本論文主要是針對以單模SOI波導構成的微環形共振腔進行元件模擬設計與特性分析，內文主要分為下列兩大項進行討論：
1. SOI波導特性：
相較於其他材料，SOI波導擁有兩項最大的優勢－與CMOS製程的高度相容性、和超高的導光層(core)/披覆層(cladding)折射率差。本論文將詳細探討SOI波導的模擬分析方法、不同情形下的模態特性，為後續元件設計立下扎實基底。
2. 微環形共振腔元件：
微環形共振腔具有高自由頻譜空間和窄頻寬等等的特性，因此常被用於光通訊/光連接方面的應用。本論文以3D-FDTD進行微環形共振腔之穿透頻譜模擬，發現許多頻譜呈現double-dip的樣貌，表示環內有一反射模態。本團隊認為該現象主要是由耦合區域中的反射造成，而非多數研究團隊認為的側壁粗糙造成之反射，文中將以4x4散射矩陣和耦合區域的模態計算進行佐證，以解釋頻譜的double-dip現象。
Double-dip現象對於需要波長選擇機制之被動元件，如光開關、濾波器等等是非常不樂見的，因此，根據single-dip條件，如何提高訊息波導－環形波導之間的能量耦合效率，便是被動環形共振腔元件設計中最重要的一環，且對於最佳化雙環光開關之設計也有正面之助益。本論文將提出3D環形共振腔結構以在低損耗之情形下達到更高的訊息波導－環形波導間能量耦合效率。
對於主動元件之設計而言，環形共振腔中的反射模態對於元件之時變儲存能量(和輸出能量)將會造成影響，本論文將推導環形共振腔元件之動態分析式，搭配新加坡IME公司之設計規則，探討不同結構下，環形共振腔光調變器之表現，並設計出高速光調變器。

The thesis is focused on designing and analyzing SOI micro-ring resonator devices:
1. SOI waveguide properties:
Highly CMOS process compatibility and large refractive index contrast between core and cladding is two of the most important advantages in SOI waveguide. This thesis will detailly introduce and discuss the simulation methods and properties of SOI waveguide.
2. SOI micro-ring devices:
Owing to the high FSR and narrow passband, small bending radius micro-rings were often used for optical communication and interconnection applications. However, double-dip effect is frequently happened on the transmission spectrum. Instead of attributing the effect to surface roughness of waveguide, our group announce that it is caused by the non-adiabatic index change in coupling region of ring devices. In this thesis, our argument will be confirmed by precise mode calculation and 3D-FDTD simulation.
Thus, how to increase the coupling coefficient between bus and ring waveguide is the most important task to eliminate double-dip effect and achieve optimized condition of double-ring optical switch device. Furthermore, the reflection mode in ring cavity will seriously affect the dynamic performance of ring resonator, or ring modulator. In this thesis, we will discuss the issue above, and propose several solutions for optical switch and ring modulator devices, which have great potential in optical communication and interconnection applications.

論文審定書 i
摘要 iii
Abstract iv
圖次 vii
第一章 緒論 1
1.1. 矽光子技術(Silicon Photonics technology) 1
1.1.1 技術背景 1
1.1.2 應用於光連接技術 4
1.2. 研究動機 7
1.3. 論文架構 7
第二章 基礎理論 8
2.1. 數值模擬方法 8
2.1.1. 有限差分法(FDM)概念 8
2.1.2. 有限差分法(FDM)求解波導模態 9
2.1.3. 有限時域差分法(FDTD)求解時域和頻域響應 13
2.2. SOI波導特性 17
2.2.1. SOI長直波導 17
2.2.2. SOI彎曲波導 19
2.3. 環形共振腔 23
2.3.1. 數學形式推導 24
2.3.2. 耦合條件 27
2.3.3. 自由頻譜空間(free spectral range, FSR) 28
2.3.4. 設計目標 29
第三章 SOI微環形共振腔被動元件之設計 31
3.1. 最佳化目標 31
3.2. SOI環形共振腔全通濾波器 33
3.2.1. Double-dip現象 33
3.2.2. 3D-FDTD模擬結果與分析 38
3.2.3. 3D-FDTD時域響應 44
3.2.4. 實驗量測結果與分析 47
3.3. 反射係數分析 52
3.4. 結構之最佳化 55
第四章 SOI微環形共振腔主動元件之設計 61
4.1. 矽光調變器之原理及機制 61
4.1.1. 調變器之物理機制 61
4.1.2. 常見矽電光調變器結構 63
4.2. 環形共振腔之暫態分析 65
4.2.1. 數學形式推導 65
4.2.2. 考慮反射係數下之動態分析 71
4.2.3. 不考慮反射係數下(傳統模型)之動態分析 72
4.3. 環形共振腔光調變器設計 75
4.3.1. 彎曲半徑R的選擇 77
4.3.2. 波導兩側平板高度(slab height)的選擇 77
4.3.3. 波導寬度W的選擇 78
4.3.4. 摻雜濃度的選擇 79
4.3.5. 波導至重摻雜區域距離的選擇 81
4.3.6. 加熱器(heater)之設計 82
4.3.7. 環形共振腔光調變器之模擬結果 83
第五章 結論 92
第六章 未來工作 95
參考文獻 98

[1] G. Moore, “Cramming More Components ontoIntegrated Circuits,” Electronics, pp. 114–117, April 19, 1965.
[2] G.P. Agrawal, Fiber-Optic Communication Systems, 4th edition., WILEY, 2010.
[3] M. A. Popovíc, “Theory and design of high-index-contrast microphotonic circuits,” PhD Dissertation, MIT, 2008.
[4] B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol., vol. 15, pp. 998–1005, 1997.
[5] V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson,"All-optical control of light on a silicon chip," Nature, vol. 431, pp. 1081–1084, 2004.
[6] F.Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O'Faolain, F. Dong, J.M. Fedeli, P. Dumon, L. Vivien, T.F. Krauss, G.T. Reed, J. Martí, "High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode," Opt Express, vol. 17, no. 24, pp. 21986–21991, 2009.
[7] Intel silicon photonics research group, Intel®, http://www.intel.com/content/www/us/en/research/intel-labs-silicon-photonics-research.html
[8] Chin-Ping Yu,”Improved Finite-Difference Frequency-Domain Method for Modal Analysis of Optical Waveguides and Photonics Crystal Devices,” NTU PHD Dissertation, 2004.
[9] W.P. Huang, C.L. Xu, S.T. Chu, S.K. Chaudhuri, "The finite-difference vector beam propagation method. Analysis and Assessment," J. Lightwave Technol., vol. 10, pp. 295–305, 1992.
[10] K. S. Yee, "Design and Modeling of Waveguide-Coupled Single-Mode Microring Resonators," IEEE Trans. Antennas Propagate., vol. AP-14, pp. 302–307, 1966.
[11] Fimmwave/Fimmprop/Omnisim, Photon Design Ltd, http://www.photond.com
[12] SMF-28 optical fiber, Corning®, http://www.corning.com
[13] B.E. Little,”Advances in microring resonator,” Proc. OSA, Intergrated Photonics Reaserch Conference, 2003.
[14] M.K. Chin, S.T. Ho, "Design and Modeling of Waveguide-Coupled Single-Mode Microring Resonators," J. Lightwave Technol., vol. 16, pp. 1433–1446, 1998.
[15] Y. Hida, Y. Hibino, M. Itoh, A. Sugita, A. Himeno, Y. Ohmori, "Fabrication of low-loss and polarisation-insensitive 256 channel arrayed-waveguide grating with 25 GHz spacing using 1.5% Δ waveguides," J. Electrics Lett., vol. 36, pp. 820–821, 2000.
[16] K. Okamoto, “Fundamentals of Optical Waveguides,” 2nd ed. Academic Press, NY, 2006.
[17] C.W. Tseng, C.W. Tsai, K.C. Lin, M.C. Lee, Y.J. Chen, "Study of coupling loss on strongly-coupled, ultra compact microring resonators," Opt. Express, vol. 21, pp. 7250–7257, 2013.
[18] C. Y. Chen,” Analysis of SOI micro-ring resonators,” M.S. thesis, NSYSU, 2014.
[19] Q. Xu, D. Fattal, R. G. Beausoleil, "Silicon microring resonators with 1.5-μm radius," Opt. Express , vol. 16, pp. 4309–4315, 2008.
[20] Q. Xu, B. Schmidt, J. Shakya, M. Lipson, "Cascaded silicon micro-ring modulators for WDM optical interconnection,"Opt. Express , vol. 14, pp. 9431–9435, 2006.
[21] B. E. Little, J. P. Laine, and S. T. Chu, "Surface-roughness-induced contradirectional coupling in ring and disk resonators," Opt. Lett., vol. 22, pp. 4–6, 1997.
[22] C. Y. Chen, C.Y. Chen, Y.J. Chen,” Analysis of SOI micro ring resonator with reflection property using low coherence interferometry method,” paper 578,OECC, 2014.
[23] Y.A. Vlasov, S.J. McNab, "Losses in single-mode silicon-on-insulator strip waveguide and bends," Opt. Express, vol. 12, pp. 1622–1631, 2004.
[24] C. W. Tsai,” SOI micro-ring resonator measurements and analysis,” M.S. thesis, NSYSU, 2013.
[25] F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O'Faolain, D. Van Thourhout, R. Baets, "Compact focusing grating couplers for Silicon-on-Insulator integrated circuits,"IEEE Photon. Technol. Lett., vol. 19, pp. 1919–1921, 2007.
[26] P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. V. Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. V. Thourhout, R. Baets, "Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography," IEEE Photon. Technol. Lett., vol. 16, pp. 1328–1330, 2004.
[27] F. Xia, M. Rooks, L. Sekaric, Y. Vlasov, "Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects," Opt. Express, vol. 15, pp. 11934–11941, 2007.
[28] J.R. Ong, R. Kumar, S. Mookherjea, "Ultra-High-Contrast and Tunable-Bandwidth Filter Using Cascaded High-Order Silicon Microring Filters," IEEE Photon. Technol. Lett., vol. 25, no. 16, pp. 1543–1546, 2013.
[29] C.Y. Wang, C.W. Tseng, C.Y. Chen, C.T. Wang, Y.J. Chen," Design and analysis of ultra small radius micro-ring resonator ", Proc. SPIE8781, Integrated Optics: Physics and Simulations, 87810A, 2013.
[30] F.Y. Gardes, J.-M. Fedeli, S Zlatanovic, H. Youfang Hu, B.P.P. Kuo, E. Myslivets, N. Alic, S. Radic,G.Z. Mashanovich, G.T. Reed, "50-Gb/s Silicon Optical Modulator," IEEE Photon. Technol. Lett., vol. 24, no. 4, pp. 234–236, 2012.
[31] X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, Y. Yu, "44-Gb/s Silicon Microring Modulators Based on Zigzag PN Junctions," Ieee Photon. Technol. Lett., vol. 24, no. 19, pp. 1712–1714, 2012.
[32] P. Dong, R. Shafiiha, S. Liao, H. Liang, N. Feng, D. Feng, G. Li, X. Zheng, A.V. Krishnamoorthy, M. Asghari, "Wavelength-tunable silicon microring modulator," Opt. Express, vol. 18, no. 19, pp. 10941–10946, 2010.
[33] T.H. Wu, J.P. Wu, Y,J, Chiu, "Low-Power-Driven and Low-Optical-Loss 40-Gb/s Electroabsorption Modulator Using Self-Aligned Two-Step Undercut-Etched Waveguide,"Electron Device Lett., vol. 33, no. 7, pp. 1021–1023, 2012.
[34] L. Vivien, L. Pavesi, Handbook of Silicon Photonics., CRC Press, 2013,
[35] C.Z. Tan, J. Arndt, "Temperature dependence of refractive index of glassy SiO2 in the infrared wavelength range," J. Phys. Chem. Solids, vol. 61, no. 8, pp. 1315–1320, 2000.
[36] G.T. Reed, G. Mashanovich, F.Y. Gardes, D. J. Thomson, "silicon optical modulators," Nature Photonics, vol. 4, pp. 518–526, 2010.
[37] K. Preston, S. Manipatruni, A. Gondarenko, C. B. Poitras, and M. Lipson, "Deposited silicon high-speed integrated electro-optic modulator," Opt. Express, vol. 17, pp. 5118–5124, 2009.
[38] C. E. Png, S. P. Chan, S. T. Lim, and G. T. Reed, "Optical phase modulators for MHz and GHz modulation in silicon-on-insulator (SOI)," J. Lightwave Technol., vol. 22, pp. 1573–1582, 2004.
[39] A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, "A high speed silicon optical modulator based on a metal-oxide-semiconductor capacitor," Nature, vol. 427, p. 615–618, 2004.
[40] D. D’Andrea, “CMOS photonics today and tomorrow,” http://www.ofcnfoec.org/osa.ofc/media/Default/PDF/2009/09-Dandrea.pdf.
[41] C. Gunn, "CMOS photonics for high-speed interconnects," Naturemicro. IEEE, vol. 26, p. 58–66, 2006.
[42] X. Tu, T.Y. Liow, J. Song, X. Luo, Q. Fang, M. Yu, G.Q. Lo, "50-Gb/s silicon optical modulator with traveling-wave electrodes," Opt. Express , vol. 21, pp. 12776–12782, 2013.
[43] T.Y. Liow, K.W. Ang, Q. Fang, J.F. Song, Y.Z. Xiong, M.B. Yu, G.Q. Lo, D.L. Kwong, "Silicon Modulators and Germanium Photodetectors on SOI: Monolithic Integration, Compatibility, and Performance Optimization," IEEE J. Selected Topics Quantum Electron., vol. 16, no. 1, pp. 307–315, 2010.