博碩士論文 107222039 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:14 、訪客IP:3.16.48.173
姓名 陳可翰(Ko-Han Chen)  查詢紙本館藏   畢業系所 物理學系
論文名稱 透過原子系統建立雷射功率標準的提案與演示
(A Proposal and Demonstration on Setting up Laser Power Standard via Atom System)
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摘要(中) 本論文提出了一種基於銫原子 6S1/2 → 7S1/2 雙光子躍遷的創新光功率量測方法。通
過研究原子躍遷中的 AC-Stark 頻移,本研究為建立功率量測標準奠定了基礎。在重力
波觀測中,準確的絕對功率量測對於確定重力波事件源的距離至關重要。然而,現有
的功率量測系統因感測器老化及量子效率不一致,導致測量結果存在偏差,需頻繁進
行校正。原子躍遷提供了一種克服這些限制的方法,使光功率量測更具穩定性和可重
現性。
本研究開發了一套基於原子的光功率量測系統,整合了碘穩頻雷射、偏頻鎖定技術
以及腔體增強的雙光子吸收光譜技術。碘穩頻雷射提供了不受 AC-Stark 頻移影響的頻
率基準,偏頻鎖定則將其穩定性轉移至從屬雷射。透過利用光強度與 AC-Stark 頻移之
間的線性關係,系統可實現準確且寬量測範圍的功率量測。腔體增強設計確保光束的
波形與原子束交互區域良好定義,進一步降低不確定性。
該系統展示了 0.56 kHz/mW 的功率頻率響應度,可量測功率的解析度為 5.4 mW,
實驗可重置性為 3 kHz。目前光功率的不準度為 ?P /P = 7 %,突顯此系統作為未來功
率校正標準基礎的潛力。
摘要(英) This dissertation introduces an innovative approach to optical power measurement using the
cesium 6S1/2 → 7S1/2 two-photon transition. The investigation of the AC-Stark shift in atomic
transitions serves as a foundation for developing a power measurement standard. In gravitational
wave observatories, accurate absolute power measurements are essential for determining source
distances of gravitational wave events. However, the existing power measurement systems suf-
fer from inconsistencies due to sensor aging and varying quantum efficiencies, necessitating
routine recalibrations. Atomic transitions provide a pathway to overcome these limitations by
enabling robust, reproducible, and digital optical power measurements.
The atom-based power measurement system developed in this work integrates an iodine-
stabilized laser, offset-locking technique, and cavity-enhanced two-photon absorption spec-
troscopy. The iodine-stabilized laser offers a frequency reference immune to the AC-Stark shift,
while offset-locking transfers its stability to the slave laser. By leveraging the linear relation-
ship between optical intensity and the AC-Stark shift, the system enables accurate and wide-
range power measurements. The cavity-enhanced design ensures well-defined beam profiles
and cross-sectional areas for atom-beam interactions, minimizing uncertainties.
The system demonstrates a power-frequency conversion factor of 0.56 kHz/mW, achieving
the power measurement resolution of 5.4 mW and a resettability of spectral measurements of
3 kHz. The current power measurement uncertainty is ?P /P = 7 % under typical operating
conditions, highlighting the potential of this system as a foundation for future power calibration
standards.
關鍵字(中) ★ 銫原子
★ 光功率標準
★ 雙光子躍遷
關鍵字(英) ★ Cesium atom
★ Power standard
★ Two-photon transition
論文目次 摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Power Calibration Methods . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Primary Standards at NIST . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.3 The Evolution of Power Meters in Gravitational Wave Observations . . 7
1.1.4 The Cesium 6S → 7S Two-photon Transition . . . . . . . . . . . . . . 10
1.2 Organization of the Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Technical Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Photon Calibrator: Principles and Applications in Gravitational Wave Observa-
tories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 The Importance of Power Stability in the Principles of Photon Calibration 16
2.1.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.4 Performance of the Photon Calibrator . . . . . . . . . . . . . . . . . . 21
2.1.5 The Calibration Model of the Mirror Displacement . . . . . . . . . . . 24
2.2 The AC-Stark shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.2 The AC-Stark Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.3 The Floquet Theorem and the Quasi-Energy Spectrum . . . . . . . . . 29

ix


2.2.4 The General Cases of the Quasi-energy Levels . . . . . . . . . . . . . 30
2.2.5 The Calculation of the AC-Stark Shift in 6S → 7S, F = 4 → F = 4
Two-photon Transition . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3 Two-Photon Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.1 Principle of the Two-Photon Transition . . . . . . . . . . . . . . . . . 40
2.3.2 Intracavity Two-Photon Absorption . . . . . . . . . . . . . . . . . . . 43
2.4 The Cross-Sectional Area of the Atom-Beam Interaction . . . . . . . . . . . . 47
3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1 Iodine-Stabilized Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.1.1 The Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1.2 The Pound-Drever-Hall Locking Method . . . . . . . . . . . . . . . . 57
3.1.3 Frequency Modulation Spectroscopy . . . . . . . . . . . . . . . . . . 59
3.1.4 The Temperature-Controlled Iodine Cell . . . . . . . . . . . . . . . . . 62
3.2 Fluorescence Detection Laser System . . . . . . . . . . . . . . . . . . . . . . 67
3.2.1 Laser Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.2 The Offset Locking Method . . . . . . . . . . . . . . . . . . . . . . . 69
3.2.3 Laser Power Stabilization . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2.4 Fluorescence Detection System . . . . . . . . . . . . . . . . . . . . . 72
3.2.5 Power Monitoring System . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3 Cavity-Enhanced Absorption Spectroscopy . . . . . . . . . . . . . . . . . . . 75
3.3.1 The Cavity Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3.2 The Cesium Vapor Cell . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3.3 Cavity Enhancement Factor . . . . . . . . . . . . . . . . . . . . . . . 81
3.3.4 Error Budget of the Cavity . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.5 The Cavity Stabilization Methods . . . . . . . . . . . . . . . . . . . . 88
3.4 The Power Measurement via the AC-Stark Shift of Atom System . . . . . . . . 91
3.4.1 The Experimental Procedure of the AC-Stark Shift Measurement . . . 91
3.4.2 The Estimation of Power Measurement Uncertainty . . . . . . . . . . . 92
3.5 The variable AC-Stark Shift Measurement with a Variable Slit . . . . . . . . . 93

x


3.5.1 The Experimental Step . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.1 Power Measurement Uncertainty of the Atom-Based System . . . . . . . . . . 99
4.1.1 The Specification of the Atom-Based Power Measurement System . . . 99
4.2 Evaluations on Each Error Source . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2.1 Uncertainty in Iodine Pressure Shift from Temperature Instabilities . . 105
4.2.2 Uncertainty Due to Electronic Drift in Master Laser . . . . . . . . . . . 107
4.2.3 Uncertainty of Radio Frequency in AOM1,2 . . . . . . . . . . . . . . 108
4.2.4 Uncertainty of the Beat Frequency . . . . . . . . . . . . . . . . . . . . 110
4.2.5 Uncertainty of the AC-Stark Shift Due to Intracavity Power Fluctuations 113
4.2.6 The Long-Term Drift in the Atom-Based System . . . . . . . . . . . . 116
4.3 The Performance of the Pound-Drever-Hall Method . . . . . . . . . . . . . . . 117
4.4 Analysis of the AC-Stark Shift Fitting with Considering the Cross-Sectional
Area of the Atom-Beam Interaction . . . . . . . . . . . . . . . . . . . . . . . 123
4.5 Other Possible Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.5.1 Unique Linewidth Broadening Caused by the Inhomogeneous AC-Stark
Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.5.2 The AC-Stark Shift Varied by Detection Aperture . . . . . . . . . . . . 133
4.5.3 The Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 133
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.1 Summary of Key Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.2 Challenges and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Appendix A A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
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指導教授 鄭王曜 井上優貴(Wang-Yau Cheng Yuki Inoue) 審核日期 2025-1-20
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