臺灣博碩士論文加值系統

氣體的Cotton-Mouton效應(1905年發現)指氣體在外加橫向磁場作用下使通過之光束產生雙折射之特性，為Kerr效應在磁場方面的類比。Cotton-Mouton效應與氣壓(P)，外加磁場強度的平方(B^2)，磁場作用區長度(LB)，通過光束之波長倒數(λ^-1)成正比。氣體平行於磁場方向與垂直於磁場方向的2種折射率使入射線偏振光在此2方向的偏振分量具有2種不同的光速，造成出射光在此2方向之偏振分量彼此具有相位差(正比於折射率差Δn)形成橢圓偏振光，各氣體Cotton-Mouton效應可由出射光之橢圓率求得並以Cotton-Mouton係數(CCM)加以區分。對於一般常見氣體此效應非常小不易測量(Δn ~ 10^-11 - 10^-16)，縱使經過1世紀，學界對各氣體Cotton-Mouton效應在溫度、 壓力、 波長、 外場強度等不同外在環境下的變化仍未有系統化的完整量測報告。而Q & A(Quantum electrodynamics test and search for Axion)實驗架構有能力對各種不同氣體的Cotton-Mouton效應提供不同氣壓下精確的量測。Q & A實驗以探測真空雙折射效應與搜尋軸子為目標[1,2]，探討參與反應的(贗)純量粒子與二光子之間的交互作用。主要以一對偏振透射方向互相直交的偏極化鏡(消光比可達92.87 dB)探測通過真空的線偏振單頻Nd-YAG固態雷射光束(λ = 1064 nm)，在橫向磁場(LB ~ 0.6 m，B ~ 2.2 T)作用下產生之真空雙折射/二色性造成之橢圓率/偏振旋轉，技術上在磁場作用區域兩端使用懸吊式(交叉擺-複擺懸吊避振)3.45 m高精細度(F ~ 30000)Fabry-Perot干涉儀，讓光在鏡面上來回反射延長磁場有效作用區以放大待測之效應。實驗過程中運用四分波片/相位可變波片補償干涉儀鏡面內秉雙折射效應，提升系統整體消光比與角度偵測靈敏度，並採用雙調制配合鎖相技術進行訊號擷取，在48天(1152小時)內擷取數據超過900小時，包含0.5 - 300 Torr間氣體N2、O2、CO2、Ar與Kr的Cotton-Mouton效應與Verdet效應(即軸向磁場存在下的法拉第旋轉效應)，以及目前系統能達到的真空狀態(3 mTorr)下超過378小時的偏振旋轉偵測鎖相累積積分，以及超過156小時的橢圓率偵測鎖相累積積分。量測到各氣體之Cotton-Mouton係數(CCM(m^-1 T^-2))為N2: (-1.74±0.13)×10^-7; O2: (-1.53±0.09)×10^-6; CO2: (-3.85±0.24)×10^-7; Ar: (3.94±0.31)×10^-9; Kr: (7.57±1.16)×10^-9。各氣體Verdet係數(Cυ(m^-1 T^-1))為N2: (2.93±0.62)×10^-4; O2: (8.43±0.17)×10^-4; CO2:(4.46±0.90)×10^-4; Ar:(4.54±1.08)×10^-4; Kr:(1.02±0.20)×10^-3。目前偏振旋轉偵測系統靈敏度達到0.93 μrad/Hz^1/2,橢圓率偵測系統靈敏度達到1.02 μrad/Hz^1/2，與本實驗在2006年達到之19.2小時偏振旋轉數據累積與偵測靈敏度1.4 μrad/Hz^1/2相比，積分時間改進19.7倍，旋轉狀態靈敏度改進30%。除上述量測重點外，本文附帶報告雙調變偵測中各種物理模型與訊號型態，偏極化鏡消光率量測，系統真空環境，磁鐵與光路附近的磁場量測，最後從現有的經驗展望Q & A實驗未來的發展重點。

Gaseous Cotton-Mouton effect (discoveredin1905) means the birefringence of light passing through gaseous medium in the presence of external transverse magnetic field. Its electric analog is the Kerr effect. The Cotton-Mouton effect is propotional to pressure (P), square of external magnetic field (B^2), effective length of magnetic field region (LB), and inverse of the wave-length of the light(λ^-1). The 2 different indices of refraction of gas for polarization components of incident linear polarized light parallel and perpendicular to the transversemagnetic field imply 2 different speeds of light. The transmitted light polarization components thus obtain phase difference
(propotional to the difference of the 2 indices of defraction Δn) and the polarization becomes elliptical. The Cotton-Mouton effects for different gases can be found by measuring the ellipticity of the transmitted light and distinguished by the Cotton-Mouton coefficients (CCM). For common gases this effect is too small to be measured (Δn ~ 10^-11 - 10^-16). That's why we can't find systemetic and complete report of the Cotton-Mouton effect of all gases under different temperature, pressure, wave-length and external field strength for over 1 century. The Q & A(Quantum electro-dynamics test and search for Axion) experiment[1,2] is capable of providing precision measurement of the Cotton-Mouton effect under different pressures. It was originally aiming at the detection of the vacuum birefringence and the search for axion and the interaction of (pseudo-)scalar particle with two photons. Basically it explores the ellipticity of vacuum birefringence and polarization rotation of vacuum dichroism generated by transverse magnetic field(LB ~ 0.6 m, B ~ 2.2 T) onto a 1064 nm Nd-YAG laser beam using a pair of cross-orientated polarizers (with an extinction ratio up to 92.87 dB). Technically it adopts a suspended 3.45 m high-finesse (F ~ 30000) Fabry-Perot interferometer (with X-pendulum-double-pendulum system for seismic noise isolation) to extend the effective length of magnetic field region by bouncing the light back and forth between cavity mirrors for amplifying the signal for detection. A quarter/variable wave plate is applied to compensate the cavity mirror birefringence and increase the system's total extinction ratio and angular detection sensitivity. By employing double-modulation and phase-lock detection techniques in signal acquiring, data-taking was successful for over 900 hours in 48 days (1152 hours), including the Cotton-Mouton effect and the Verdet effect (i.e. Faraday rotation in the presence of axial magnetic field) of N2, O2, CO2, Ar and Kr of pressure ranging from 0.5 to 300 Torr, and polarization rotation in vacuum (3 mTorr) for 378 hours and ellipticity in vacuum for 156 hours. The Cotton-Mouton coefficients(CCM in m^-1 T^-2) are N2: (-1.74±0.13)×10^-7; O2: (-1.53±0.09)×10^-6; CO2: (-3.85±0.24)×10^-7; Ar: (3.94±0.31)×10^-9; Kr: (7.57±1.16)×10^-9. The Verdet coefficients (Cυ in m^-1 T^-1) are N2: (2.93±0.62)×10^-4; O2: (8.43±0.17)×10^-4; CO2:(4.46±0.90)×10^-4; Ar: (4.54±1.08)×10^-4; Kr: (1.02±0.20)×10^-3. The current sensitivity is 0.93 μrad/Hz^1/2 for polarization rotation, and1.02 μrad/Hz^1/2 for ellipticity. Compared to the intergration time 19.2 hours and sensitivity 1.4 μrad/Hz^1/2 for polarization rotation in 2006, an improvement factor of 19.7 in intergration time and 30% in sensitivity of polarization rotation are achieved. Besides the points mentioned above, this thesis also reports on more detailed models and signal analyses in this double modulation scheme, as well as the measurement of extinction ratio of polarizers/analyzers, the vacuum pressure and the measurement of magnetic field of the rotating magnet around the optical path. In the end, we give an outlook for future development of this experiment.

論文摘要....................................iii
Abstract......................................v
誌謝.........................................ix

1 導論........................................1
1.1 Cotton-Mouton效應與其歷史發展.............1
1.2 QED真空雙折射.............................6
1.3 (贗)純量場與軸子理論......................8
1.4 真空雙折射實驗與Q & A實驗之歷程..........10
1.5 論文章節概要.............................14

2 Q & A實驗概觀..............................15
2.1 綜觀.....................................15
2.2 雷射與光學系統...........................21
2.2.1 入射端光學元組件.......................21
雷射...................................21
光學隔離器.............................23
電光相位調制器.........................24
模態匹配透鏡組.........................24
光接收器...............................24
起偏器.................................25
2.2.2 Fabry-Perot干涉儀光學性質..............25
2.2.3 出射端光偏振偵測元件...................27
四分波片/相位可變波片..................27
偏振旋轉調制器.........................30
檢偏器.................................30
後端光接收器...........................30
2.3 干涉儀懸吊與系統控制.....................33
2.3.1 懸吊系統...............................33
交叉擺X-Pendulum.......................36
複擺、鏡面與反饋質量...................36
2.3.2 縱向控制...............................41
2.4 旋轉磁鐵與轉速偵測.......................47

3 橫(軸)向磁場作用下的偏振旋轉與雙折射.......55
3.1 雙主軸非等量相位延遲(雙折射).............56
3.1.1 極小相位延遲近似與修正量...............58
3.1.2 橢圓率之意義...........................60
3.2 雙主軸非等量衰減(二色性).................63
3.3 軸向磁場法拉第旋轉.......................65
3.4 橢圓率檢偏法光路元件與交互作用...........66
3.4.1 雙折射量測.............................71
3.4.2 二色性或偏振旋轉量測...................76

4 檢偏儀消光率量測...........................81
4.1 撓性結構旋轉微動平台.....................82
4.2 光干涉法角位移偵測.......................85
4.3 消光率數據Monte-Carlo運算................92

5 真空系統與阻尼減振.........................99
5.1 Q & A實驗真空系統綜觀....................99
5.2 泵浦與抽/釋氣速率.......................100
5.2.1 泵浦..................................100
5.2.2 氣導與釋氣............................100
連續流長圓管氣導......................103
分子流長圓管氣導......................104
Q & A實驗總氣導.......................104
Q & A實驗腔體釋氣率與終極氣壓.........105
5.3 隔膜型態真空壓力計......................107
5.4 交叉擺與複擺阻尼減振....................110

6 旋轉磁鐵與光路附近的磁場量測..............119
6.1 干涉儀鏡面CM2附近直流、交流磁場量測.....119
6.2 旋轉磁鐵橫向磁場量測....................125
6.3 旋轉磁鐵軸向磁場的產生與量測............132
6.4 以螺線管校正Bell探針與測磁通時變率......140

7 氣體Cotton-Mouton與Verdet效應.............149
7.1 訊號擷取與數據預處理....................153
7.2 Interpolation法鎖相.....................154
7.3 複數向量頻譜與相位補償..................159
7.4 氣體Cotton-Mouton效應...................167
7.5 氣體Verdet效應..........................180

8 3 mTorr真空狀態下累積鎖相積分.............197
8.1 偏振旋轉鎖相積分378小時.................197
8.1.1 圖8.1-圖8.8作圖解釋...................198
8.1.2 圖8.1-圖8.8圖形解讀...................201
頻率ωm處訊號..........................201
頻率2ωm處訊號.........................209
8.2 雙折射鎖相積分156小時...................212
8.2.1 圖8.9-圖8.16作圖解釋..................212
8.2.2 圖8.9-圖8.16圖形解讀..................216
頻率2ωm處訊號.........................216
頻率ωm處訊號..........................222
8.3 腔體釋氣過程中的雙折射與偏振旋轉........222

9 討論與展望................................237

附錄A LabVIEW數據處理程式...................241
A.1 數據處理流程............................241

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