本論文係研究雙變曲率光纖微透鏡與980nm高功率幫浦雷射間耦光機制，藉由單模光纖干涉儀進行光纖透鏡之相位分佈量測及波前傳播量測，並量測其光纖透鏡的光場，與雷射光源的光場變化相比較，從波前與光場這兩方面探討所設計的光纖透鏡是否與980 nm高功率幫浦雷射的近場傳播波前相匹配。
相位分佈量測是利用單模光纖干涉儀之參考光纖與量測光纖產生的干涉條紋來分析，藉由量測不同平面的相位分佈情形，觀察光經過光纖透鏡後在空氣中的光波前傳播情形，從量測結果觀察到經過光纖透鏡後，光傳播方式為曲面波，在距離透鏡頂端10 μm處有似焦平面的狀況，高斯公式擬合曲線經過此範圍產生相位反轉的現象，從原本開口向上的曲線，曲率半徑由大變小，經此平面後，其曲線變為開口向下，曲率半徑由小開始漸漸變大，形成光波先聚焦後再發散的現象。
在光場量測上，改變不同架構去量測光纖透鏡光場圖案變化，藉由CCD量測，可以在遠場量測到其光纖透鏡呈垂直向橢圓的光場，隨著距離拉遠其橢圓形的光場也漸漸變大。從遠場量測到的光束寬度數據，對近場做光束寬度大小推導，可以分析到在z=10.5 μm時，光纖透鏡短軸與長軸在光束寬度大小相同，這時光場圖案呈現圓形。因此，其光纖透鏡傳播過程從一水平向的橢圓場形，在光束寬度相同時呈現圓形場形，隨傳播距離增加形成垂直向橢圓場型向遠距離傳播。
　　從波前和光場兩部分來探討雷射與光纖透鏡間的耦合效果，可發現為光纖透鏡與980nm幫浦雷射波前傳播同為曲面波，光場的變化於z=10μm附近產生，其趨勢也互相吻合為圓形場型，兩者模態匹配，因此光纖透鏡在與雷射光源耦合上比平端光纖的耦合效果好而達到比較高的耦光效率。此研究可提供確實的方法去量測光纖微透鏡的近場波前特性。
關鍵詞：980nm幫浦雷射、光纖近場、光纖微透鏡、單模光纖干涉儀、光場

In order to understand the coupling mechanism between hyperboloid microlensed fiber (HMF) and 980nm pumping laser, the phase distribution and intensity distribution of propagating beam from HMF were measured. A single mode fiber interferometer was employed to measure the phase distribution of the HMF and a CCD with photodetector was employed to measure the intensity distribution of HMF along the Z-axis. A good understanding of the near-field phase and intensity distributions of laser and fiber are essential for micro-optic designs with better mode matching to achieve efficient coupling between lasers to fibers.
The wavefront distribution was measured by analyzing interference fringes generated from the reference beam and the measured beam. According to the measured results, the wavefront of the HMF is curved and there was a focal particular plane at z = 10μm. The wavefront inverted as the wavefront propagated through the particular plane. For the intensity distribution of propagating beam through HMF, a CCD with photodetector was employed to investigate the variation of the beam spot profile. The mode field of HMF was a longitudinal ellipse in the far field. As we calculated intensity distribution of z < 50μm, it could be found the mode field distribution at z = 10-μm had a circular shape with a radius of 2.2 μm. These results indicated the consistency between the measured wavefront radius of curvatures and intensity distribution of lensed fiber at 10 μm along the z axis.
The results show that the mode matching of wavefront and spot size for laser diode and lensed fiber in the near-field region. This study may provide an essential method for the wavefront distributions of hyperboloid microlensed fiber measurement.

Keywords: 980 nm pumping laser, hyperboloid microlensed fiber, interferometer, mode field

中文摘要 i
Abstract ii
誌謝 iv
目錄 v
圖目錄 vi
表目錄 xi
第一章 緒論 1
1.1　研究背景 1
1.2　研究動機 2
1.3　文獻回顧 3
1.3.1 近場量測 3
1.3.2 光纖微透鏡 5
1.4　論文架構 6
第二章 理論基礎 7
2.1　雷射原理 7
2.2　單模光纖干涉儀之原理 9
2.3　傅立葉分析 10
2.4　高斯光束傳播與模態耦合理論 12
2.4.1 高斯光束 12
2.4.2 模態耦合 16
2.5　雙曲線光纖微透鏡 18
2.5.1 雙曲線光纖微透鏡曲率設計 18
2.5.2 雙曲線光纖微透鏡研製原理 22
第三章 雷射近場實驗架構 25
3.1　單模光纖干涉儀架構 25
3.2　光纖近場量測 37
3.3　光場量測架構 41
第四章 近場相位分佈量測結果及分析 45
4.1　第一型量測架構量測 45
4.1.1 平端光纖相位分佈量測 46
4.1.2 光纖透鏡相位分佈量測 47
4.2　第二型量測架構量測 50
4.2.1 平端光纖相位分佈量測 50
4.2.2 光纖透鏡相位分佈量測 53
4.3　光場量測結果 56
4.3.1 第一型光場量測架構結果 56
4.3.2 第二型光場量測架構結果 58
4.3.3 第三型光場量測架構結果 60
4.3.4 光纖透鏡光束寬度推導 71
第五章 結論與未來工作 75
參考文獻 77

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