摘要

本論文利用理論模擬的方式，觀察藍寶石(三氧化二鋁)所設計的共振腔在四光繞射時之共振情形。本文主要分成三個部分，第一部分透過多光繞射繞射理論，用旋轉矩陣建立直角坐標後，用程式確認在14.41905keV的能量下確認以原子面(1 3 28)在倒空間中建立的Edward sphere所伴隨的其他倒晶格點，確定原子面(2 2 0)與原子面(-1 1 28)同時在Edward sphere上，加上入射光(0 0 0)而形成四光繞射的模式。接著以原子面(-1 1 28)在倒空間中建立的新的Edward sphere，而形成另一組四光繞射(-2 -2 0)與(-3 -1 28)。
接著利用動力繞射理論，在14.41905keV的能量下，進行兩光的計算，首先是兩光(0 0 0)與(1 3 28)背向繞射光的例子，計算其共振腔之共振情形，另外則是透過光學路徑的可逆關係，利用在四光的情況下14.41905keV 所激發的另外兩外兩道繞射光(-1 1 28)與(2 2 0)，作為新的斜向入射光，以避開共振腔的第一片晶體所造成的能量吸收和反射，而設計的斜向入射共振腔，在只考慮兩光的條件下，由此觀察其共振情形。
第三部分同樣的在14.41905keV能量掃描下所產生的(1 3 28)面之背向繞射光，並同時另外激發了(2 2 0)與(-1 1 28)兩個面之繞射光，觀察四光之間的交互作用與影響，並以此觀察以四光而建立的共振腔之共振行為，最後則是計算在四光的情況下之斜向入射共振腔之共振情形。本文主要討論的內容包括調整共振腔晶體厚度，晶體之間的間距，藉此觀察正向入射共振腔與斜向入射共振腔之反射率與穿透率共振行為和其變化。最後作結論與探討未來之發展方向。

Abstract

We report on the investigation of resonant behavior of X-ray cavity in sapphire crystal with the calculation of dynamical theory. At 14.41905 keV, the incident beam will excite a back diffraction(1 3 28) beam. At the same time, the incident beam also excite the other two diffraction beam (2 2 0) and (-1 1 28). We divide the article into three parts. First part we use computer program to build a Edward sphere and make sure the reciprocal lattice points (1 3 28),(2 2 0) and (-1 1 28) will be on the Edward sphere at 14.41905 keV. Then build a new Edward sphere to construct a new four-beam diffraction with (0 0 0),(-1 1 28),(-2 -2 0) and (-3 -1 28).
Second part we only consider two-beam diffraction case. We choose (0 0 0) and (1 3 28) to build a Fabry-Perot cavity designed by two parallel sapphire crystals mirrors and make calculation to observe the resonator behavior. Second, different with traditional normal incidence, we use the inclined beam as our incident beam to build a new kind of Fabry-Perot cavity. Because of reversible of light beam root, we use the (-1 1 28) or (2 2 0) diffraction light beam as our incident direction. We calculate and investigate the resonant behavior of the inclined-incidence X-ray cavity.
Third, we consider four-beam case. At this time we again make calculation of the normal-incidence X-ray cavity and inclined-incidence X-ray cavity. With the adjustment of crystal thickness and crystal gap, we observe resonant patterns of two different cavities. Finally, we compare the inclined- incidence case to the normal -incidence case, analyzing the intensity and resonant efficiency of two cases.

參考文獻
[1]張櫻議.(2005). X光共振腔的可行性研究 ,碩士論文 ,國立清華大學物理系.

[2]邱茂森.(2008). X光共振腔之24光動力繞射計算 ,博士論文 ,國立清華大學物理系.

[3]黃亮諭.(2009). 藍寶石X光共振腔之可行性研究 ,碩士論文 ,國立清華大學物理系.

[4]蔡一葦.(2014). 多共振腔系統、藍寶石X光共振腔及建置時間解析繞射系統 ,博士論文 ,國立清華大學物理系.

[5]S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, (2005) Phys. Rev. B 63, 094111(1-12).

[6]Y.-H. Wu, Y.-W. Tsai, C.-H. Chu, W.-C. Liu, Y.-Y. Chang, and S.-L. Chang (2015) O.E. Vol.23, Issue 8,9994.

[7]Shvyd’ko Yuri.(2004). X-Ray Optics : High-Energy-Resolution Application, Berlin : Springer

[8]Chang,S.-L. (2004). X-Ray Multiple-Wave Diffraction Theory and Application, Berlin : Springer.