在本論文中，我們將電磁波打入滑軌式波導金屬微米環結構， 研究如何能使電磁波透過滑軌式彎曲波導，在金屬微米環上激發出最多的表面電漿。

我們提出一種分析方法，能夠得知表面電漿有效的激發條件為何，進而節省製成成本、省去實驗上嘗試錯誤的時間。我們以保角映射法結合亥姆霍茲方程式，計算在不同激發條件下，電磁波在彎曲波導內的等效入射角，得到不同模態電磁波之等效入射角與波導寬關係圖。並利用色散曲線圖去預測表面電漿的共振角。當等效入射角等於表面電漿共振角時，則能在金屬微米環上激發出最多的表面電漿。

對於理論分析結果的準確性，我們使用COMSOL數值分析軟體來做結構模擬，驗證出理論分析的結果具有相當的準確性。本論文的滑軌型波導表面電漿偏極子金微米環結構，其表面電漿共振角在色散曲線的預測下為17.1度，而在我們所提出的分析方法中為17.2度，誤差為0.5%，可有效預測並節省製成上的嘗試時間。

In this paper, we study the condition to excite the surface plasmon in the pulley-type metallic microring structure. Helmholtz equation is applied to determine the equivalent incidence angle of the curved waveguide with different-order in the TM modes by the conformal transformation method. The surface plasmon excitation angle is confirmed by the finite-element method. The pulley-type metallic microring structure is analyzed for different structures to obtain stronger surface plasmon excitation.

[1] Paul V. Lambeck, "Integrated opto-chemical sensors", Sensors and Actuators B 8, 103 (1992).
[2] Tobias Holmgaard, Zhuo Chen, Sergey I. Bozhevolnyi, Laurent Markey and Alain Dereux, "Dielectric-loaded plasmonic waveguide-ring resonators", Opt. Express 17, 2968 (2009).
[3] J. Homola, J. Ctyroky, M. Skalsky, J. Hradilova P. Kolarova, "A Surface plasma resonance based integrated optical sensor", Sensors and Actuators B 39, 286 (1997).
[4] R. D. Harris, J. S. Wilkinson, "Waveguide surface plasmon resonance sensors", Sensors and Actuators B 29, 261 (1995).
[5] Srinivasan Iyer, Sergei Popov, Ari. T. Friberg, "Linear birefringence in split-ring resonators", Opt. Lett. 37, 2043 (2012).
[6] Sanahui Xiao, Liu Liu, Min Qiu, "Resonator channel drop filters in a plasmon-polaritons metal", Opt. Express 14, 2932 (2006).
[7] Yun Shen and Guo Ping Wang, "Gain-assisted time delay of plasmons in coupled metal ring resonator waveguides", Opt. Express 17, 12807 (2009).
[8] X. Zhao, J. M. Tsai, H. Cai, X. M. Ji, J. Zhou, M. H. Bao, Y. P. Huang, D. L. Kwong, A. Q. Liu, "A nano-opto-mechanical pressure sensor via ring resonstor", Opt. Express 20, 8535 (2012).
[9] A. V. Krasavin, A. V. Zayats, "Electro-optic switching element for dielectric-loaded surface plasmon polariton waveguides", Applied Phys. Lett. 97, 041107 (2010).
[10] Dennis Lehr, Jorg Reinhold, Illia Thiele, Holger Hartung, Kay Dietrich, Christoph Menzel, Thomas Pertsch, Ernst-B. Kley and Andreas Tunnermann, "Enhancing second harmonic generation in gold nanoring resonators filled with Lithiμm Niobate", Nano Lett. 15, 1025 (2015).
[11] Sanshui Xiao, Liu Liu, and Min Qiu, "Resonator channel drop filters in a plasmon-polaritons metal", Opt. Express 14, 2932 (2006).
[12] Odysseas Tsilipakos, Traianos V. Yioultsis and Emmanouil E. Kriezis, "Theoretical analysis of thermally tunable microring resonator filters made of dielectric-loaded plasmonic waveguides", J. Appl. Phys. 106, 093109 (2009).
[13] Ram Prakash Dwivedi, El-Hang Lee, "A compact plasmonic tunable filter using elasto-optic effects", Opt. & Laser Technology 44, 2130 (2012).
[14] Ruben Salvador, Alejandro Martinez, Carlos Garcia-Meca, Ruben Ortuno, and Javier Marti, "Analysis of hybrid dielectric plasmonic waveguide", IEEE Journal of Selected Topics in Quantμm Electronics 14, 1496(2008).
[15] Tobias Holmgaard, Zhuo Chen1, Sergey I. Bozhevolnyi, Laurent Markey, and Alain Dereux, "Dielectric-loaded plasmonic waveguide-ring resonators", Opt. Express 17, 2968 (2009)
[16] G Della Valle and Sergey I. Bozhevolnyi, "Metal split-cylinder resonators for plasmonic nanosensing", J. Opt. 13, 095001 (2011).
[17] Chia-Yang Tsai, Jyun-Wei Lin, Che-Yao Wu, Pin-Tso Lin, Tsan-Wen Lu, and Po-Tsung Lee, "Plasmonic coupling in gold nanoring dimmers: Observation of coupled bonding mode", Nano Lett. 12, 1648 (2012).
[18] Rachel Near, Christopher Tabor, Jinsong Duan, Ruth Pachter, and Mostafa El-Sayed, "Pronounced effect of anisotropy on plasmonic properties of nanorings fabricated by electron beam lithography", Nano Lett. 12, 2158 (2012).
[19] Ryan M. Briggs, Jonathan Grandidier, Stanley P. Burgos, Eyal Feigenbaμm, and Harry A. Atwater, "Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides", Nano Lett. 10, 4581 (2010).
[20] Sergey I. Bozhevolnyi, Valentyn S. Volkov1, Eloïse Devaux, Jean-Yves Laluet, and Thomas W. Ebbesen,"Channel plasmon subwavelength waveguide components including interferometers and ring resonators", Nature 440, 508 (2006).
[21] Lorena O Diniz, Euclydes Marega Jr, Frederico D Nunes, and Ben-Hur V Borges, "A long-range surface plasmon-polariton waveguide ring resonator as a platform for (bio)sensor applications", J. Opt. 13, 115001 (2011).
[22] R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrμm", Philosophical Magazine 4, 396 (1902).
[23] D. Pines and D. Bohm, "A collective description of electron interations: Coulomb interactions in a degenerate electron gas", Phys. Rev. 92, 609 (1953).
[24] R. H. Ritchie, "Plasma losses by fast electrons in thin films", Phy. Rev. 106, 874, (1957).
[25] N. W. Ashcroft, and N. D. Mermin, Solid State Physics., Harcourt., (1976).
[26] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings., Springer-Verlag., Berlin (1998).
[27] A. V. Krasavin and A. V. Zayats, "Electro-optic switching element for dielectric-loaded surface plasmon polariton waveguides", Appl. Phys. Lett. 97, 041107 (2010).
[28] Davod Ahmadian, Changiz Ghobadi, and Javad Nourinia, "Ultra-compact two-dimensional plasmonic nano-ring antenna array for sensing applications", Opt Quant Electron 46, 1097 (2014).
[29] Davod Ahmadian, Changiz Ghobadi, and Javad Nourinia, "Tunable Plasmonic Sensor With Metal–Liquid Crystal–Metal Structure", IEEE Photonics Journal 7, 4800310 (2015).
[30] 邱國斌、蔡定平，「金屬表面電漿簡介」，物理雙月刊， 28，472頁 (2006).
[31] Kenji Kawano and Tsutomu Kitoh, Introduction to optical waveguide analysis, John Wiley and Sons, New York, 2001.
[32] Jianming Jin, The Finite Element Method in Electromagnetics, John Wiley and Sons, 2nd edition.
[33] 宋明哲，複合式單胞光子晶體光纖設計與分析，碩士論文，交通大學電子物理所，新竹 (2007)。
[34] Hunsperger, R.G, Integrated Optics: Theory and Technology, Springer-Verlag, 1982.
[35] K. Okamoto, “Fundamentals of Optical Waveguide, ” First edition, Academic.
[36] R. Schinzinger and P. A. A. Laura, Conformal Mapping: Method and Application, First Edition, Dover.
[37] https://commons.wikimedia.org/wiki/File:Conformal_map.svg
[38] 林詩雅，表面電漿偏極子金屬微米環研究，碩士論文，中央大學光電所 (2016)。