平面波展開法於磁化色散性光子晶體特性分析之應用

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姓名

黃偉恩(Wei-en Huang) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

平面波展開法於磁化色散性光子晶體特性分析之應用

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摘要(中)

本篇論文採用平面波展開法 ( plane wave expansion ) 計算外加磁場後，電磁波在色散性介質光子晶體的能帶結構 ( band structure )。對於未加磁場的介電質，我們使用Drude modol 形式的色散型介電係數 ( permittivity )。本論文主要探討外加磁場對於色散性光子晶體能帶結構圖的影響，並討論利用能帶結構改變後所出現的光子能隙 ( photonic band gap ) 來控制電磁波在色散性光子晶體內部傳播狀態的可能性，以設計可操控光傳播的可調式光子晶體元件。

摘要(英)

In this thesis, we use plane wave expansion (PWE) method to calculate the band structures of two-dimentional dispersive and magnetized dielectric photonic crystals consisting of periodically arranged cylinders whose permittivity has the Drude model type dispersion before applying the magnetic field. My research is mainly about the effects on the band structure when the external magnetic field is applied to the dispersive photonic crystals. Based on the band structure characteristics we also discuss the possibility of designing tunable photonic component to control the propagation of light by tuning the photonic band gap via changing the intensity of the applied external magnetic field.

關鍵字(中)

★ 平面波展開法
★ 磁化
★ 光子晶體
★ 色散

關鍵字(英)

論文目次

摘要....................................................i
Abstract ..............................................ii
致謝 .................................................iii
目錄 ..................................................iv
圖目錄 ................................................vi
表目錄 ..............................................viii
一、緒論 ................................................1
1.1 光子晶體簡介 ....................................1
1.2 論文方向 ........................................3
二、光子晶體理論基礎 .....................................4
2.1 傅立葉級數與倒晶格向量 ...........................4
2.1.1 一維傅立葉級數 ...........................4
2.1.2 二維傅立葉級數與倒晶格向量 .................5
2.2 介電函數與結構因子 ...............................8
2.2.1 介電函數之傅立葉展開 ......................8
2.2.2 結構因子之數值計算 .......................10
2.2.3 二維倒晶格向量之座標變換 ..................12
2.3 波動方程式 .....................................14
2.4 平面波展開─純量波法 .............................16
2.5 平面波展開─向量波法 .............................19
2.5.1 向量波法由k向量求頻率 ....................19
2.5.2 向量波法由k向量求頻率─二維空間 ............21
三、色散性光子晶體理論之計算 .............................23
3.1 色散性模型 .....................................23
3.1.1 Drude Model ............................23
3.1.2 Lorenz Model ...........................26
3.2 色散性光子晶體之平面波展開計算 ...................28
3.2.1 平面波展開法由值求頻率 ..................28
3.3磁化之色散性光子晶體 .............................33
3.3.1 平面波展開法 ............................33
四、磁化色散性光子晶體模擬與分析 .........................40
4.1 磁化色散性光子晶體能帶分析 .......................40
4.2 磁場對光子晶體的影響 ............................45
五、結論與未來展望 ......................................60
5.1 結論 ..........................................60
5.2 未來展望 .......................................60
參考文獻 ...............................................61

參考文獻

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指導教授

欒丕綱(Pi-gang Luan)

審核日期

2015-1-29

推文