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研究生： 鄭鈺齡
Yu-ling Cheng
論文名稱： 變換光學應用於非磁性隱形斗篷之設計
Design the nonmagnetic invisibility cloak using transformation optics
指導教授： 欒丕綱
Pi-Gang Luan
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 光電科學與工程學系
Department of Optics and Photonics
畢業學年度： 99
語文別： 中文
論文頁數： 54
中文關鍵詞： 超潁 、超材料 、隱形斗篷 、變換光學 、非磁性
外文關鍵詞： invisibility cloak, transformation optics, nonmagnetic, metamaterial
相關次數： 點閱：11  下載：0 
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    • 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.

    摘要 ............................................................................................................................... I ABSTRACT ................................................................................................................. II 致謝 ............................................................................................................................. III 目錄 ............................................................................................................................. IV 圖目錄 ......................................................................................................................... VI 表目錄 ...................................................................................................................... VIII 第一章 緒論/簡介 ................................................................................................. - 1 - 第二章 理論分析 ................................................................................................... - 3 - 2-1波動方程式 ..................................................................................................... - 3 - 2-2 J. B. PENDRY的空間座標變換理論 ................................................................ - 4 - 2-3二維圓柱形隱形斗篷的介質參數 ................................................................. - 9 - 2-4二維任意形狀隱形斗篷的介質參數 ........................................................... - 11 - 2-5簡化參數 ....................................................................................................... - 11 - 第三章 數值模擬與結果分析............................................................................. - 13 - 3-1理想隱形斗篷 ............................................................................................... - 14 - 3-2 非磁性隱形斗篷 ........................................................................................... - 16 - 3-2-1 線性轉換 .............................................................................................. - 17 - 3-2-2 二次拋物線轉換 .................................................................................. - 19 - 3-2-3 高次轉換 .............................................................................................. - 21 - 3-3 曲線擬合法(CURVE-FITTING METHOD) ......................................................... - 25 - V 3-4以雷達散射截面(RCS)綜合比較 ................................................................. - 29 - 3-5 任意形狀隱形斗篷 ....................................................................................... - 34 - 3-5-1 明確函數表示法(Closed form expression) .......................................... - 34 - 3-5-2 數值近似表示法(Numerical approximation) ...................................... - 34 - 3-5-3 另類方法設計任意形狀隱形斗篷 ...................................................... - 34 - 第四章 結論與未來展望..................................................................................... - 39 - 4-1結論 ............................................................................................................... - 39 - 4-2未來展望 ....................................................................................................... - 39 - 參考資料 ................................................................................................................. - 40 -

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