本論文以對稱性頻域有限差分法分析、計算微波及介電質彎曲波導的能量反射、穿透係數及輻射耗損 。
一般常見的介電質積體光波導有許多部分是彎曲形式的，此彎曲波導在場型分析時須考慮到不同座標系統的場。例如輸入、輸出波導位於直角座標區域、而中段彎曲波導部份則位於圓柱座標區域，在本論文中將兩區域簡稱為混合座標系統。
分析一般彎曲波導，目前常用的方法是時域有限差分法，雖然時域有限差分是個有效的分析方法，但是對於分析較大尺寸的彎曲波導元件時，需要大量的記憶體與計算時間且對於波導輸出入的吸收邊界問題較不易處理，故我們開發特殊混合座標系統、頻域有限差分法來分析此問題，可以使用精確之模態吸波邊界、並減少未知電磁變數量。
我們修正了混合座標系統、頻域有限差分法兩個不同座標系統相遇界面上場點之有限差分法的係數。同時使用了Thomas 方法來解頻域有限差分法所產生的巨大聯立方程式。雖然FD-FD 在計算量會相對FD-TD 提高許多，但是應用於彎曲波導的模擬時有許多優點，處理彎曲波導在特定頻率或波長分析的問題，通常在頻域計算所得的解較為正確且頻域有限差分亦可與模態解析解合併處理。若彎曲波導為一對稱結構，頻域有限差分可依對稱性有效減少計算的區域因而減少矩陣的計算量，可以大大提高計算效能、與精密度。

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第一章 導論............................................................................1
1.1 簡介..................................................................................1
1.2 動機..................................................................................3
第二章 介紹頻域有限差分....................................................4
2.1 頻域有限差分(FD-FD)...................................................4
2.2 一維有限差分..................................................................5
2.3 二維有限差分..................................................................7
2.4 頻域有限差分應用於混合座標系統............................10
第三章 混合座標系統交界面的內差應用.........................19
3.1 小曲率半徑彎曲波導的分析計算................................19
3.2 混合座標系統中內差法的應用...................................20
3.3 三點內差公式的推導....................................................24
3.4 四點內差公式的推導....................................................26
3.5 四點內差公式的在混合座標中的應用........................28
3.6 共軛場特性的應用........................................................31
3.7 內差法取點應用和驗證................................................33
第四章 頻域有限差分法分析彎曲波導.............................46
4-1 前言...............................................................................46
4-2 微波彎曲波導基本簡介...............................................46
4-3 微波彎曲波導模擬分析...............................................47
4-4 頻域有限差分法分析彎曲波導...................................48
4-5 微波彎曲波導的模擬計算...........................................51
4-6 介電質彎曲波導的模擬計算.......................................69
第五章 結論與未來研究.....................................................79
參考文獻 .............................................................................82
附錄一 To analyze bending waveguide by CTMIE.......84
附錄二 Hertz Vector...........................................................92
附錄三 To plot bending waveguide by FD-FD..............96

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