現今，由於以矽為基板的微環形元件因為其小尺寸、可因應各式各樣的應用、具有量產的能力，以及可在現存的互補金屬氧化半導體(CMOS)基礎製程機台上製作的潛力，使得此元件正吸引許多研究工作的注意;因此，在分析三維高折射率比(HIC)的彎曲波導與元件時，具嚴謹而又有效率的數值方法，其需求與日俱增。
這篇論文的主題主要是開發一連串嚴格且有效率的數值方法,並用這些方法去分析三維具高折射率的彎曲波導、半圓耦合器(half-ring coupler)、全環形波長交錯器(all-microing interleaver)以及特別分析以矽為基板具有金屬氧化半導體橫截面之高速微環型電光調變器。藉由等效折射率法(EIM)、保角轉換(conformation transformation)以及光束傳遞法(BPM)我們提出一方法用來解一彎曲肋形(rib)介電波導的相似橫向電場模態(TE-like modes)。彎曲損失、傳遞常數和模態電場的徑向分佈可以得到。藉由應用有限差分時域法(FDTD)模擬工具，我們也可以得到S矩陣的參數用來精確地描述同向耦合器(co-direction)與半圓耦合器(half-ring coupler)。此外，以S矩陣為基礎，我們可以得到單臂(single-arm)和雙臂(double-arm)微環形共振腔的穿透(through)與取出(drop)光譜。以上述的方法為基礎，對於全環形波長交錯器與半圓耦合器的許多新
穎觀念被提出，且最重要的是，我們提供對於互補金屬氧化半導體製程相容與以矽為基板之具有金屬氧化半導體橫截面的高速微環型電光調變器的完整電光特性分析。對於半圓耦合器和全環形波長交錯器:首先，我們發現在半圓耦合器中只要適當地選擇間隙寬度，其輸入(input)電場與穿透(through)或者是擷取(drop)電場可以有pi相位的跳躍現象；第二，將此相位跳躍的現象應用在單臂(single-arm)與雙臂(double-arm)微環形元件上，其穿透與擷取端的頻譜相對於與無此相位跳躍現象的穿透與擷取端的頻譜會位移一半的自由頻譜範圍(FSR)；第三，利用這一半自由頻譜範圍的位移，我們提出第一個新穎的全環形波長交錯器，且我們在數值上驗證此概念；為了得到比較寬的3 dB 頻寬，比較高的串音(cross-talk)以及比較低的插入損失(IL)，二階全環形波長交錯器也被提出並且在數值上被驗證。
對於具有金屬氧化半導體電容結構的電光微環型光調變器:我們目標是利用自由載子效應在一個具有金屬氧化半導體橫截面的微環型調變器用以達到高速的電光調變；首先，為了最佳化橫截面尺寸，我們提出一容易理解的優化程序用以達到容易耦光、單模條件、傳播常數匹配、忽略彎曲損失以及進而達到最大化自由載子色散效應的需求；第二，利用上述的方法與二維的MEDICI模擬工具與藉由自由載子色
散效應，我們針對一具有金屬氧化半導體結構的單臂微環形光調變器，在矽、二氧化矽與絕緣體(SOI)的晶片上，提出嚴格又廣泛的電性與光性分析。我們針對調變器之SPC的p型多晶矽半導體與n型單晶矽在各個不同的參雜濃度下，操作在3.3伏特電壓下之調變速度、操作功率與插入損失作分析。對於p型多晶矽半導體與n型單晶矽半導
體的參雜濃度皆為3×1018 cm−3下，調變器操作在74 GHz的調變速度下，切換一次所需4.6×10−2 pJ/cm2的操作功率可以達到。對於40 GHz的操作，在SPC的p型多晶矽半導體，10-12 dB的插入損失可以達到，且在退火良好的p型多晶矽半導體，意即沒有光學損失的p型多晶矽半導體，9 dB的插入損失可以達到；第三，在此調變器上，為
了達到理論上無窮大的消光比(ER)，臨界耦合(critical coupling)的設計被應用上;然而，由於臨界耦合條件對於許多因素非常敏感，例如:在耦合區附近，bus與微環形波導間的不完美造成間隙寬度之製成誤差、MOS微環形器的溫度漂移(drifting)以及光源的波長漂移；因此，針對這些變化與漂移所造成的臨界耦合的容許誤差，我們做廣泛地分析與討論；第四，藉由應用自由載子色散效應，我們數值上展示這些變化與漂移錯誤是可以被補償至某種程度。為了盡可能地讓這些變化與漂移錯誤使得消光比的下降降低；第五，我們以這些變化與漂移錯誤分析與補償為基礎，針對MOS電容單臂微環型光調變器提出一操作方法。

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