本論文致力於研究利用快速準絕熱動態(FAQUAD)理論作用在三根波導的結構而達到不同比例分光的功能，並且這三根波導保有絕熱消跡(Adiabatic Elimination, AE)的特性。藉由定義線性矽光子元件的絕熱參數，以快速準絕熱動態來固定該絕熱參數為一常數，以達到重新分配波導沿傳播方向的絕熱特性與改變元件的結構，因此當光功率在波導間耦合時，不需要的高階模態不會被激發出來進而造成干擾耦合。
基於絕緣層覆矽(silicon-on-insulator, SOI)的線性AE波導，藉由改變中間波導與其他兩根波導之間的間距以達成不同比例分光的功能，接著透過快速準絕熱動態理論優化後的長度並去做模擬，以3-dB分光器為例可以從629.6μm縮短至224.9μm，其操作頻寬在100nm(1500nm~1600nm)下的穿透率保持3±1dB之間，另外在寬度的製程容忍度上在-50nm~+30nm之間能夠保持3±1dB之間。同理，透過改變中間波導與外側波導之間的間距也能做出70% / 30%、90% / 10%等等不同比例的分光器，其操作頻寬與製程容忍度也有相當良好的特性。

We present a broadband and high fabrication tolerance arbitrary power splitter based on silicon-on-insulator (SOI) three waveguides. We change the gap between the middle waveguide and the outer waveguides to achieve arbitrary power split ratio, satisfying the adiabatic elimination (AE) condition at the same time. We redistribute the adiabaticity parameter of linear AE waveguides by the fast quasiadiabatic dynamics, so we can shorten the device length and achieve broad bandwidth and high fabrication tolerance. We take a 3-dB coupler as an example, and simulate the linear AE waveguide and the fast quasiadiabatic elimination (FAQUE) waveguide. We can find that the FAQUE waveguide length is 224.9μm, which is shortened by 404.7μm compared to the linear AE waveguide length. The ±1dB bandwidth is 100nm (1500~1600nm) for the FAQUE device. The fabrication tolerance is 80nm (-50~+30nm). Similarly, We change the gap between the middle waveguide and the outer waveguides at the output to achieve arbitrary power splitter such as 30%/70% or 80%/20% power splitter. These power splitters also are broadband and have high fabrication tolerance.

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