先進重力波輸入光學系統之發展與特性研究｜國立中央大學博碩士論文系統

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研究生：	詹承翰 Cheng-Han Chan
論文名稱：	先進重力波輸入光學系統之發展與特性研究 The Development and Characterization of Input Optics for Advanced Gravitational Wave Detector
指導教授：	井上悠貴 Yuki Inoue
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2025
畢業學年度：	113
語文別：	英文
論文頁數：	154
中文關鍵詞：	重力波、重力波探測器、雷射光學、雷射穩壓
外文關鍵詞：	Gravitational Wave, Gravitational Wave Detector, Lasre Optics, Laser intensity stabilization
相關次數：	點閱：7 下載：0
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自從 LIGO 在 2015 年首次偵測到重力波訊號以來，科學家們便開始尋找由\textbf{中等質量黑洞（Intermediate-Mass Black Holes, IMBH）}所產生的其他重力波事件。因此，對於更低頻段重力波訊號的需求日益增加，而新一代的重力波探測器正是以此為主要設計目標。其中包括第二代與第三代的觀測設施，例如進階 LIGO（aLIGO）、Virgo、KAGRA，以及未來規劃中的台灣 CHRONOS 計畫。在本論文中，我將介紹 CHRONOS 系統，並探討其輸入光學系統（Input Optics）的研製與特性化。這項研究首先展示了 Michelson 干涉儀的性能，而其後續的 Sagnac 干涉儀則將被應用於 CHRONOS 的 extbf{速度計（Speed Meter）}之研發。
輸入光學的主要功能，是將穩定的雷射注入 Michelson 干涉儀，並確保其強度與頻率在 $\mathrm{TEM_{00}}$ 模態下保持穩定。在本研究中，我們使用功率 0.5 W、波長 1064 nm 的雷射。首先進行模態匹配 (mode matching) ，以符合預模態清理器（Pre-Mode Cleaner, PMC）的最佳腔體條件 (cavity condition) 與對準配置。經由實驗確認，輸入至 PMC 的雷射光束品質達到 extbf{x-軸 $M^2_x = 0.99 \pm 0.01$ 與 y-軸 $M^2_y = 0.98 \pm 0.02$}。隨後測得 \textbf{PMC 的精細度（finesse）約為 128.3668}。透過電光調制器（EOM），我們產生 Pound-Drever-Hall（PDH）誤差信號，並將雷射鎖定於 PMC 腔體條件內，以獲得高斯光束形貌與最大輸出功率。同時，利用聲光調制器（AOM）與主動控制器 Optical-Follower Servo，我們有效抑制了透射光中的相對功率雜訊，並測得 extbf{在 0.1 赫茲頻率附近之相對功率雜訊約 (Relative power noise) 為 -90 dB}。接著，我們引入參考腔體 (Reference Cavity) ，並應用 PDH 技術進一步穩定雷射的頻率雜訊。最後，針對未來的研究方向，我們計畫在輸出光學端透過光電探測器觀測干涉條紋訊號，並進行 Michelson 測試，即將 Michelson 干涉儀鎖定並重建其重力波應變訊號。

Ever since the first detection of gravitational wave signals by LIGO in 2015, scientists were looking for other gravitational wave signals produced by \textbf{Intermediate-Mass Black Holes (IMBH)}. Hence, the need for lower stain frequencies of gravitational wave signal is needed, and the next generation of gravitational wave detector is mainly designed to detect such signals. These including second- and third-generation observatories like aLIGO (Advanced LIGO), Virgo, KAGRA, and the proposed future detectors such as the CHRONOS in Taiwan. In this thesis, I will introduce the CHRONOS system and the development and characterization of Input Optics, which will be first demonstration of the Michelson interferometers and its successor, a Sagnac interferometer, will later be used to develop the \textbf{Speed Meter} for CHRONOS.

Input Optics provides a stable laser into the Michelson interferometer, with its intensity and frequency are stabilized in a $\mathrm{TEM_{00}}$ mode. In my study, we implement a 0.5 watt laser with its wavelength of 1064 nano-meter. We first do the mode matching to fit the best alignment and cavity condition for Pre-Mode Cleaner (PMC), and we confirm the alignment to PMC has \textbf{beam quality of $M^2_x=0.99\pm0.01$ for x-axis and $M^2_y=0.98\pm0.02$ for y-axis}. Then we measure \textbf{the finesse of PMC is about 128.3668}. With the usage of electro-optical modulator, we are able to generate a Pound-Drever-Hall error signal to lock the laser within the cavity condition of PMC, this created a clean Gaussian beam shape for maximum power. And with acousto-optic modulator we can use an active controller, Optical-Follower Servo, to mitigate the relative power noise from the transmitted beam and we measured the \textbf{relative power noise is about -90 dB around 0.1 Hz frequncy region}. Next, we employ a reference cavity, and use Pound-Drever-Hall method to stabilized the frequency noise. Finally, for our further development plan, we want to see the fringe signal by the readout photodetector at the Output Optics, and we perform the Michelson Test, which is lock the Michelson interferometer and reconstruct the stain signal of the interferometer.

中文目錄
Abstract
Acknowledgment
List of Figures
List of Tables
Introduction
Gravitational Wave Science 4
1 2.2 2.3 Gravitational Wave Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1 Einstein field equation in weak field . . . . . . . . . . . . . . . . . . . . . 4
1.2 Linearized Einstein field equation . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Gravitational Wave Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Binary black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Binary neutron stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Neutron star-Black hole binary . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Supernovae and gravitational collapse . . . . . . . . . . . . . . . . . . . . 14
2.5 Stochastic background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Summary
Gravitational Wave Detectors 16
1 Gravitational Wave Interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.1 Michelson Interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 Fabry-Perot Michelson Interferometer . . . . . . . . . . . . . . . . . . . . 20
1.3 Sagnac Interferometer and Speed Meter . . . . . . . . . . . . . . . . . . . 23
2 3.3 3.4 Ground-based Gravitational Wave Detectors . . . . . . . . . . . . . . . . . . . . 24
2.1 LIGO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 KARGRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Virgo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Space-based Gravitational Wave Detectors . . . . . . . . . . . . . . . . . . . . . 26
3.1 LISA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 DECIGO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
CHRONOS System 29
1 4.2 4.3 4.4 4.5 Overview of CHRONOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Science of CHRONOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1 Cryogenic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Cross torsion bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 Quantum non-demolition speed meter . . . . . . . . . . . . . . . . . . . 30
Noise sources of CHRONOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1 Thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Quantum noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Vacuum noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Seismic noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Intensity noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.6 Frequency noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Requirements of Input Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1 Target of CHRONOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Input Optics in CHRONOS . . . . . . . . . . . . . . . . . . . . . . . . . 38
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Hardware of Input Optics and Control System 5.1 5.2 5.3 5.4 40
Overview of Input Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Optical path of Input Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Beam Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1 Laser beam waist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Items in Input Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 Seed laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Mirrors and lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 Electro-optic modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4 Acousto-optic modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.5 Beam profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.6 Photo detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Feedback Theory of Input Optics . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.1 Pound–Drever–Hall method . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 Feedback circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Mode Cleaner 59
1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Requirement of Mode Cleaner . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Pre-Mode Cleaner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.1 Temperature model of PMC . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.2 TTFSS Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Beam Characterization of PMC . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.1 Mode matching around EOM . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2 Mode matching before PMC . . . . . . . . . . . . . . . . . . . . . . . . . 65
PZT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Temperature Monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.1 Temperature control board . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Heater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Temperature measurement of PMC . . . . . . . . . . . . . . . . . . . . . . . . . 69
PMC Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.1 PMC Locking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.2 Transfer function measurement . . . . . . . . . . . . . . . . . . . . . . . 73
7.3 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
PMC Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
8.1 Beam quality measurement . . . . . . . . . . . . . . . . . . . . . . . . . 79
8.2 Finesse measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Intensity Stabilization 85
1 Principle of Intensity Stabilization (IS) . . . . . . . . . . . . . . . . . . . . . . . 85
2 7.3 7.4 7.5 7.6 Optical-Follower Servo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.1 Circuit of OFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.2 Measurement of OFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Beam Characterization for IS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.1 Mode matching around AOM . . . . . . . . . . . . . . . . . . . . . . . . 91
AOM Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.2 AOM efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Feedback Control of Optical-Follower Servo . . . . . . . . . . . . . . . . . . . . . 94
5.1 OFS setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2 Power spectrum of noise measurement . . . . . . . . . . . . . . . . . . . 94
5.3 Transfer function of OFS . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Frequency Stabilization 101
1 8.2 8.3 8.4 8.5 Principle of Frequency Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . 101
1.1 Quarter wave plate and polarizing beamsplitter . . . . . . . . . . . . . . 101
Reference Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Beam Characterization of RC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.1 Mode matching around second EOM . . . . . . . . . . . . . . . . . . . . 107
3.2 Mode matching before RC . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Measurement of Frequency Stabilization . . . . . . . . . . . . . . . . . . . . . . 109
4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Integration Test 112
1 9.2 9.3 9.4 Purpose of Integration Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
1.1 Reconstruction of h(t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Main Interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
2.1 Michelson interferometer layout . . . . . . . . . . . . . . . . . . . . . . . 115
2.2 Multiple-stage suspension system . . . . . . . . . . . . . . . . . . . . . . 116
Beam Characterization of Input Laser . . . . . . . . . . . . . . . . . . . . . . . . 119
3.1 Mode matching to the main output . . . . . . . . . . . . . . . . . . . . . 119
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Discussion 122
1 Stability of PMC Locking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
2 Relative Power Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
2.1 Noise model of relative power noise . . . . . . . . . . . . . . . . . . . . . 122
2.2 Improvement of relative power noise . . . . . . . . . . . . . . . . . . . . 124
3 Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.1 PMC transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.2 OFS transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4 Further Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.1 Circulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.2 Moving to underground facility . . . . . . . . . . . . . . . . . . . . . . . 126
Conclusion 128
Bibliography 130

                                

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