臺灣博碩士論文加值系統

錐型波導(tapered waveguide)通常被使用在光斑轉換器(spot-size converter)及功率分配器(power divider)上。一般來說，這些元件的輻射現象是很難用光束傳播法(beam propagation method, BPM) 和時域有限差分法(finite-difference, time-domain, FD-TD)來分析。我們應用全特微模態展開方法(full eigenmode expansion technique, FEMET)研究漸變形(adiabatic)介電質錐型波導的傳播情形。
漸變型介電質錐型波導通常被認為無反射及輻射情況之元件，輸入波導的導波模態會逐步地轉換成相對應的輸出波導的導波模態，為一對一(one to one) 的模態演化(mode evolution)，且無模態轉換(mode conversion)的情形發生。然而，當輸出波導不支援相對應的入射導波模態(incident guiding mode)時，則此導波模態可能會激發出其他更高階的導波模態而造成模態轉換或激發出高階輻射模態而產生輻射現象。有趣的是我們將探討模態轉換與輻射現象情形，並且利用數值實驗來觀察此現象。
另外針對全特徵模態展開方法特性，我們使用傾斜直線波導(tilted straight waveguide)結構來當做分析範例，利用座標轉換的方式求出傾斜直線波導精確場型分佈，與數值模擬結果比較，以驗證全特徵模態展開的精確性。

Tapered waveguides are often used as spot-size converters and power dividers. In general, radiation in these devices is hard to analyze by either BPM or FD-TD methods. We apply the full eigenmode expansion technique (FEMET) to study the propagation of an adiabatic dielectric tapered waveguide.
We often assume that wave propagation in an ideal “adiabatic” dielectric waveguide suffer no reflection nor radiation loss. It is especially true for the fundamental mode propagation in an “adiabatic” dielectric waveguide. Thus, the fundamental mode of the input waveguides will be converted to the corresponding fundamental mode of the output waveguide whenever the two are connected by an adiabatically tapered waveguide. However, the higher-order modes do not always propagate through the tapered waveguide when the output waveguide does not support that particular guiding mode. It is interesting to predict such radiation phenomena and to observe them in a numerical experiment.
In this thesis we consider the titled straight waveguide (TSR) as our test example. Since TSR has an exact solution in its natural coordinate system, we can study computational characteristics of FEMET via TSR examples. Using FEMET and FD-FD method, we carefully examine mode evolution, conversion radiation and reflection of many quasi-adiabatic tapered waveguides. Finally the apparent visual radiation angles are defined and computed as function of taper angle core/cladding indices and incident mode order for both TE and TM mode cases.

第一章 導論 1
1. 1 簡介.............................................................................1
第二章 FEMET理論分析錐形波導 4
2. 1 FEMET理論基本觀念...............................................4
2. 2 TE與TM極化入射FEMET理論架構與推導...........6
第三章 FEMET理論分析傾斜直線波導 12
3. 1 傾斜直線波導介紹...................................................12
3. 2 傾斜直線波導理論...................................................14
3. 3 數值模擬結果與討論...............................................19
第四章 漸變形錐型波導分析 36
4. 1 漸變形錐型波導定義...................................................36
4. 2 漸變形錐型波導分析介紹...........................................37
4. 3 TE基模入射漸變形錐型波導分析.............................39
4. 4 漸變形錐型波導輻射機制...........................................49
4. 5 輻射模擬結果與討論...................................................52
4. 6 FEMET與FDFD之分析結果比較.............................71
第五章 結論與未來工作 79
參考文獻 80
中英對照表 81

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