光子晶體異常折射之研究

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游政峰(Jeng-Feng You) 查詢紙本館藏

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光電科學與工程學系

論文名稱

光子晶體異常折射之研究

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摘要(中)

負折射研究在2003年被科學（Science）雜誌選為十大科技成果之一，而光子晶體是能達成負折射現象的其中一個方法。本論文從光子晶體的基本理論談起，並應用用時域有限差分法（FDTD）於光子晶體發生負折射的頻段，驗證光子晶體的負折射理論。文中比較了理論預測與FDTD模擬結果在幾個情況下的差異性。我們首先改變光子晶體表面，並觀察其對負折射的影響。之後我們探討在負折射的情況下，能流在光子晶體內流動的空間分布特性，以及其與介電質柱之關係。而我們也利用此特性重新解釋了在三角晶格光子晶體中，當電磁波沿方向入射時，其負折射的異常現象。

關鍵字(中)

★ 負折射
★ 異常折射
★ 光子晶體

關鍵字(英)

論文目次

摘要...................................................................Ⅰ
目錄.................................................................Ⅱ
圖索引...............................................................Ⅳ
第一章緒論…………………………………………………………………………..1
1﹒1光子晶體的發展…………………………………………………………..1
1﹒2光子晶體的理論工具……………………………………………………..2
1﹒2﹒1平面波展開法……………………………………………………2
1﹒2﹒2時域有限差分法…………………………………………………3
1﹒3負折射的原理………………………………………………………………4
第二章光子晶體理論架構…………………………………………………………..7
2﹒1光子晶體的概念……………………………………………………………7
2﹒2一維光子晶體的傳輸矩陣法………………………………………………7
2﹒3波動方程式………………………………………………………………...11
2﹒4光子晶體的平面波展開法……………………………………………….13
第三章 FDTD理論架構…………………………………………………………….15
3﹒1馬克斯威爾方程式……………………………………………………….15
3﹒2基本理論………………………………………………………………….15
3﹒3穩定條件………………………………………………………………….17
3﹒4邊界理論………………………………………………………………….18
3﹒4﹒1 Mur邊界理論………………………………………………….19
3﹒4﹒2 Berenger的PML邊界理論…………………………………..20
3﹒5時域有限差分法的二維平面程式……………………………………….25
3﹒5﹒1 Ez、Hx、Hy的計算……………………………………………25
3﹒5﹒2 邊界處理……………………………………………………….28
第四章光子晶體的負折射研究……………………………………………………32
4﹒1光子晶體的負折射理論………………………………………………….32
4﹒1﹒1光子晶體的負折射理論驗證（正方晶格）…………………..35
4﹒1﹒2光子晶體的負折射理論驗證（三角晶格）…………………..41
4﹒2光子晶體的負折射表面特性探討……………………………………….46
4﹒3光子晶體負折射能流探討……………………………………………….50
4﹒4光子晶體負折射柱子間的電容效應…………………………………….57
第五章結論…………………………………………………………………………63
參考資料……………………………………………………………………………..66

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指導教授

欒丕綱(Pi-Gang Luan)

審核日期

2005-7-5

推文