以座標轉換發展的裝置是近年來熱門的研究項目，許多學者以此法投入各個相關領域，從電磁波到光學、熱傳導、聲學等等，都獲得許多豐碩的成果。然而在設計這些裝置時常得到的結果需要複雜的材料，因此簡化材料參數或運用非常重要。而在本文中將使用保角變換處理座標轉換及中性內含物兩個問題，首先在座標轉換的部分，以電磁波為物理模式，在此以三個轉換函數發展出的三個裝置進行模擬及分析，分別為定向發射器，波導彎曲及方向天線。另外一部份則是以熱的中性內含物為概念，發展出任意形狀的隱型裝置，這樣的裝置並不需要複雜的材料。而使用保角變換的方法分析使用後的效果，可以將材料係數大大的簡化，使得原本異向且非均質的材料，最後只要使用等向性的材料甚至是單一材料即可達成所需要的成效。

In this thesis, transformation optics and neutral inclusion based on the conformal mapping method are used to control the propagation of electromagnetic wave and thermal field respectively. The devices designed by transformation optics usually lead to a medium with complex anisotropic and inhomogeneous properties, Conformal mapping on the other hand is a good method which allows us to design the transformed medium with isotropic properties. In the first part, under coordinate invariance and conformal mapping, we simulate the functions of directional emission, wave bending and directional antennas. In the second part, we introduce a different type of invisible cloak, which is referred to as neutral cavity. Based on the concept of neutral inclusion, some simulation results are presented using the conformal mapping method.

Abramowitz, M. and Stegun, I. A. (1964). Handbook of mathematical functions: with formulas, graphs, and mathematical tables, Courier Corporation.

Alù, A. and Engheta, N., Achieving transparency with plasmonic and metamaterial coatings, Physical Review E 72(1), 016623 (2005).

Chen, H. and Chan, C., Acoustic cloaking in three dimensions using acoustic metamaterials, Applied Physics Letters 91(18), 183518 (2007).

Chen, H., Chan, C. T. and Sheng, P., Transformation optics and metamaterials, Nature Materials 9(5), 387-396 (2010).

Chen, H., Leonhardt, U. and Tyc, T., Conformal cloak for waves, Physical Review A 83(5), 055801 (2011).

Chen, T., Weng, C.-N. and Chen, J.-S., Cloak for curvilinearly anisotropic media in conduction, Applied Physics Letters 93(11), 114103 (2008).

Churchill, R. V. and Brown, J. (1990). Complex Analysis and Applications, McGraw-Hill, New York.

Cojocaru, E., Exact analytical approaches for elliptic cylindrical invisibility cloaks, JOSA B 26(5), 1119-1128 (2009).

Cummer, S. A., Popa, B.-I., Schurig, D., Smith, D. R., Pendry, J., Rahm, M. and Starr, A., Scattering theory derivation of a 3D acoustic cloaking shell, Physical Review Letters 100(2), 024301 (2008).

David, K. C., Field and wave electromagnetics, Addison-Wesley publications, (1983).

Dede, E. M., Nomura, T. and Lee, J., Thermal-composite design optimization for heat flux shielding, focusing, and reversal, Structural and Multidisciplinary Optimization 49(1), 59-68 (2014).

Fan, C., Gao, Y. and Huang, J., Shaped graded materials with an apparent negative thermal conductivity, Applied Physics Letters 92(25), 251907 (2008).

Grossman, S. I. and Derrick, W. R. (1988). Advanced engineering mathematics, Harpercollins College Div.

Guenneau, S. and Amra, C., Anisotropic conductivity rotates heat fluxes in transient regimes, Optics Express 21(5), 6578-6583 (2013).

Guenneau, S., Amra, C. and Veynante, D., Transformation thermodynamics: cloaking and concentrating heat flux, Optics Express 20(7), 8207-8218 (2012).

Han, T., Bai, X., Gao, D., Thong, J. T., Li, B. and Qiu, C.-W., Experimental demonstration of a bilayer thermal cloak, Physical Review Letters 112(5), 054302 (2014).

Han, T., Yuan, T., Li, B. and Qiu, C.-W., Homogeneous thermal cloak with constant conductivity and tunable heat localization, Scientific Reports 3, (2013).

Jiang, W. X., Chin, J. Y., Li, Z., Cheng, Q., Liu, R. and Cui, T. J., Analytical design of conformally invisible cloaks for arbitrarily shaped objects, Physical Review E 77(6), 066607 (2008).

Jiang, W. X., Cui, T. J., Ma, H. F., Yang, X. M. and Cheng, Q., Layered high-gain lens antennas via discrete optical transformation, Applied Physics Letters 93(22), 221906 (2008).

Jiang, W. X., Cui, T. J., Ma, H. F., Zhou, X. Y. and Cheng, Q., Cylindrical-to-plane-wave conversion via embedded optical transformation, Applied Physics Letters 92(26), 261903 (2008).

Lan, C., Bi, K., Gao, Z., Li, B. and Zhou, J., Achieving bifunctional cloak via combination of passive and active schemes, Applied Physics Letters 109(20), 201903 (2016).

Leonhardt, U., Notes on conformal invisibility devices, New Journal of Physics 8(7), 118 (2006).

Leonhardt, U., Optical conformal mapping, Science 312(5781), 1777-1780 (2006).

Leonhardt, U. and Philbin, T. G., Transformation optics and the geometry of light, Progress in Optics 53, 69-152 (2009).

Leonhardt, U. and Tyc, T., Broadband invisibility by non-Euclidean cloaking, Science 323(5910), 110-112 (2009).

Li, H., Xu, Y. and Chen, H., Conformal cloaks at eigenfrequencies, Journal of Physics D: Applied Physics 46(13), 135109 (2013).

Ma, Y., Wang, N. and Ong, C., Application of inverse, strict conformal transformation to design waveguide devices, JOSA A 27(5), 968-972 (2010).

Mei, Z. L. and Cui, T. J., Arbitrary bending of electromagnetic waves using isotropic materials, Journal of Applied Physics 105(10), 104913 (2009).

Milton, G. W., The theory of composites, UK: Cambridge University Press, May 2002.(2002).

Milton, G. W., Briane, M. and Willis, J. R., On cloaking for elasticity and physical equations with a transformation invariant form, New Journal of Physics 8(10), 248 (2006).

Milton, G. W. and Serkov, S. K., Neutral coated inclusions in conductivity and anti–plane elasticity. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society,(2001).

Narayana, S., Savo, S. and Sato, Y., Transient heat flux shielding using thermal metamaterials, Applied Physics Letters 102(20), 201904 (2013).

Nehari, Z. Conformal mapping, Courier Corporation, (1975).

Norris, A. and Shuvalov, A., Elastic cloaking theory, Wave Motion 48(6), 525-538 (2011).

Norris, A. N. ,Acoustic cloaking theory. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society,(2008).

Park, G., Kang, S., Lee, H. and Choi, W., Tunable Multifunctional Thermal Metamaterials: Manipulation of Local Heat Flux via Assembly of Unit-Cell Thermal Shifters, Scientific Reports 7, (2017).

Pendry, J. B., Schurig, D. and Smith, D. R., Controlling electromagnetic fields, Science 312(5781), 1780-1782 (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 equations, Photonics and Nanostructures-fundamentals and Applications 6(1), 87-95 (2008).

Raza, M., Liu, Y., Lee, E. H. and Ma, Y., Transformation thermodynamics and heat cloaking: a Review, Journal of Optics 18(4), 044002 (2016).

Schmiele, M., Varma, V. S., Rockstuhl, C. and Lederer, F., Designing optical elements from isotropic materials by using transformation optics, Physical Review A 81(3), 033837 (2010).

Schurig, D., Mock, J., Justice, B., Cummer, S. A., Pendry, J. B., Starr, A. and Smith, D., Metamaterial electromagnetic cloak at microwave frequencies, Science 314(5801), 977-980 (2006).

Shen, X. and Huang, J., Thermally hiding an object inside a cloak with feeling, International Journal of Heat and Mass Transfer 78, 1-6 (2014).

Shen, X., Jiang, C., Li, Y. and Huang, J., Thermal metamaterial for convergent transfer of conductive heat with high efficiency, Applied Physics Letters 109(20), 201906 (2016).

Tang, L., Yin, J., Yuan, G., Du, J., Gao, H., Dong, X., Lu, Y. and Du, C., General conformal transformation method based on Schwarz-Christoffel approach, Optics Express 19(16), 15119-15126 (2011).

Tichit, P.-H., Burokur, S. N. and de Lustrac, A., Ultradirective antenna via transformation optics, Journal of Applied Physics 105(10), 104912 (2009).

Turpin, J. P., Massoud, A. T., Jiang, Z. H., Werner, P. L. and Werner, D. H., Conformal mappings to achieve simple material parameters for transformation optics devices, Optics Express 18(1), 244-252 (2010).

Vemuri, K. P. and Bandaru, P. R., Geometrical considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials, Applied Physics Letters 103(13), 133111 (2013).

Wu, Q., Xu, Y., Li, H. and Chen, H., Cloaking and imaging at the same time, EPL (Europhysics Letters) 101(3), 34004 (2013).

Xiong, Z., Xu, L., Xu, Y.-D. and Chen, H.-Y., Broadband illusion optical devices based on conformal mappings, Frontiers of Physics 12(5), 124202 (2017).

Xu, H., Shi, X., Gao, F., Sun, H. and Zhang, B., Ultrathin three-dimensional thermal cloak, Physical Review Letters 112(5), 054301 (2014).

Xu, L. and Chen, H., Conformal transformation optics, Nature Photonics 9(1), 15-23 (2015).

Yang, T.-Z., Su, Y., Xu, W. and Yang, X.-D., Transient thermal camouflage and heat signature control, Applied Physics Letters 109(12), 121905 (2016).

Yao, K. and Jiang, X., Designing feasible optical devices via conformal mapping, JOSA B 28(5), 1037-1042 (2011).

Yuan, X., Lin, G. and Wang, Y., Design of elliptic cylindrical thermal cloak with layered structure, International Journal of Modern Physics B 31(1), 1650244 (2017).

Zhang, J., Luo, Y., Chen, H. and Wu, B.-I., Manipulating the directivity of antennas with metamaterial, Optics Express 16(15), 10962-10967 (2008).

Zhou, X. and Hu, G., Design for electromagnetic wave transparency with metamaterials, Physical Review E 74(2), 026607 (2006).

翁崇寧，轉換材料在不同物理與彈性問題之理論及等校行為探討，國立成功大學土木所博士論文 (2010)

柯嵋鐘，利用保角變換解析含孔洞或內含物的傳導問題，國立成功大學土木所碩士論文 (2001)