本論文主要是利用理論模擬的方式，探討三氧化二鋁 ( 藍寶石 ) 為材料的X光共振腔系統的共振效應，主要分為兩部份，第一部份是利用矩陣轉換的方式建立直角座標，模擬出複繞射定碼程式，藉此檢驗繞射面 ( 0 0 30 ) 在入射光能量為14.3148keV下為純兩光的背向射繞面，其結果是相當接近的，而第二部份則是在利用動力繞射理論，探討在上述的繞射面及能量下藍寶石X光共振腔的共振行為，使用的程式為Yu. P. Stetsko博士所寫的程式，討論範圍包含能量掃描下的反射率與穿透率共振行為，並在此探討Finesse[1]，以及不同能量下晶體內和共振腔內外的強度分布，最後則是提供色散表面及線性吸收係數的變化情形。

This thesis investigates the resonant behavior in X-ray resonant cavity of sapphire by using the method of theoretical calculations based on the dynamical theory of X-ray diffraction. There are two parts in this thesis. In the first part, we build up the coordinates system using the matrix algebra and try to develop an indexing program to examine whether the diffraction ( 0 0 30 ) is a two-beam back reflection case at the photon energy of 14.3148 keV. In the second part, we use another computer program written by Dr. Yu. P. Stetsko based on the dynamic diffraction theory to deal with the resonant behavior of X-ray photons in a resonant cavity of sapphire for the (0 0 30) back reflection. By performing the calculations for reflectivity and transmissivity as a function of the photon energy, the finesse and the intensity distributions inside and outside the crystal cavity are given. Furthermore, the coordinates of the dispersion surface and the linear absorption coefficient are also calculated.

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