本篇論文的架構可以分成二大部分，我們提出一種計算多層介質的方法我們稱之為電場或磁場耦合方程式，可以用來解反射，穿透及模態的理論架構，然後我們藉由傳統的方法驗證我們的方法。
然後藉由多層介質的理論計算的耦合方程式的結果，應用阻抗匹配的方法，設計多層大角度抗反射膜。我們的方法可以針對任何角度入射之平面波，進行最佳化的設計，可以達到單一頻率，單一平面波全部穿透。然後以前者設計出來的鍍膜，作為半導體雷射抗反射膜，經由聯立的積分方程式的解，來進行不連續介面的光場分析，並且藉此找出最好的穿透設計。我們發現多層的設計可以再降低單層抗反射膜的反射率。我們以此多層鍍膜與半導體雷射結合的設計，其反射率可由單層設計的0.085%降到5層設計的0.056%，降低了約33%的反射率。

Thin-film theorems are well developed and so are the fabrication processes. Yet under some special conditions, traditional methods (such as the ABCD matrix and the transmission matrix methods) will lead to a serious numerical error. In this thesis, we propose a new method called Couple E/H field formulation, which will overcome this numerical problem in simulating characteristics of complex multi-layered structures. We have verified both the algorithm and its results with the traditional techniques.
By extending the impedance matching principle, we came out with a multi-layer anti-reflection coating design optimized for a time-harmonic plane wave incidence with any incident angle. Such a design allows for more plane waves with adjacent angles to pass through the coating layers with minimal reflection.
Furthermore, we apply this AR coating design to facets of semiconductor lasers. Our calculation shows that multi-layer coating does a better job than a single layer coating. The reflectivity of a laser diode from single layer coating 0.085% to 5 layer coating 0.056%, which is a 33% improvement.

摘要 II
內容目錄 IV
圖表目錄　　　　　　　　　　　　　　　　　　　　　　　　VI
第一章 導論 1
1. 1 內容簡介 1
1. 2 論文架構 3
第二章 電場耦合與磁場耦合方程式的理論分析 4
2. 1 橫向電場模態 6
2. 2 橫向磁場模態 12
第三章 鍍膜的設計方法與改進方法 17
3. 1 橫向電場模態的鍍膜設計方法與改進方法 17
3. 2 橫向磁場模態的鍍膜設計方法與改進方法 22
第四章 平行層波導與多層鍍膜耦合的理論架構與數值的
結果 27
4. 1 平行層波導與多層鍍膜耦合理論架構的推導 27
4. 2 數值結果與探討 34
第五章 結論 56
參考資料 58
中英對照表 　　　　 60　

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