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以作者查詢圖書館館藏 、以作者查詢臺灣博碩士 、以作者查詢全國書目 、勘誤回報 、線上人數：22 、訪客IP：18.219.116.93
姓名 鄭鈺齡(Yu-ling Cheng) 查詢紙本館藏 畢業系所 光電科學與工程學系 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)相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 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。
摘要(英) 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.
關鍵字(中) ★ 超潁
★ 超材料
★ 隱形斗篷
★ 變換光學
★ 非磁性關鍵字(英) ★ invisibility cloak
★ transformation optics
★ nonmagnetic
★ metamaterial論文目次 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 -
參考文獻 [1] J. B. Pendry, D. Schurig, and D. R. Smith, Controlling Electromagnetic Fields, Science 312, 1780-1782 (2006)
[2] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Metamaterial Electromagnetic Cloak at Microwave Frequencies, Science 314, 977-980 (2006)
[3] D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Composite Medium with Simultaneously Negative Permeability and Permittivity, Phys. Rev. Lett. 84, 4184-4187 (2000)
[4] 欒丕綱, 陳啓昌, 光子晶體, 從蝴蝶翅膀到奈米光子學, Photonic Crystals ,五南圖書出版公司, 台灣 (2005), ISBN: 957-11-4027-9
[5] Steven G. Johnson, Coordinate Transformation & Invariance in Electromagnetism, notes for the course 18.369 at MIT (2010)
[6] D. Schurig, J. B. Pendry, and D. R. Smith, Calculation of material properties and
ray tracing in transformation media, Opt. Express, 14, 21, 9794-9804 (2006)
[7] Wenshan Cai, Uday K. Chettiar, Alexander V. Kildishev, Vladimir M. Shalaeva, and Graeme W. Milton, Nonmagnetic cloak with minimized scattering, Appl. Phys. Lett. 91, 111105 (2007)
- 41 -
[8] Jingjing Zhang, Yu Luo, and Niels Asger Mortensen, Minimizing the scattering of a nonmagnetic cloak, Appl. Phys. Lett. 96, 113511 (2010)
[9] Xiaofei Xu, Yijun Feng, Lin Zhao, Tian Jiang, Chunhua Lu, and Zhongzi Xu, Designing the coordinate transformation function for non-magnetic invisibility cloaking, J. Phys. D: Appl. Phys. 41, 215504 (2008)
[10] Wei Yan, Min Yan, and Min Qiu, Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering, Appl. Phys. Lett. 93, 021909 (2008)
[11] André Nicolet, Frédéric Zolla, and Sébastien Guenneau, Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section, Opt. Lett. 33, 14, 1584-1586 (2008)
[12] Hua Ma, Shaobo Qu, Zhuo Xu, and Jiafu Wang, Numerical method for designing approximate cloaks with arbitrary shapes, Phys. Rev. E 78, 036608 (2008)
[13] Jingjing Yang, Ming Huang, Chengfu Yang, Zhe Xiao, and Jinhui Peng, Metamaterial electromagnetic concentrators with arbitrary geometries, Opt. Express, 17, 22, 19656-19661 (2009)
[14] Min Yan, Zhichao Ruan, and Min Qiu, Cylindrical Invisibility Cloak with Simplified Material Parameters is Inherently Visible, Phys. Rev. Lett. 99, 233901 (2007)
- 42 -
[15] 王新榮, 陳時錦, 劉亞忠, 有限元素法及其應用 初版, 中央圖書出版社, 台灣 (1997), ISBN: 957-637-348-4
[16] 倪光正, 楊仕友, 邱捷, 工程電磁場數值計算 第2版, 機械工業出版社, 中國大陸 (2010), ISBN: 978-7-111-29431-3
[17] 王薔, 李國定, 龔克, 電磁場理論基礎, 五南圖書出版公司, 台灣 (2003),
ISBN: 957-11-3124-5
[18] 鄒兆南, 向量與張量分析 初版, 中央圖書出版社, 台灣 (2001),
ISBN: 957-637-365-4
[19] Min Yan, Zhichao Ruan, and Min Qiu, Scattering characteristics of simplified cylindrical invisibility cloaks, Opt. Express, 15, 26, 17772-17782 (2007)
[20] U. Leonhardt, Optical conformal mapping, Science 312, 1777-1780 (2006).
指導教授 欒丕綱(Pi-Gang Luan) 審核日期 2011-7-6 推文 plurk
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