本論文致力於研究絕緣層矽(silicon-on-insulator, SOI)分光器之理論分析與數值模擬。首先，我們介紹四個不同的分光器波導系統之基本理論，並使用 FDTD 模擬軟體設計出四個不同結構的分光器系統。四個分光器系統擁有各自的優點及缺點，我們從中分析出在何種需求下該應用何種分光器系統，亦即我們藉由此此分析以選用最佳的波導分光器。此外，本論文著重在利用絕緣層覆矽材料為基礎以具體實現波導分光器，並以縮小元件尺寸與增加元件操作頻寬為研究方向、以促進高密度積體光路的發展。

This thesis is devoted to theoretical investigation and numerical simulations of 3-dB 2×2 couplers for 220 nm Silicon-on-Insulator (SOI) platform. We begin by introducing the operation principle of four different waveguide splitter systems, then we use the three-dimensional Finite-Difference Time-Domain (3D-FDTD) method to perform simulations. We design four different splitter systems, including Directional Couplers (DC), Broadband Directional Couplers (BDC), Multimode Interferometers (MMI), and Adiabatic Couplers (AC). Then we compare the four waveguide splitter systems to evaluate the performance of each coupler design. We analyze the imbalance (IM), coupling variation, the input/output insertion loss (IL), and footprint of the designs. Each design has its own advantages and disadvantages, and the design choices are dictated by the requirements.

中文摘要 ...iii
Abstract ...iv
Acknowledgements ...v
Table of Contents ...vi
List of Figures ...viii
Chapter 1 Introduction ...1
1.1 Motivation ...1
1.2 Introduction ...2
1.3 Organization of the Thesis ...4
Chapter 2 Theoretical Analysis ...5
2.1 Theory of Mainstream Algorithms ...5
2.1.1 Beam Propagation Method (BPM) ...6
2.1.2 EigenMode Expansion Method (EME) ...8
2.1.3 Finite Difference Time Domain (FDTD) ...11
2.1.4 Comparison of Mainstream Algorithms ...14
2.2 FDTD simulation with Lumerical tool ...16
2.2.1 Mesh refinement ...16
2.2.2 Mesh refinement choices ...17
Chapter 3 Simulation Results and Discussion ...20
3.1 Directional Coupler ...21
3.2 Broadband Directional Coupler ...25
3.3 Multimode Interference ...30
3.4 Adiabatic Coupler ...35
3.5 Comparison of Performance ＆ Discussion ...40
Chapter 4 Conclusion and Perspectives ...42
4.1 Conclusion ...42
4.2 Perspectives ...42
Reference ...44

[1]H. Morino, T. Maruyama, and K. Iiyama, Reduction of wavelength dependence of coupling characteristics using Si optical waveguide curved directional coupler. Journal of Lightwave Technology, 2014. 32(12): p. 2188-2192.
[2]Z. Lu, et al., Comparison of Photonics 3-dB 2× 2 Couplers for 220 nm Silicon-on-Insulator Platform. IEEE 12th International Conference on Group IV Photonics (GFP), 2015: p. 57-58.
[3]Z. Lu, et al., Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control. Optics Express, 2015. 23(3): p. 3795-3808.
[4]H. Yun, et al., 2× 2 adiabatic 3-dB coupler on silicon-on-insulator rib waveguides. SPIE, 2013. 8915: p. 89150V-89150V-6.
[5]J. Van Campenhout, et al., Low-power, 2× 2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks. Optics Express, 2009. 17(26): p. 24020-24029.
[6]B.E. Little, et al., Ultra-compact Si-SiO 2 microring resonator optical channel dropping filters. IEEE Photonics Technology Letters, 1998. 10(4): p. 549-551.
[7]H. Yamada, et al., Si photonic wire waveguide devices. IEEE Journal of Selected Topics in Quantum Electronics, 2006. 12(6): p. 1371-1379.
[8]H. Fukuda, et al., Ultrasmall polarization splitter based on silicon wire waveguides. Optics Express, 2006. 14(25): p. 12401-12408.
[9]C.A. Brackett, Dense wavelength division multiplexing networks: Principles and applications. IEEE Journal on Selected Areas in Communications, 1990. 8(6): p. 948-964.
[10]P.B. Catrysse, Integration of optical functionality for image sensing through sub-wavelength geometry design. SPIE, 2015. 9481: p. 948102-948102-8.
[11]K. Okamoto, Fundamentals of optical waveguides (Second Edition). Academic Press, 2010: p. 329-330.
[12]J. Van Roey, J. van der Donk, and P.E. Lagasse, Beam-propagation method: analysis and assessment. Journal of the Optical Society of America, 1981. 71(7): p. 803-810.
[13]M.F.O. Hameed, and S.S. Obayya, Ultrashort silica liquid crystal photonic crystal fiber polarization rotator. Optics Letters, 2014. 39(4): p. 1077-1080.
[14]D.F.G. Gallagher, and T.P. Felici, Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons. SPIE, 2003. 4987: p. 69-82.
[15]K. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on Antennas and Propagation, 1966. 14(3): p. 302-307.
[16]P.G. Luan, and Q.C. Chen, Photonic Crystals. Wu-Nan Book Inc, 2010: p. 304-307.
[17]D. Gallagher, Photonic CAD matures. IEEE LEOS NewsLetter, 2008. 22(1): p. 8-14.
[18]Mesh refinement. Lumerical Knowledge Base, 2003. Retrieved from http://www. lumerical.com
[19]K. Okamoto, Fundamentals of optical waveguides (Second Edition). Academic Press, 2010: p. 167-168.
[20]K. Okamoto, Fundamentals of optical waveguides (Second Edition). Academic Press, 2010: p. 46-51
[21]K. Jinguji, et al., Mach-Zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio. Electronics Letters, 1990. 26(17): p. 1326-1327.