本次實驗的最終目標是量測出真空雙折射效應。根據氣體的Cotton-Mouton效應，偏振光束通過氣體介質時，如果氣體介質中存在一與偏振光束垂直(橫向)的外加磁場，此外加磁場會讓垂直磁場方向與水平磁場方向的折射率有所差異，產生微弱的氣體雙折射現象。然而，此氣體雙折射的訊號大小與氣體介質的氣體濃度及偏振光束光程成正比，真空雙折射效應的訊號只會比氣體雙折射訊號更小且更難量測。因此，我們將Fabry-Perot干涉儀作為共振腔，以增加偏振光束的等效光程，並使用名為2x2 2D X Pendulum的懸吊結構，懸掛用於共振腔的反射鏡，濾除地面震動等外界雜訊。2x2 2D X Pendulum 由八組X Pendulum以彈簧鋼薄片並排串接組成，而X Pendulum只要經過適當的設置與調整，就會有“短擺長、長週期”的特性。因此，本文將介紹X Pendulum的特性與結構演進，量測分析X Pendulum在不同設置下的功率密度頻譜圖，並對頻譜圖中的差異作討論。經一系列的實驗量測，我們知道了結構對稱性對X Pendulum的重要性，與結構瑕疵及環境隨時間對X Pendulum的影響，量測到擺長為22.5公分的2x2 2D X Pendulum，在兩個方向的共振頻率分別為0.2197 Hz與0.1857 Hz，推算出共振腔頻率變化量在2.5小時會有最小的Allan Deviation，Allan Deviation的數量級約為10^-11 mm。

In this experiment, our end goal is to measure the vacuum birefringence effect. According to the gaseous Cotton-Mouton effect, when a polarized beam passes through gaseous medium where exist an external transverse magnetic field perpendicular to the polarized beam, the transverse magnetic field will make the indices of refraction perpendicular to external transverse magnetic field differ from the indices of refraction parallel to external transverse magnetic field, resulting in weak gaseous birefringence. However, the signal strength of gaseous birefringence is proportional to the gas concentration of gaseous medium and the optical path length of polarized beam, the signal of vacuum birefringence will only be weaker and difficult to measure than the signal of gaseous birefringence. Thus, we take Fabry–Pérot interferometer as an optical cavity to increase the equivalent optical path length of polarized beam, and use a suspension structure called 2x2 2D X Pendulum to suspend the mirrors for the optical cavity to filter out external noise such as seismic vibration. 2x2 2D X Pendulum consists of 8 X Pendulum connected side by side in series with spring steel sheets. With proper set and adjustment, X Pendulum will have the characteristics of “short pendulum.” Therefore, this thesis will introduce the characteristic and structural evolution of X Pendulum, measure and analyze the power density spectrum of X Pendulum under different settings, and discuss the difference in spectrums. After a series of experimental measurements, we know the importance of structural symmetry to X Pendulum, and the effect of structural defects and environment on X Pendulum over time. We also measured the resonance frequencies of 2x2 2D X Pendulum with a pendulum length of 22.5 cm in two directions are 0.2197 Hz and 0.1857 Hz respectively. It is also deduced that the optical cavity frequency change will have the smallest Allan Deviation of displacement at 2.5 hours, and the deduced Allan Deviation of cavity displacement is of the order of 10^-11 mm.

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