雷射干涉儀重力波天文台（LIGO）通過具有諧振信號回收腔的公里級雷射干涉儀檢測
重力波信號。諧振放大的效果與測量帶寬成反比，現系統之測量頻率為100Hz。通過使用負色散濾波器補償相位延遲，可以實現在1-2 kHz 範圍內具有更高靈敏度的寬帶檢測。西澳大學David Blair 博士提出使用懸掛在強場光學共振腔中的微諧振器“Cat-flap”視作負色散濾波元件，其中Cat-flap 由亞毫米級的擺錘與納米級厚度的薄膜連接組成。

本論文基於負色散濾波器的要求和光彈效應的機理，提出了一種設計，製作，評估和
分析Cat-flap 的完整方法，將Cat-flap 優化為雙條紋的懸掛結構並驗證其機械特性優於其他結構。通過ANSYS 暫態動力學分析證明此結構之Cat-flap 的品質係數（Q）可以達到10^6，並且具有較低的基頻（81Hz）。

而後使用振鈴系統測量通過半導體技術製造的上述規格之Cat-flap，得到其實際機械性能與模擬結果存在差異，其中測量所得之品質係數接近1500，且其基頻為54Hz。詳盡的損耗分析，我們推定表面損耗為主要損耗，其理論品質因子小於8000-40000。

根據上述測量結果，我們通過理論計算得出，在25 kHz 的光學彈簧頻率下可將Cat-flap的品質因子提高到10^8 以滿足負色散振子的應用需求。

Laser Interferometer Gravitational-Waves Observatory (LIGO) detects gravitational-waves signals by km-scale laser interferometers with resonant signal recycling cavities. The resonant amplification is inversely proportional to the bandwidth which is only 100 Hz Broadband detection with better sensitivity in the range of 1-2 kHz can be achieved by compensating for phase delay with a negative dispersion filter. Dr. David Blair proposed to use a micro-resonator
"Cat-flap" suspended in an optical cavity as a negative dispersion filter. The Cat-flap consisting of sub-millimeter scale micromirrors supported by nanometer-thickness flexures. The micromirror pendulum is designed to achieve the lowest possible flexure stiffness, which enables maximal dilution of mechanical losses through the use of optical springs.

In this thesis, we propose a complete method to design, fabricate, evaluate and analyze a Cat-flap, based on the requirement of negative dispersion filter and the mechanism of optical spring effect, we optimize Cat-flap as dual-stripe structure and validate its mechanical performance by ANSYS transient dynamics analysis, which demonstrated its Q-factor can approach to 10^6 and have a low fundamental frequency, 81Hz.

The fabricated Cat-flap measured by the ring-down system to evaluate its actual mechanical prosperity exists discrepancy with simulation results, which Q-factor approach to 1500, the fundamental frequency is 54Hz. After thorough losses analysis, the surface loss is deduced as the predominant loss, which Qsurface is smaller than 8000-40000.

According to the measurement result, the Q-factor can be enhanced to 10^8 at an optical spring frequency of 25 kHz to meet the specification of negative dispersion filter.

目錄
致謝...............................................................2
Abstract...........................................................4
摘要...............................................................5
目錄........................................................... 7
圖目錄........................................................ 10
表目錄........................................................ 13
第一章、研究背景及導論............................................................. 1
1.1前言....................................................... 14
1.2研究動機.................................................... 15
1.2.1量測雜訊：Noise sources..........................................................15
1.2.2.降低量子雜訊的機制：.......................................................... 18
1.3 白光共振腔與機械耦合振子Cat-flap背景介紹............................................................ 25
第二章、通過數值模擬軟體ANSYS 及COMSOL設計最佳結構之Cat-flap.......................................................... 29
2.1 光彈簧勢阱場下Cat-flap 結構之振動頻率的要求............................................................ 29
2.2 使用COMSOL分析振動模態優化Cat-flap懸吊結構............................................................ 32
2.3 使用有限元素分析法設計並分析振動模態且優化雙吊帶Cat-flap懸吊結構............................................................ 35
2.4 使用暫態動力分析並計算Cat-flap品質係數............................................................ 35
2.4.1. 暫態動力分析（Transient dynamic analysis）：.................................................. 36
2.4.2. 瑞利阻尼模型（Rayleigh damping model）：..................................................... 37
2.4.3. 暫態動力分析（Transient dynamic analysis）操作流程介紹............................................................ 39
第三章、雙吊帶懸掛結構Cat-flap製作及分析........................................................... 45
3.1雙面吊帶結構之光機械元件製程流程：.......................................................... 45
第四章、雙吊帶懸掛結構Cat-flap測量及各項損耗分析............................................................ 55
4.1雙吊帶懸掛Cat-flap之室溫系統下振動頻率及機械損耗之測量：........................................................ .... 55
4.2雙吊帶懸掛Cat-flap之室溫系統下之量測結果與討論：.......................................................... 57
4.3多種能量損耗來源之分析與討論：.......................................................... 59
4.3.1. 夾具之夾持反衝損耗：........................................................... 60
4.3.2. gas damping損耗分析：.......................................................... 61
4.3.3. Akhiezer損耗分析：.......................................................... 62
4.3.4. Thermoelastic damping(TED) 數值分析：......................................................... 63
4.3.5. 表面損耗（Surface loss）數值分析：......................................................... 66
第五章、總結與未來展望............................................................ 68
5.1. 總結：................................................... 68
5.2. 未來展望：.......................................................... 70
附錄一. 光彈簧作用下之光場頻率ωopt及Qf估算以本文之Cat-flap製程及測量參數為基準（courtesy of Dr sundae Chen）：.........................................................72
附錄二. 各尺寸的Cat-flap之振動模態分析（ANSYS）..................................................... 79
參考文獻 ...............................................................89

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