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研究生:蔡育霖
研究生(外文):Yu-lin Tsai
論文名稱:電磁波在不同形狀轉換材料的模擬
論文名稱(外文):Simulation of Electromagnetic Wave in Arbitrary Transformation Media
指導教授:陳東陽陳東陽引用關係
指導教授(外文):Tung-yang Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:68
中文關鍵詞:簡化隱形斗篷高階座標轉換集中器任意形狀轉換材料隱形斗篷
外文關鍵詞:concentratorquadratic transformationarbitrary shapecloakingtransformation optics
相關次數:
  • 被引用被引用:4
  • 點閱點閱:258
  • 評分評分:
  • 下載下載:57
  • 收藏至我的研究室書目清單書目收藏:0
本文利用座標之間的轉換關係設計任意形狀的轉換材料(如隱形斗篷、集中器),並模擬電磁波在任意形狀轉換材料中的傳播情形。由於理想隱形斗篷的材料在內圈邊界上會有奇異性的情形,因此本文利用保持色散關係的不變性將隱形斗篷材料係數簡化,一階座標轉換簡化下的隱形斗篷在外邊界會有阻抗不連續的情況,故以二階座標轉換設計隱形斗篷再將其材料係數簡化,使得簡化後的隱形斗篷外邊界阻抗能連續,二階座標轉換簡化後的隱形斗篷不僅能夠消除材料的奇異性,其散射情形也比一階轉換簡化後的隱形斗篷小。圓柱集中器可以將入射光往中心集中使得能量進入內圈部份甚至提高進入內圈的能量。運用座標轉換函數設計任意多邊形的集中器,如此即可依照不同形狀的要求製造集中器。數值模擬亦證實任意形狀集中器能使入射光經過材料後能回到原來路徑如同將內圈材料隱形,本文亦探討集中裝置的其他應用。
In this work we design invisibility cloaks for electromagnetic waves and light concentrators of arbitrary shapes based on coordinate transformations. Simplified material parameters are proposed using quadratic transformation functions which, in contrast to linear transformation, will enable us to eliminate the singularity at inner boundary and also diminish the scattering field outside the cloaking layer. By selecting appropriate transformation functions cylindrical and other profiles of concentrators are studied as well. Our results are confirmed by numerical simulations based on finite element calculations. Some potential application are also envisaged based on the concept of transformation optics.
目錄
中文摘要...............................................................................................................................I
ABSTRACT....................................................................................................................... II
誌謝....................................................................................................................................III
目錄....................................................................................................................................IV
表目錄................................................................................................................................VI
圖目錄............................................................................................................................... VII
圖目錄............................................................................................................................... VII
符號表..................................................................................................................................X
第一章 緒論......................................................................................................................... 1
第二章 基本理論................................................................................................................. 5
2.1 傳導方程式的不變性 ................................................................................................ 5
2.2 聲波方程式的不變性 ................................................................................................ 6
2.3MAXWELL 方程式的不變性....................................................................................... 7
第三章多邊形柱體屏蔽效應............................................................................................. 9
3.1 柱體截面形狀邊緣與座標軸垂直的隱形斗篷 ........................................................ 9
3.2 柱體截面形狀邊緣與座標軸垂直的隱形斗篷 ...................................................... 12
3.3 模擬柱體截面形狀邊緣與座標軸垂直的隱形斗篷電磁波屏蔽效應 .................. 14
3.4 模擬柱體截面形狀邊緣與座標軸不垂直的隱形斗篷電磁波屏蔽效應 .............. 16
3.5 三維正方體隱形斗篷 .............................................................................................. 19
3.6 正方體隱形斗篷模擬結果 ...................................................................................... 21
第四章隱形斗篷材料係數的簡化................................................................................... 22
4.1 簡化隱形斗篷以及高階座標轉換 .......................................................................... 22
4.2 橢圓隱形斗篷理想以及簡化材料係數 .................................................................. 25
4.3 橢圓理想隱形斗篷以及簡化隱形斗篷模擬結果 .................................................. 28
V
4.4 矩形隱形斗篷的簡化 .............................................................................................. 31
4.5 矩形簡化隱形斗篷模擬結果 .................................................................................. 33
4.6 任意形狀隱形斗篷的簡化 ...................................................................................... 35
第五章集中器................................................................................................................... 38
5.1 圓柱集中器............................................................................................................. 38
5.2 集中器對內圈形狀的影響..................................................................................... 45
5.3 任意多邊形集中器................................................................................................. 47
5.4 非線性座標轉換集中器......................................................................................... 50
第六章結論與未來展望................................................................................................... 53
參考文獻............................................................................................................................. 54
附錄 A 基本電磁波理論................................................................................................... 57
附錄 B 色散關係不變....................................................................................................... 66
自述.................................................................................................................................... 68
Balanis, C. A., “Advanced engineering electromagnetics.”, John Wiley & Sons, Inc., 1989.
Bekefi, G. and Barrett, A. H., “Electromagnetic Vibrations, Waves, and Radiation.”, The
Massachusetts Institute of Technology, 1977.
Cai, W., Chettiar, U. K., Kildishev, A. V., and Shalaev, V. M., “Optical cloaking with
metamaterials.”, Nature Photonics 1, 224-227 (2007a).
Cai, W., Chettiar, U. K., Kildishev, A. V., Shalaev, V. M., and Milton, G. W. “Nonmagnetic
cloak with minimized scattering.”, Appl. Phys. Lett. 91, 111105 (2007b).
Cheng, D. K., “Field and Wave Electromagnetics, 2nd Edition”, Addison-Wesley Publishing
Company, Inc., 1989.
Chen, H. and Chan, C. T., “Acoustic cloaking in three dimensions using acoustic
metamaterials.”, Appl. Phys. Lett. 91, 183518 (2007).
Chen, H., Zhang, X., Luo, X., Ma, H. and Chan, C. T., “Reshaping the perfect electrical
conductor cylinder arbitrarily.”, New J. Phys. 10, 113016 (2008).
Chen, T. and Weng, C. N., “Invisibility cloak with a twin cavity.”, Opt. Exp. 17, 10, 8614
(2009).
Chen, T., Weng, C. N. and Chen, J. S., “Cloak for curvilinearly anisotropic media in
conduction.”, Appl. Phys. Lett. 93, 114103 (2008).
Cummer, S. A. and Schurig, D., “One path to acoustic cloaking.”, New J. Phys. 9, 45
(2007).
Cummer, S. A., Popa, B. I., Schurig, D., Smith, D. R., and Pendry, J., “Full-wave
simulation of electromagnetic cloaking structures.”, Phys. Rev. E 74, 036621 (2006).
Huang, Y., Feng, Y., and Jiang, T., “Electromagnetic cloaking by layered structure of
homogeneous isotropic materials.”, Opt. Exp. 15, 18, 11133 (2007).
Jacob, Z., Alekseyev, L. V. and Narimanov, E., “Optical Hyperlens: Far-field imaging
beyond the diffraction limit.”, Opt. Exp. 14, 18, 8247 (2006).
Jiang, W. X., Chin, Y. J., Li, Z., Cheng, Q., Liu, R. and Cui, T. J., “Analytical design of
conformally invisible cloaks for arbitrarily shaped objects.”, Phys. Rev. E 77, 066607
(2008a).
Jiang, W. X., Cui, T. J., Yu, G. X., Lin, X. Q., Cheng, Q. and Chin, J. Y., ”Arbitrarily
elliptical-cylindrical invisible cloaking.”, J. Phys. D: Appl. Phys. 41, 085504 (2008b).
Kildishev, A. V. and Narimanov, E., “Impedance-matched hyperlens.”, Opt. Lett. 32, 23,
3432 (2007).
Leonhardt, U., “Optical conformal mapping.”, Science 312, 1777 (2006).
Luo, Y., Chen, H., Zhang, J., Ran, L. and Kong, J. A., “Design and analytical full-wave
validation of the invisibility cloaks, concentrators, and field rotators created with a general
class of transformations.”, Phys. Rev. B 77, 125127 (2008).
Li, C. and Li, F., “Two-dimensional electromagnetic cloaks with arbitrary geometries.”,
Opt. Exp. 16, 17, 13414 (2008).
Ma, H., Qu, S., Xu, Z., and Wang, J., “Approximation approach of designing practical
cloaks with arbitrary shapes.”, Opt. Exp. 16, 20, 15449 (2008a).
Ma, H., Qu, S., Xu, Z., and Wang, J., “Numerical method for designing approximate cloaks
with arbitrary shapes.”, Phys. Rev. E 78, 036608 (2008b).
Milton, G. W., Briane, M. and Willis, J. R., “On cloaking for elasticity and physical
equations with a transformation invariant form.”, New J. Phys. 8, 248 (2006).
Milton, G. W., Nicorovici, N.-A. P., McPhedran, R. C., Cherednichenko, K. and Jacob, Z.,
“Solutions in folded geometries, and associated cloaking due to anomalous resonance.”,
New J. Phys, 10, 115021 (2008).
Narimanov, E., Alekseyev, L. V. and Jacob, Z., “Optical hyperspace: negative refractive
index and subwavelength imaging in anisotroptic dielectric metamaterials.”, Proc. of SPIE
6328, 63280I-1 (2006).
Narimanov, E. and Shalaev, V. M., “Beyond diffraction.”, Nature 447, 266 (2007).
Pendry, J. B., “Negative Refraction Makes a Perfect Lens.” Phys. Rev. Lett. 85, 3966
(2000).
Pendry, J. B., Schurig, D. and Smith, D. R., “Controlling electromagnetic fields.”, Science
312, 1780 (2006).
Rahm, M., Schurig, D., Roberts, D. A., Cummer, S. A., Smith, D. R. and Pendry, J. B.,
“Design of electromagnetic cloaks and concentrators using form-invariant coordinate
transformations of Maxwell’s equation.”, Photonics and Nanostructures-Fundamentals
and Applications 6, 87-95 (2008).
Schurig, D., Pendry, J. B. and Smith. D. R., “Calculation of material properties and ray
tracing in transformation media.”, Opt. Exp. 14, 21, 9794 (2006a).
Schurig, D., Mock, J. J., Justice, B. J., Cummer, S. A., Pendry, J. B., Starr, A. F. and Smith,
D. R., “Metamaterial electromagnetic cloak at microwave frequencies.”, Science 314,
977-980 (2006b).
Schurig, D., “Transformation optics and metamaterials, a path to interesting devices.”,
Young Scientist Meeting on Metamaterials, (2006c).
Shalaev, V. M., “Transforming Light.” Science 322, 384-386 (2009).
Tichit, P. H., Kanté, B., Burokur, S. N. and Lustrac, A., “Design of polygonal and elliptical
invisibility cloaks.”, Institut d’Electronique Fondamentale, CNRS UMR 8622-Universit
Paris Sud 11-91405 Orsay-France (2008).
Veselago, V. G., “The electrodynamics of substances with simultaneously negative values
of �� and �� .”, Sov. Phys. Usp. 10, 509 (1968).
Wu, Q., Zhang, K., Meng, F. and Li, L., “Material parameters characterization for arbitrary
N-sided regular polygonal invisible cloak.”, J. Phys. D: Appl. Phys. 42, 035408 (2009).
Yan, M., Ruan, Z., and Qiu, M., “Scattering characteristics of simplified cylindrical
invisibility cloaks.”, Opt. Exp. 15, 26, 17772 (2007).
You,Y., Kattawar, G. W., Zhai, P. W. and Yang, P., “Invisibility cloaks for irregular particles
using coordinate transformations”, Opt. Exp. 16, 9, 6134 (2008).
Zhang, J., Luo, Y., Chen, H. and Wu, B., “Cloak of arbitrary shape”, J. Opt. Soc. Am. B 25,
11, 1776 (2008).
賈起民, 鄭永令, “電磁學”, 亞東書局 (1989).
陳俊杉, “圓柱或球形異向性材料的屏蔽模擬”,國立成功大學碩士論文 (2008).
欒丕綱, 陳啓昌, “光子晶體-從蝴蝶翅膀到奈米光子學”, 五南出版社, 台灣 (2005).
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