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研究生： 莊于臻
Chuang, Yu-Chen
論文名稱： 以不變量原理達成三波導分光/耦合器
Fast Three-Waveguide Beam Splitter/Coupler based on Invariant Engineering
指導教授： 曾碩彥
Tseng, Shuo-Yen
學位類別： 碩士
Master
系所名稱： 理學院 - 光電科學與工程學系
Department of Photonics
論文出版年： 2014
畢業學年度： 102
語文別： 英文
論文頁數： 101
中文關鍵詞： 波導 、三波導耦合
外文關鍵詞： waveguide, three-waveguide directional coupler
相關次數： 點閱：109  下載：5 
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    • 我們以Lewis-Riesenfeld 不變量算符逆向操作法，在三波導上，成功地將光從一根波導輸入轉成從另外一根波導輸出達成波導間的能量轉換，並且模擬在不同的路徑下的轉換效果加以分析比較。另外，從用來表達出口端能量大小的已知數學形式中，設計不同出口端的能量分割比例，利用光束傳播法來模擬成功地達成能量的分割。最後，利用特定的耦合波導結構，做出量子阿達馬閘。

    We propose fast beam coupling in a three waveguide directional coupler based on Lewis-Riesebfeld invariant theory. The design of beam power converter/splitter using the dynamical invariant is discussed. We use the closed form expressions for the modal power at the ouput for converter/splitter to design various approaches and simulate by beam propagation method in a three waveguide system. We successfully transfer/split power form one waveguide to another or the others in different designed paths. Besides, we use a specific waveguide system to create a quantum Hardamard gate.

    摘要 i Abstract ii 致謝 iii Table of Contents iv List of Figures vi Chapter 1 Introduction 1 Chapter 2 Fundamentals of Optical Waveguides 2 2.1　Wave theory of optical waveguides 2 2.2　Effective index method 5 2.3　Coupled mode theory 8 2.3.1　Codirectional couplers 15 2.3.2 Coupling Coefficients for Slab Waveguides 18 Chapter 3 Analogy between Waveguide Optics and Quantum Theory 20 3.1　The adiabatic three-level system in quantum theory 20 3.2 Lewis-Riesenfeld invariant theory 26 3.3　Similarity between waveguide optics and quantum mechanics 33 Chapter 4 Simulation Results and Discussion 36 4.1　Coupled mode equations based on invariant theory 38 4.1.1 One to one by coupled mode theory 41 4.1.2 One to two by coupled mode theory 45 4.1.3 One to three by coupled mode theory 50 4.1.4 Arbitrary split ratios by coupled mode theory 55 4.2 BPM Simulation results 60 4.2.1 One to one by BPM 62 4.2.1.1 Bandwidth Analysis 65 4.2.2 One to two by BPM 69 4.2.3 One to three by BPM 73 4.2.4 Arbitrary split ratios 78 4.2.5 Hadamard Gate 83 Chapter 5 Conclusion 90 Reference 91 Appendix 94 Appendix A 94 Appendix B 96 Appendix C 98 Appendix D 100

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