在本論文研究中，我們利用外加磁場的方式來控制表面電漿的特性，並且將其應用在半導體-介電質堆疊而成的多層膜結構上。多層膜結構可視為一非等向性材料，並且隨著不同方向及大小的外加磁場可具有不同的介電係數張量。但由於外加磁場產生電子迴旋運動(cyclotron motion)的關係，使其產生不對稱的現象，我們將以色散關係式來加以說明。
我們藉由選擇適合的方向以及調整適當的外加磁場大小來控制整體多層膜的材料特性，並將其和超解析透鏡結合，使其在不改變結構以及材料的情況下，可以在不同的波段達到次波長解析的效果。透過有限元素分析軟體COMSOL驗證了我們理論及方法的正確性，並且我們也可以使用不同大小的外加磁場來改變解析的能力，這是目前已被提出的超解析透鏡沒有辦法做到的。

The main idea of this investigation is to build a system to subwavelength imaging. By using transfer matrix method and the effective medium approach of the investigated components, the ability of breaking optical diffraction limitation is elucidated. Based on the derived theory results, the finite element method (FEM) based electromagnetic commercial software COMSOL is taken to prove the feasibility of this proposed device.
We proposed and analyze a multilayered Semiconductor-dielectric structure for subwavelength resolution at terahertz region by controlling the magnitude of external magnetic field. Our methodology provide a way to multi-functional material, real-time subwavelength imaging, and high-density optoelectronic components with considering the effects of abnormal diffraction feature.

[1] D. A. Schultz, “Plasmon resonant particles for biological detection”, Current Opinion in Biotechnology, Vol. 14, No. 1, pp. 13-22, 2003.
[2] M. Moskovits, “Surface-enhanced spectroscopy”, Reviews of Modern Physics, Vol. 57, No. 3, pp. 783-826, 1985.
[3] Zhaowei Liu, Hyesog Lee, Yi Xiong, Cheng Sun, Xiang Zhang, ”Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects”, Science, Vol. 315, No. 5819, pp. 1686, 2007.
[4] E. Hecht, “Optics”, Addison Wesley, San Francisco, pp. 606-620, 2002.
[5] V. G. Veselago,” The electrodynamics of substances with simultaneously negative value of and ”, Soviet Physics Uspekhi, Vol. 10, No. 4, pp. 509-517, 1968.
[6] 邱國斌, 蔡定平, ”左手材料奈米平板的表面電漿量子簡介”, 物理雙月刊, 25卷, 3期, pp. 373-383, 2003.
[7] A. V. Sokolov, “Opticheskie svolstva metallov”, Academy of Sciences of USSR, Vol. 55, 1971.
[8] J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, ” Magnetism from conductors and enhanced nonlinear phenomena”, IEEE Transactions on Microwave Theory and Techniques, Vol. 47, pp. 2075-2084, 1999.
[9] R. A. Shelby, D. R. Smith, S. Schultz, “Experimental Verification of a Negative Index of Refraction”, Science, Vol. 292, No. 5514, pp. 77-79, 2001.
[10] J. B. Pendry, “Negative Refraction Makes a Perfect Lens”, Physical Review Letters, Vol. 85, No. 18, 2000.
[11] J. B. Pendry, “Imaging the near field”, Journal of modern optics, Vol. 50, No. 9, pp. 1419-1430, 2003.
[12] I. D. Rukhlenko, M. Premaratne, G. P. Agrawal, ”Plasmonic Modes of Metamaterial-Based Slot Waveguides”, Advances in OptoElectronics, Vol. 2012, pp. 1-5, 2012.
[13] Ammon Yariv, Pochi Yeh, “Optical electronics in modern communications”, oxford university press, New York, pp. 546-551, 2007.
[14] B. Wood, J. B. Pendry, D.P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system”, Physical Review B, Vol. 74, Issue 11, 2006.
[15] B. H. Cheng, Y. Z. Ho, Y. C. Lan, D. P. Tsai, “Optical Hybrid-Superlens Hyperlens for Superresolution Imaging”, IEEE Journal of Selected Topics in Quantum Electronics, Vol. 19, No. 3, 2013.
[16] M. S. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures”, Surface Science Reports, Vol. 41, Issues 1-8, pp. 1-416, 2001.
[17] H. Raether, “Surface Plasmons on Smooth and Rough Surfaces and on Gratings”, Springer, New York, pp. 4-37, 1988.
[18] H. A. Atwater, “The Promise of Plasmonics”, Scientific American, Vol. 296, Issue 4, pp. 56-62, 2007.
[19] 邱國斌, 蔡定平, 金屬表面電漿簡介, 物理雙月刊, 28, 2期, pp. 472-485, 2006.
[20] A. V. Zayats, I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons”, Physics Reports, Vol. 408, Issue 3-4, pp. 131-314, 2005.
[21] A. Drezet, A. Hohenau, J.R. Krenn, M. Brun, S. Huant, “Surface Plasmon mediated near-field imaging and optical addressing in nanoscience”, Micron, Vol. 38, Issue 4, pp. 427-437, 2007.
[22] A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection”, Zeitschrift für Physik, Vol. 216, Issue 4, pp. 398-410, 1968.
[23] M. S. Kushwaha, P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration”, Physical Review B, Vol. 36, No. 11, pp. 5960-5967, 1987.
[24] M. S. Kushwaha, P. Halevi, “Magnetoplasma modes in thin films in the Faraday configuration”, Physical Review B, Vol. 35, No. 8, pp. 3879-3889, 1987.
[25] M. S. Kushwaha, P. Halevi, ” Magnetoplasmons in thin films in the perpendicular configuration”, Physical Review B, Vol. 38, No. 17, pp. 428-435, 1988.
[26]王剛, 安琳, “COMSOL Multiphysics工程實踐與理論仿真-多物理場數值分析技術”, 電子工程出版社, 北京, pp. 36-46, 2012.
[27] J. G. Rivas, C. Janke, P. H. Bolivar, H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures”, Optics Express, Vol. 13, Issue 3, pp. 847-859, 2005.
[28] Y. S. Jin, G. J. Kim, S. J. Jeon, “Terahertz Dielectric Properties of Polymers”, Journal of the Korean Physical Society, Vol. 49, No. 2, pp. 513-517, 2006.