有關雙纖衣摻稀土元素光纖之模態雙折射(Modal–birefringence)及應力分佈量測方法，近年來被廣泛的研究，如：雙纖衣摻鐿(ytterbium)光纖、雙纖衣摻銣(neodymium)光纖等，而本篇論文，主要著重於探討雙纖衣Cr4+:YAG 晶體光纖，在研製上對雙折射造成之影響。由應力的分佈量測，指出應力為造成光纖雙折射的主要來源，但會產生雙折射的機制有很多，如:應力引起、纖心及內纖衣幾何結構不對稱、材料本質、光纖彎曲或扭轉等。為了瞭解其造成雙折射之真正來源，本論文首先利用偏光顯微鏡，觀測其應力分佈情況，而後參考文獻上，量測雙折射的實驗架構(Scanning Wavelength Method)自行架設可量測各種晶體之雙折射系統，並成功量測到雙折射晶體YVO4、及本實驗室雙纖衣Cr4+:YAG 晶體光纖之雙折射量值，再利用Jones 矩陣、Mueller矩陣，應力光學定律、光彈及數學上估計模態雙折射公式等，分別計算其應力強度分佈、干涉亮暗紋產生條件並估算出因纖心及內纖衣橢圓率所造成之模態雙折射，即以數學理論來驗證實驗之合理性，最後再與其他雙纖衣摻稀土元素光纖做比較。

Modal birefringence and stress distribution measurement in doubt-clad rare-earth-doped fibers are reported. For example, doubt –clad ytterbium-doped fiber and doubt –clad neodymium -doped fiber. In this paper, I am interested in the effect of fabrication on birefringence of Cr4+: YAG double-clad crystal fiber. A knowledge of stress distribution in the fiber would indicate the origin of birefringence.Since fiber birefringence can be produced by different mechanisms.For example,stress-induced birefringence,geometrical anisotropy of a non-circular fiber core and inner-cladding, intrinsic birefringence, fiber bending and twist.To understand the origin of birefringence, I have obtained the stress distribution pattern in Polarization Optical Microscopy.Using scanning wavelength method (Phase Retardation), I set-up the system successfully and measured the group modal birefringence of bulk:YVO4 crystal and Cr4+ :YAG double-clad crystal fiber. I also used Jones matrix, Mueller matrix,stress optics law, photoelastic
and mathematical formulas on the estimated modal birefringence to calculate the stress intensity distribution and interference light conditions and estimate the modal birefringence ,and then compared with other rare earth-doped fiber.

中文摘要 i.
英文摘要 ii.
致謝 iii.
圖目錄 vii.
表目錄 x.
第一章 序論
1.1 前言&研究動機 1.
1.2 本文架構 3.
第二章 雙折射晶體材料
2.1晶體之光學性質 5.
2.2何謂雙折射(Birefringence)及相位延遲(Retardation) 10.
2.3 應力光學定律(Stress-Optical Law) 15.
第三章 基本的偏振光學及晶體光學理論
3.1 光的偏振特性 18.
3.2光的偏振種類 20.
3.3偏振光以 Jones Matrix 表示法 23.
3.4偏振光以 Stokes Parameter表示法 27.
3.5波卡球(Poincare Sphere) 30.
3.6 極化光學元件: 以 Jones / Mueller Matrix表示 32.
第四章 具雙折射特性之雙纖衣Cr+4:YAG晶體光纖生長配製
4.1雙纖衣Cr4+:YAG晶體光纖之生長架構及方法 39.
4.2雙纖衣Cr4+:YAG 晶體光纖之成份分析 46.
第五章 雙纖衣Cr4+:YAG晶體光纖之雙折射特性量測
5.1常見量測雙折射之方法 49.
5.2 法一：偏光顯微鏡(Polarization Optical Microscopy)
5.2.1簡介 50.
5.2.2 POM觀測雙折射晶體之工作原理及結果 51.
5.2.3 利用Jones Matrix解釋干涉條紋光強度 54.
5.2.4 利用光彈(photoelasticity)解釋干涉亮暗紋產生條件 57.
5.2.5 雙纖衣Cr4+:YAG晶體光纖之應力分佈 60.
5.3 法二：Scanning Wavelength Method
5.3.1 簡介 63.
5.3.2 工作原理及公式推導 64.
5.3.3量測不同元件之干涉頻譜結果及討論
5.3.3.1 YVO4雙折射晶體 67.
5.3.3.2 Cr4+:YAG鉻晶棒 70.
5.3.3.3 雙纖衣Cr4+:YAG晶體光纖 72.
第六章 結論和未來展望
6.1 結論 82.
6.2 未來展望 83.
參考文獻 84.

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