本論文致力於研究絕熱消跡(Adiabatic Elimination)並加入波導耦合的理論並藉由絕緣層覆矽(silicon-on-insulator, SOI)的方式來做出極化分光器(Polarization Beam Splitter)。首先會探討絕熱消跡之三長直波導狀況，再藉由耦合理論，來分析絕熱消跡之三長直波導的eigenmode，透過嚴謹的數學方式來做出極化分光的效果。
將帶有絕熱消跡的極化分光的三長直波導做出來後，建立於絕熱消跡的數學上加入絕熱的過程做出絕熱彎曲波導來全面優化三長波導，使極化分光的頻寬及製程容忍度能夠得到有效的提升，另一方面也能夠透過此方式來提升絕熱消跡的效果。
由於絕熱彎曲波導的元件長度較三長直波導長上許多，所以為了能夠縮短絕熱彎曲波導，但還是能夠達到絕熱的效果，可以藉由絕熱捷徑(Shortcuts to Adiabaticity)的方式，能夠使本來較長的絕熱彎曲波導縮短，但元件效果仍然接近絕熱的狀況。

This thesis is devoted to the study of adiabatic elimination in optical waveguides and to design a polarization beam splitter based on the silicon-on-insulator (SOI) platform. Firstly, we discuss the conditions for adiabatic elimination in three waveguides, then we design polarization splitters based on shortcuts to adiabatic elimination.
After the three straight waveguides system satisfying adiabatic elimination and polarization splitting are formed, the adiabatic process is added to the process of adiabatic elimination to fully optimize the three waveguides, so that the bandwidth of the polarization splitting and process tolerance can be effectively improved. In addition, it can also enhance the effect of adiabatic elimination.
Since the length of the adiabatic three waveguides is much longer than the three straight waveguides, we use shortcuts to adiabaticity to shorten the adiabatic three waveguides. It can shorten the adiabatic three waveguides ,and the device performance is still close to the adiabatic device.

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