具有空間反射對稱之準一維光子晶體之介面態與札克相分析

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姓名

王柏瑜(Po-Yu Wang) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

具有空間反射對稱之準一維光子晶體之介面態與札克相分析
(The Interface States and Zak Phase Analysis of Quasi One-Dimensional Photonic Crystals with Space Inversion Symmetry)

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摘要(中)

本論文研究如何對一具有空間反射對稱的準一維光子晶體結構計算其札克相，並藉札克相來判斷此光子晶體結構在何種情況下會有介面態。本論文探討的第一類系統是含一排或多排週期分布介電質柱，上下以完美導體為邊界的準一維光子晶體結構。本論文探討的第二類系統則是以二維光子晶體系統為背景的光子晶體波導，並在其中置入一排週期分布介電質柱所形成的波導。對這兩類準一維光子晶體結構，介面態的出現都符合根據札克相所做的拓樸判斷。

摘要(英)

This thesis investigates how to calculate the Zak phase for a quasi-one-dimensional photonic crystal structure with spatial reflection symmetry and then uses the Zak phase to determine under what conditions this photonic crystal structure will exhibit interface states.
The first type of systems explored in this paper are quasi-one-dimensional photonic crystal structures consisting of one or more rows of periodically distributed dielectric columns, with perfect conductors as boundaries on the top and bottom. The second type of systems studied are photonic crystal waveguides based on a two-dimensional photonic crystal system, with one row of periodically distributed dielectric columns forming the waveguides. For both kinds of quasi-one-dimensional photonic crystal structures, the appearance of interface states confirms the topological predictions made based on the Zak phase.

關鍵字(中)

★ 光子晶體
★ 札克相

關鍵字(英)

論文目次

摘要 I
Abstract II
誌謝 III
目錄 V
圖目錄 VI
第一章緒論 1
1.1光子晶體簡介 1
1.2光子晶體概論 2
1.3光子晶體的應用 4
1.4貝里相與札克相 5
1.5 本文架構 7
第二章札克相與光子晶體理論 8
2.1 電磁波方程式以及波動方程式 8
2.2 光子晶體平面波展開法 11
2.3 貝里相(Berry phase) 12
2.4 札克相(Berry phase) 15
2.5 一維多層膜理論能帶反轉之現象 16
2.6在一維多層膜中的介面態(Edge state) 17
2.7 邊界條件之設定 18
2.7.1週期性邊界條件 18
2.7.2 完美匹配層 19
2.7.3 完美電導體邊界條件 20
第三章、研究方法 22
3.1模擬架構 22
3.1.1 網格的設定 22
3.2 頻帶結構的模擬 23
3.3 札克相的計算方法 25
3.4 光子晶體之能帶拓樸性質反轉 28
3.4.1模擬光子晶體的能帶結構以及布洛赫模態 28
3.4.2計算出兩光子晶體的札克相 30
3.4.3光子晶體帶隙的札克相反轉 32
3.5 光子晶體之能帶拓樸性質反轉 33
3.5.1結構及參數設定 33
3.5.2散射邊界條件介紹 34
3.5.3 一維光子晶體拓樸介面態 34
第四章、研究結果與討論 35
4.1 在準一維的光子晶體中接合後的介面態 35
4.2將準一維結構在y方向上做重複排列 36
4.3 將Type-A、Type-B週期延伸接合後放入光子晶體波導 40
4.3.1 設計符合的光子晶體波導 40
4.3.2計算Type-A、Type-B在波導中的札克相 42
4.3.3 將Type-A、Type-B分別放入光子晶體波導模擬場圖 47
4.3.4 在光子晶體波導中模擬出界面態 49
第五章、結論與未來展望 52
5.1 結論 52
5.2未來展望 53
參考文獻 54

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指導教授

欒丕綱

審核日期

2024-8-17

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