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研究生: 吳研慶
Wu, Yen-Ching
論文名稱: 利用光子晶體產生沿單一方向傳播的拓樸邊緣態
Using Photonic Crystals Topological Insulator to Create One-Way Propagation Edge States by Finite-Difference Time-Domain Method
指導教授: 張世慧
Chang, Shih-Hui
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: 2021
畢業學年度: 109
語文別: 中文
論文頁數: 62
中文關鍵詞: 光子晶體偽自旋拓樸邊緣態單一方向傳播有限差分時域法
外文關鍵詞: photonic crystal, pseudospin, topological edge states, one-way propagation, FDTD
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  • 口試委員審定書 I 中文摘要 II Abstract III 誌謝 XII 目錄 XIII 圖目錄 XV 符號 XVIII 第一章 序論 1 1.1 前言 1 1.2 研究動機 2 1.3 本文內容 2 第二章 研究相關理論 3 2.1 光子晶體(photonic crystal) 3 2.2 晶格與倒晶格(lattice and reciprocal lattice) 3 2.3 布洛赫定理(Bloch’s Theorem) 6 2.4 布里淵區(Brillouin zone) 6 2.5 能帶結構(band structure) 7 2.6 拓樸學(topological) 9 2.7 霍爾效應(Hall effect) 10 2.8 量子霍爾效應(quantum Hall effect) 11 2.9 哈爾丹模型(Haldane model) 14 2.10 量子自旋霍爾效應(quantum spin Hall effect) 17 第三章 數值模擬方法 19 3.1 有限差分法 (Finite Difference method) 19 3.2 有限差分時域法 (Finite-Difference Time-Domain method) 19 3.3 卷積完美匹配層 (Convolutional Perfect Matching Layer, CPML) 23 3.4 週期性邊界條件(Periodic Boundary Condition) 26 3.5 利用FDTD去計算能帶結構 27 第四章 研究結果與討論 29 4.1 光子晶體模擬結構 29 4.2 光子晶體的能帶結構 30 4.3 偽自旋 37 4.4 拓樸邊緣態 39 4.5 有限的單一邊界拓樸邊緣態 42 4.6 有限的被包圍邊界拓樸邊緣態 50 4.7 免疫結構缺陷的邊緣效應 52 4.8 拓樸絕緣體製成的共振腔 54 第五章 結論與未來展望 58 5.1 結論 58 5.2 未來展望 58 參考文獻 60

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