本論文致力於研究快速準絕熱動態(FAQUAD)理論運用於不同型態之波導，透過定義一高折射率差矽光子元件的絕熱參數，以快速準絕熱動態固定絕熱參數為一常數，重新分配波導沿傳播方向的絕熱性，因此進行光功率耦合時，非需要的高階模態將不會被激發進而干擾耦合結果。
依據3-dB分光器基於絕緣層覆矽(silicon-on-insulator, SOI)脊狀波導設計與模擬結果，使用快速準絕熱動態理論計算過後波導耦合長度最短可達7.1μm，耦合效率大於傳統耦合長度100μm以上的線性絕熱分光器，以達到300nm(1400nm~1700nm)操作頻寬時分光輸出差保持在5dB以下；寬度製程容忍度在正負40nm時分光輸出差保持在1dB以下。
此外，運用快速準絕熱動態方法改進矽鍺光調變器與矽波導之間垂直漸逝耦合。依據模擬結果，使用快速準絕熱動態重新設計線性錐形波導長度可使元件長度由250μm減少至25μm。考慮材料吸收，長度縮短也使插入損耗由3dB降低至1.35dB。

We present a short and broadband 3-dB splitter based on silicon-on-insulator (SOI) rib waveguides. The tapered couplers are designed using the fast quasiadiabatic dynamics (FAQUAD) protocol to homogeneously distribute adiabaticity over the length. The FAQUAD protocol is suitable for SOI structure which provides high index contrast. Our simulations show that the shortest coupler can be achieved at 7.1μm long; and for lengths greater than or equal to 23.7μm, the devices have high tolerance to fabrication errors and 300 nm bandwidth.
In addition, we use the FAQUAD protocol to redesign the taper waveguide of SiGe electroabsortion modulators (EAMs). In this way, we get a much shorter length taper for vertical coupling from silicon strip waveguide to SiGe EAMs. Simulation results show that the SiGe taper waveguide length can be shrunk from 250μm to 25μm, and the insertion loss from material absorption can be reduce from 3dB to 1.35dB by optimizing the taper profile.

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