雷射干涉重力波天文台(Laser Interferometer Gravitational-Wave Observatory, LIGO)利用大型麥克森干涉儀偵測重力波，在2015年已成功量測到頻率100 Hz的重力波訊號。為了實現偵測到1-2 kHz的重力波訊號及提升偵測器靈敏度，透過光機械微諧振器的負色散效應補償相位延遲可以實現此目標，因此西澳大學團隊設計一個名為cat-flap的諧振器元件。
先前應馬可學長已成功製作出雙吊帶懸掛cat-flap結構並透過室溫機械損耗系統量測cat-flap的品質係數(Qm)，但其品質係數僅有0.14×10^4，且量測結果有拍頻現象。為了提升cat-flap本身的品質係數及找出拍頻現象的原因，本論文將以此cat-flap結構為基底並通過兩種方式進行cat-flap的優化，分別為優化cat-flap的懸掛薄膜尺寸(第三章)及優化cat-flap鐘擺輪廓(第五章)。
第三章利用ANSYS模擬不同薄膜尺寸找到懸掛薄膜對於cat-flap品質係數及基頻的關係，透過室溫系統量測的結果顯示，其品質係數從0.14×10^4提升至0.59×10^4。由於量測結果與模擬仍存在差異，因此透過觀察cat-flap的實際結構和模擬結構，發現模擬的鐘擺輪廓是無任何缺陷的理想結構，而實際製作的cat-flap鐘擺輪廓則有不規則的凹凸。因此我們在第五章提出優化cat-flap鐘擺輪廓的方法，經由ANSYS模擬得知cat-flap鐘擺輪廓的缺陷對品質係數有顯著的影響同時也發現和拍頻現象有關。而我們從cat-flap的製程步驟得知KOH濕蝕刻為造成輪廓缺陷的主因，並透過ANSYS模擬KOH濕蝕刻前後的品質係數分別為10.58×10^4及0.49×10^4 ，接著針對cat-flap鐘擺輪廓提出製程改善，期待cat-flap的鐘擺輪廓接近於KOH蝕刻前形貌，最後評估cat-flap經由製程改善後的品質係數從0.49×10^4提升至9.16×10^4。
本論文透過優化cat-flap的懸掛薄膜及優化cat-flap的鐘擺輪廓均有使其品質係數獲得提升，其中優化cat-flap鐘擺輪廓的品質係數更是高於優化前的18.7倍，因此在理想光彈簧頻率100 kHz下可將cat-flap的品質因子提升至約10^10 order以滿足負色散振子的應用需求。

The Laser Interferometer of Gravitational-Wave Observatory (LIGO) set up a large-scale Michelson interferometer to detect weak gravitational wave signals. In 2015, a 100 Hz gravitational wave signal has been successfully measured. To detect the 1-2 kHz gravitational wave signals and increase the sensitivity of the detector, the phase delay can be compensated by the negative dispersion effect of the optomechanical micro-resonator. Therefore, the University of Western Australia team designed a cat-flap as the optomechanical micro-resonator.
In Ying Mark's master thesis, a two-stripe suspension cat-flap structure has been successfully fabricated and the Q-factor (Qm) of the cat-flap measured through the ring-down system, the Q-factor (Qm) was 0.14×10^4, and the measurement results occurred beat frequency phenomenon. To improve the Q-factor (Qm) of the two-stripe suspension of cat-flap and find out the cause of the beat frequency phenomenon, we will use this cat-flap structure as the basis and optimize the two-stripe of suspension cat-flap in two methods: Optimize the dimension of cat-flap suspension film (Chapter 3) and optimize cat-flap pendulum contour (Chapter 5).
We used ANSYS to simulate several suspension films dimensions to find the trend of the suspension film dimension on the Q-factor (Qm) and fundamental frequency of cat-flap. Through the ring-down system, the Q-factor (Qm) measurement results have been increased from 0.14×10^4 to 0.59×10^4. However, it exists a discrepancy between the simulation and measurement results. Through observing the real structure and simulation structure of cat-flap, we found that the simulation structure is the ideal structure of the pendulum contour, and the contour of the cat-flap pendulum which is fabricated has severe roughness, hence we propose a method to optimize the contour of the cat-flap pendulum. Through ANSYS simulation, it is known that the defects of the cat-flap pendulum contour have a significant impact on the Q-factor (Qm), and meanwhile, it is also related to the beat frequency. Therefore, we started from the cat-flap fabrication processes to find out that KOH etching is the main cause of pendulum contour defects, and then we used ANSYS to simulate the Q-factor (Qm) before and after KOH etching, which are 10.58×10^4 and 0.49×10^4 respectively. It is proposed to improve the cat-flap fabrication process and hope that the pendulum contour of cat-flap will close to the shape before KOH etching. Finally, the Q-factor (Qm) of cat-flap after fabrication improvement has been evaluated from 0.49×10^4 (after KOH etching) to 9.16×10^4.
In this thesis, the Q-factor (Qm) of cat-flap has been improved by optimizing the cat-flap suspension film and optimizing the cat-flap pendulum contour. The Q-factor (Qm) of the cat-flap pendulum contour optimization increased by 18.7 times. Therefore, the final quality factor of the cat-flap can be improved under the ideal optical spring frequency of 100 kHz, which is about 10^10 order to meet the requirements of negative dispersion oscillators.

Abstract I
摘要 III
致謝 IV
目錄 VI
圖目錄 VIII
表目錄 XI
第一章 前言及研究動機 1
1-1 前言 1
1-2 研究動機 2
1-2.1 光學稀釋效應(optical dilution effect)介紹 3
1-2.2 優化雙吊帶懸掛cat-flap之動機 4
1-3 論文架構 7
第二章 雙吊帶懸掛 cat-flap 之品質係數介紹及問題闡述 9
2-1 機械損耗與品質係數之關係 9
2-1.1 機械損耗原理與量測訊號處理介紹 9
2-1.2 室溫量測系統介紹 11
2-2 夾具設計與品質係數之關係 11
2-2.1 雙吊帶懸掛cat-flap與夾具模態模擬分析 11
2-2.2 夾具設計結果 12
2-3 品質係數量測結果(拍頻現象) 14
第三章 優化雙吊帶懸掛 cat-flap 懸掛薄膜 16
3-1 透過模擬軟體 ANSYS 優化cat-flap結構 16
3-1.1 模態分析 16
3-1.2 暫態動力分析 16
3-1.3 模擬流程介紹 18
3-2 優化前後之模擬結果比較 19
3-3 優化後cat-flap製作流程 21
3-4 品質係數量測結果 26
第四章 優化後雙吊帶懸掛 cat-flap 之高反射鏡薄膜鍍製 29
4-1 高反射鏡薄膜介紹 29
4-2 高反射鏡cat-flap製作流程 30
4-2.1 製作流程介紹 30
4-3 品質係數量測結果 35
第五章 優化雙吊帶懸掛 cat-flap 鐘擺結構 37
5-1 透過 ANSYS 模擬軟體確認拍頻現象的來源 37
5-2 評估造成 cat-flap 鐘擺結構缺陷之原因 38
5-3 透過ANSYS模擬實際樣品(KOH蝕刻前後)之品質係數差異 40
5-4 透過MATLAB 與ANSYS 分析找出鐘擺輪廓對品質係數之影響因子 46
5-4.1 Cat-flap鐘擺輪廓取樣率與網格收斂分析 46
5-4.2 透過MATLAB 隨機產生高斯分布並建立雙吊帶懸掛 cat-flap 結構 48
5-4.3 探討高斯分布參數對鐘擺結構之影響 49
5-5 cat-flap製程改善 50
5-6 評估製程改善後cat-flap之品質係數 52
第六章 結論與未來工作 56
6-1 結論 56
6-2 未來工作 58
附錄A ANSYS共振模態模擬流程 59
附錄B ANSYS暫態分析模擬流程 70
參考文獻 79

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