利用表面繞射的方式來達到廣角入射波導管的實驗已被証實可行，本論文主要在於討論以廣角入射的方法將X光引入分光波導管。此分光波導管的主要功能為讓波導管中傳播的X光改變行進方向，進而將一道光分為二道。波導管使用之基底材料為矽，在其上蝕刻出一矩形導管，並在四周鍍金，導管在中段以後分岔為二，分岔部份與前半部直線部份夾0.3°，這個角度小於X光對於矽金的全反射角，藉此改變X光行進方向，並達到分光效果。實驗更進一步改變不同的出口端設計，希望能控制出光方向。

理論部份以馬克斯威爾方程式為基礎，計算出波導管中電磁波傳播的模式，並分析在非允許模式下的效應與TE mode和TM mode的差異。在非允許模式的情況下電磁波的傳播形式將以允許模式來展開，由此可發現波導管出光口的電磁波分佈將出現振盪的效應。而計算出之TE、TM mode差異其結果因在小角度下而差異甚小。

實驗部份利用同步輻射光源及八環繞射儀來進行。實驗結果可觀測到波導管明顯的波導效應。在不同出口端設計的部份並無達到控制方向的目的，這應與製程控制有關。而在進一步的實驗分析後，我們相信分光波導管具有分光的效應。

Wide-angle incident X-ray waveguide making use of surface diffraction has recently been proved feasible. This thesis reports on the possibility of using Y-shaped waveguides for X-ray beam splitting at wide-angle incidence. The main function of this splitting waveguide is to change the direction of X-ray beam when propagating in the waveguide, and to divide the incident beam into two bunches. The preparation of the splitting waveguides involves etching a rectangular waveguide on a silicon wafer. The waveguide is then coated with gold thin films. The angle of beam splitting is about 0.3°, relative to the incident beam. This angle is smaller than the critical angle of the total external reflection from the interface of silicon and gold. Therefore, the power loss due to change of the direction of the X-rays is negligibly small.

The theoretical calculation of this wave-guiding effect due to diffraction is based on Maxwell’s equations, where the mode of electromagnetic wave-propagating in the waveguide is considered. When a mode is not allowed as a TE or a TM mode, then the mode can be expressed as the superposition of the allowed TE or TM modes. Consequently, the intensity of electromagnetic wave oscillates. Also, because the angle of splitting is very small, the difference between TE and TM mode is almost undetectable.

The experiment is carried out at the National Synchrotron Radiation Center (NSRRC). An 8-circle diffractometer is used to perform the (113) surface diffraction with the photon energies close to 8.878 keV. Wave guiding effects and beam slitting are observed. Detailed analysis of the degree of beam splitting is also reported.

第 1 章 導言
第 2 章 理論基礎
2.1 廣角入射之繞射幾何
2.2 司乃耳定律和全反射
2.3 波導原理
2.3.1 波場計算
2.3.2 TE與TM mode
2.4 平面波導管之傳播模式
2.4.1 TE 與TM mode電磁場形式
2.4.2 模式與入射角之關係
2.5 非允許模式之傳播
第 3 章 樣品製備
3.1 設計
3.2 製作
3.2.1 光罩製作
3.2.2 黃光蝕刻
3.2.3 鍍金
3.2.4 雷射切割
3.2.5 成品
第 4 章 實驗方法
4.1 光源與儀器
4.2 實驗步驟
第 5 章 分析
5.1 理論模擬
5.1.1 模擬方法
5.1.2 各種類型波導管之模擬
5.1.3 TE mode與TM mode之比較
5.2 數據分析
5.2.1 波導與分光效應
5.2.2 轉動phi軸對分光之影響
5.2.3 波導管的模式效應
第 6 章 結論與展望
附錄 分光波導管強度分佈模擬程式
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