本論文中，我們提出了具表面電漿偏極子金屬微米環的滑軌式波導結構，並於金屬環內部產生奈米尺度的磁場。以多重物理量耦合模擬(COMSOL Multiphysics)分析在砷化鎵(GaAs)基板上之砷化銦鎵(InGaAs)波導及金屬微米環結構的特性。
我們先於金屬環表面設定正電荷，再由滑軌式InGaAs波導入射電磁波，在金屬環及介電質介面則引發表面電漿偏極子，此表面電漿偏極子會依循入射光行進方向運行，且帶動金屬環上的正電荷流動，形成電流。根據Biot-Savart law判斷，如此可在金屬環內中心區域形成奈米尺度的磁場。

In this thesis, we study the surface plasmon polariton effect on a metallic micro-ring to generate a nano-magnetic field. The structure consists of a metallic micro-ring and InGaAs pulley-type waveguide on GaAs substrate. COMSOL Multiphysics is used to analyze the device. Positive charges are positioned on the metallic micro-ring. The surface plasmon polariton is induced on the surface of metallic micro-ring by launching the light into the InGaAs waveguide. The propagation of the surface plasmon polariton along the direction of the incident light drives the charge flow to form an electric current on the metallic micro-ring. According to Biot-Savart law, it can form a nano-magnetic field in the center region of the metallic micro-ring.

[1] H. Kuwata, H. Tamaru, K. Esumi, and K. Miyano,“Resonant light scattering from metal nanoparticles: Practical analysis beyond Rayleigh approximation", Appl. Phys. Lett. 83, 4625 (2003).
[2] S. Nie and S. R. Emory, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering", Science 275, 1102 (1997).
[3] H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering", Phys. Rev. Lett. 83, 4357 (1999).
[4] Paul V. Lambeck, "Integrated opto-chemical sensors", Sensors and Actuators B 8, 103 (1992).
[5] Tobias Holmgaard, Zhuo Chen, Sergey I. Bozhevolnyi, Laurent Markey and Alain Dereux, "Dielectric-loaded plasmonic waveguide-ring resonators", Opt. Express 17, 2968 (2009).
[6] 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).
[7] R. D. Harris, J. S. Wilkinson, "Waveguide surface plasmon resonance sensors", Sensors and Actuators B 29, 261 (1995).
[8] Srinivasan Iyer, Sergei Popov, Ari. T. Friberg, "Linear birefringence in split-ring resonators", Opt. Lett. 37, 2043 (2012).
[9] Sanahui Xiao, Liu Liu, Min Qiu, "Resonator channel drop filters in a plasmon-polaritons metal", Opt. Express 14, 2932 (2006).
[10] Yun Shen and Guo Ping Wang, "Gain-assisted time delay of plasmons in coupled metal ring resonator waveguides", Opt. Express 17, 12807 (2009).
[11] 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).
[12] A. V. Krasavin, A. V. Zayats, "Electro-optic switching element for dielectric-loaded surface plasmon polariton waveguides", Applied Phys. Lett. 97, 041107 (2010).
[13] 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 Lithium Niobate", Nano Lett. 15, 1025 (2015).
[14] Sanshui Xiao, Liu Liu, and Min Qiu, "Resonator channel drop filters in a plasmon-polaritons metal", Opt. Express 14, 2932 (2006).
[15] 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).
[16] Ram Prakash Dwivedi, El-Hang Lee, "A compact plasmonic tunable filter using elasto-optic effects", Opt. & Laser Technology 44, 2130 (2012).
[17] Ruben Salvador, Alejandro Martinez, Carlos Garcia-Meca, Ruben Ortuno, and Javier Marti, "Analysis of hybrid dielectric plasmonic waveguide", IEEE Journal of Selected Topics in Quantum Electronics 14, 1496(2008).
[18] Tobias Holmgaard, Zhuo Chen1, Sergey I. Bozhevolnyi, Laurent Markey, and Alain Dereux, "Dielectric-loaded plasmonic waveguide-ring resonators", Opt. Express 17, 2968 (2009)
[19] G Della Valle and Sergey I. Bozhevolnyi, "Metal split-cylinder resonators for plasmonic nanosensing", J. Opt. 13, 095001 (2011).
[20] 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).
[21] 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).
[22] Ryan M. Briggs, Jonathan Grandidier, Stanley P. Burgos, Eyal Feigenbaum, and Harry A. Atwater, "Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides", Nano Lett. 10, 4581 (2010).
[23] 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).
[24] 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).
[25] R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum", Philosophical Magazine 4, 396 (1902).
[26] D. Pines and D. Bohm, "A collective description of electron interations: Coulomb interactions in a degenerate electron gas", Phys. Rev. 92, 609 (1953).
[27] R. H. Ritchie, "Plasma losses by fast electrons in thin films", Phy. Rev. 106, 874, (1957).
[28] N. W. Ashcroft, and N. D. Mermin, Solid State Physics., Harcourt., (1976).
[29] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings., Springer-Verlag., Berlin (1998).
[30] A. V. Krasavin and A. V. Zayats, "Electro-optic switching element for dielectric-loaded surface plasmon polariton waveguides", Appl. Phys. Lett. 97, 041107 (2010).
[31] 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).
[32] Davod Ahmadian, Changiz Ghobadi, and Javad Nourinia, "Tunable Plasmonic Sensor With Metal–Liquid Crystal–Metal Structure", IEEE Photonics Journal 7, 4800310 (2015).
[33] 邱國斌、蔡定平，「金屬表面電漿簡介」，物理雙月刊， 28，472頁 (2006).
[34] Kenji Kawano and Tsutomu Kitoh, Introduction to optical waveguide analysis, John Wiley and Sons, New York, 2001.
[35] Jianming Jin, The Finite Element Method in Electromagnetics, John Wiley and Sons, 2nd edition.
[36] 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)。
[37] Hunsperger, R.G, Integrated Optics: Theory and Technology, Springer-Verlag, 1982.