本論文探討光波在雙軸晶體中的圓錐折射 (conical refraction) 現象。以介紹錐型折射歷史與應用開始，帶入Fresnel's equation of wave normals，推導 normal surface與 index ellipsoid，藉此定性分析內圓錐折射，接續推導分析外圓錐折射，並比較內、外圓錐折射的關係與差異。
利用Hamilton's principle分析圓錐折射的入射光束，並解釋圓錐折射成像上的Double Bright Rings, Poggendorff's Dark Ring and Raman Spot。詳細推導 Belskii 和 Khapalyuk 的精確近軸理論 (the Belskii-Khapalyuk's exact paraxial theory)，模擬以此為主要方法，接著介紹近似方法以快速求得光強度。詳細解釋線偏振入射光，成像偏振態分布不同於過往之研究結果。最後探討若晶體具有光學活性 (optical activity) 與磁光效應 (magneto-optical effect) 情形下，入射光的光強度分布。推演解釋過程中皆有模擬圖、手繪圖與之對應。
第四章、首先模擬歷史上圓錐折射相關數據，再比較光波入射勻向 (isotropic)、單軸 (uniaxial) 與雙軸 (biaxial) 晶體的差別；接著模擬在焦平面上，隨機偏振、特殊偏振入射光的光型成像，後模擬隨距離不同的變化；比較與探討多種不同狀況的光強度分布趨勢。延伸模擬探討晶體具光學活性 (optical activity) 情形下，不同偏振態、不同旋性入射光，其成像的光強度分布、與趨勢變化。

In this thesis, we analyze in detail the phenomena of conical refraction in biaxial crystals. In chapter 2, we introduce the history and applications of conical refraction in the beginning. After that, we derive the equations of normal surface and index ellipsoid via Fresnel′s equation of wave normal and the energy density of the light, respectively, to study the internal conical refraction. Likewise, we derive in detail the external conical refraction based on the principle of duality. Finally, we compare the internal with external conical refractions and sum them up.
In the chapter 3, we start with exploiting Hamilton′s principle to resolve the incident beam of conical refraction and explains double bright rings, Poggendorff′s dark circle and Raman spot of conical refractive image. We then derive the main formulas of Belskii-Khapalyuk′s exact paraxial theory, and discuss the approximation method, which is the main reference of the simulation method used in this thesis. Most importantly, for linearly polarized light, we report and explain an interesting new finding concerning the angular distribution of the polarization state of the refracted light that is different from the usual result got in previous researches. Finally, we discuss the light intensity distribution in chiral and magneto-optical crystals for various polarization states of incident light.
In chapter 4, we simulate conical-refraction-related phenomena after introducing the simulation parameters. The intensity patterns on the focal plane for non-polarized and specific polarized light are both simulated. We also study how the intensity and polarization of the refracted light changes in the space when different polarization states of the incident light are considered. We finally analyze how the refracted light intensity for unpolarized and specific polarized incident light changes when optical activity is present.

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