dimensional space, we show that for TM wave the permeability can be reduced to 1 in the geometric optics limit.We therefore, we can avoid using magnetic materials in this case. The coordinate transformation functions exert influences on the simplified nonmagnetic material parameters. If we properly design the coordinate transformation functions, we can get better material parameters for the cloak. Carefully dealing with the impedance matching and space singularity problem, we can reduce the scattering dramatically and improve the cloaking effect. Also we study the arbitrary shape cloak devices. The numerical simulations using the Finite Element Method (FEM) confirm our designs and theory.
