多模干涉器(multi-mode interference devices , MMI）具有特定比例的光功率分離及結合的功能，能有效的作為光訊號的迴路，且因具有頻帶寬、波長極化不敏感等特性，故適合應用在光學積體化上，基於自我成像原理(self-imaging principle)，MMI 形成多個模態後，而產生相互干涉的作用、以達到光功率分離及結合的功能。
　
一般在設計MMI 之前，會先使用商業軟體來進行模擬分析，包括了BPM、FD-TD、FD-FD、mode matching 等理論，然而市面上許多的商業軟體並未考慮反射的情況，且計算時間過長，所以還需要更好的方法來分析。因此我們提出兩種新式的理論，一種是不考慮反射的近似理論，全特徵模態展開法(full eigen-mode expansion technique, FEMET)，另一種方法則是將反射的情況加入的精確理論，耦合橫向模態積分方程式(coupled transverse mode integral equation, CTMIE)。
　
比較FEMET 與CTMIE 數值模擬上的結果，發現CTMIE 理論計算精準，但在撰寫程式方面困難，且運算時間會較長於FEMET；而FEMET雖然為近似解，但在設計參數正確時，計算的準確度與CTMIE相當，運算時間亦較少，適合做快速且精準的模擬分析。

Multimode interference (MMI) devices operate based on the self-imaging principle. A single mode input from the input waveguide is converted to multiple modes in the interference region. By properly choosing the width and length of this section, energy distribution at the output end forms a specified ratio. Thus the MMI device is commonly used as the optical power divider in the integrated optics. The MMI devices operate at a high bandwidth and are insensitive to polarization and small variation of device dimensions.
　
In general, MMI manufactures use commercial simulation software to design MMI devices. However, the beam propagation method (BPM), which is the most commonly used method, assumes small angle approximation and ignores wave reflections. Other more rigorous numerical methods such as finite-difference time-domain (FD-TD) and mode matching methods consume too much computer resources and are therefore can not handle large devices like the MMIs. Therefore, we propose two novel numerical schemes to study MMI devices. The first one called full eigen-mode expansion technique (FEMET) includes all necessary modes but neglects reflection at the dielectric discontinuities. The other method considers all modes traveling in both directions is based on the coupled transverse mode integral equation (CTMIE) formulation. It is most rigorous among all methods and is capable of handling very large device structures.
　
In this thesis, we report the demonstration of MMI devices by efficient FEMET and rigorous CTMIE methods. Comparing the two novel studies, the CTMIE approach although highly accurate, it is much more complex and is very difficult to program. It also spends much more computer time than FEMET. On the other hand, FEMET method, being an approximate theory, produces results that are very close to that of the CTMIE results for MMI devices that are correctly designed. We found that either one of the two novel methods are able to compute quickly and accurately for adiabatic MMI devices.

第一章 導論 1
1. 1 簡介 ......... 1
1. 2 多模干涉器的近似理論 ......... 3
1. 3 ABCD matrix 模態解 ......... 10
第二章 FEMET 理論分析MMI 17
2. 1 FEMET 理論基本觀念 ......... 17
2. 2 TE 入射FEMET 理論架構與推導 ......... 19
2. 3 數值模擬結果 ......... 23
第三章 CTMIE 理論分析MMI 34
3. 1 CTMIE 理論基本觀念 ......... 34
3. 2 對稱性理論 ......... 36
3. 3 TE 入射CTMIE 理論場量積分形式推導 ......... 38
3. 4 PQRS 聯立積分方程矩陣 ......... 45
3. 5 重疊積分 ......... 48
3. 6 數值模擬結果 ......... 55
第四章 比較與討論 64
第五章 1×4 MMI 高階模態效應 76
5. 1 元件架構 ......... 76
5. 2 高階模態效應 ......... 79
5. 3 結果討論 ......... 83
參考文獻 88
中英文對照表 90

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