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研究生:王琮右
研究生(外文):Tsung-You Wang
論文名稱:耦合波法於週期性光柵之繞射分析
論文名稱(外文):Coupled-wave analysis of optical diffraction for periodic gratings
指導教授:薛文証
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:工程科學及海洋工程學研究所
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:146
中文關鍵詞:週期性光柵繞射效率耦合波分析
外文關鍵詞:periodic gratingsdiffraction efficiencycoupled-wave analysis
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本論文主要目的在於研究週期性光柵的繞射效率。本文利用嚴格耦合波方法研究週期性光柵繞射特性,本文首先推導在TE和TM兩種偏極模式下的耦合波方程,並分別利用完整矩陣法和傳接矩陣法兩種數值分析方法求解耦合波方程。最後並分別對不同結構的週期性光柵的繞射特性進行分析,包含光柵週期,光柵深度,光柵工作週期,入射波入射角度和光柵區域介質等參數對光柵繞射特性的影響,並探討完整矩陣與傳接矩陣兩種數值方法的收斂性與準確性。
The purpose of this research is to study the diffraction efficiency of periodic gratings. We derive the coupled wave equations for TE and TM polarization using rigorous coupled wave analysis. Then, the diffraction characteristic of the periodic gratings is investigated. The coupled wave equations are solved by two numerical methods, including full matrix method and transfer matrix method. The effect of grating period, grating depth, duty cycle, incident angle and the permittivity in grating region on the grating diffraction efficiency are investigated. Finally, we study the accuracy and the stability of the computation on diffraction efficiency using both of the numerical methods.
摘要…………………………………………………………………i
目錄……………………………………………………………………iii
表目錄…………………………………………………………………vi
圖目錄………………………………………………………………vii
符號表……………………………………………………………xii

第一章 導論………………………………………………………1
1.1 背景與研究動機………………………………………………1
1.2 文獻回顧………………………………………………………4
1.3 論文架構………………………………………………………6
第二章 光柵繞射理論……………………………………………8
2.1 光柵繞射基本理論……………………………………………8
2.2馬克斯威爾方程………………………………………………10
2.3 週期性光柵結構………………………………………………13
2.4 嚴格耦合波繞射理論…………………………………………14
2.4.1 TE偏極……………………………………………………15
2.4.2 TM偏極……………………………………………………19
第三章 光柵繞射效率分析方法…………………………………25
3.1 完整矩陣法於光柵繞射效率的分析…………………………25
3.1.1 TE偏極……………………………………………………25
3.1.2 TM偏極……………………………………………………29
3.2 傳接矩陣法於光柵繞射效率的分析…………………………32
3.2.1 TE偏極……………………………………………………33
3.2.2 TM偏極……………………………………………………36
第四章 週期性光柵模擬和分析…………………………………39
4.1 介電光柵繞射效率分析………………………………………39
4.1.1 光柵深度的影響…………………………………………39
4.1.2 光柵工作週期的影響……………………………………42
4.1.3 光波入射角度的影響……………………………………45
4.1.4 光柵區域介質的影響……………………………………47
4.2 金屬光柵繞射效率分析………………………………………49
4.2.1 光柵深度的影響…………………………………………50
4.2.2 光柵工作週期的影響……………………………………53
4.2.3 光波入射角度的影響……………………………………55
4.2.4 光柵區域介質的影響……………………………………57
4.3金屬光柵的繞射角度…………………………………………59
4.4 諧和波收斂性的影響…………………………………………61
第五章 結論與展望………………………………………………141
5.1 結論…………………………………………………………141
5.2 未來與展望…………………………………………………143
參考文獻………………………………………………………………144
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