本研究為使用全自動機械化控制一次研磨製程研製雙變曲率光纖微透鏡，用來提高單模光纖與980nm高功率幫浦雷射間之耦合效率及良率。本光纖微透鏡之製程優點為研磨步驟簡化，研磨時間減少及大幅減少光纖微透鏡中心與光纖中心之偏心量。此外，在熔燒成型透鏡過程中，僅需以微熔燒方式進行拋光，故可省去尖點去除的步驟，對於光纖微透鏡之曲率半徑可有較佳控制，因此光纖微透鏡製程之重複性及良率提高，可降低研磨成本。
本研究分別研討以光纖外徑、與以核心內徑定義光纖之幾何中心，經耦合效率量測證實，以光纖核心內徑邊緣決定偏心量，為較準確並符合理論之量測方式。
實驗研製共45根之光纖微透鏡中，在平均耦光效率大於84%之前提下，當短軸曲率半徑為2.4至2.9μm，即短軸曲率半徑之容忍範圍為0.5μm時，僅需將偏心量控制在小於0.6μm，即可達成。而當短軸曲率半徑為2.4至3.7μm，雖然短軸曲率半徑之容忍範圍較大(1.3μm)，但其偏心量，必須控制在小於0.3μm。
由於光纖微透鏡製造技術上，其偏心量控制較短軸曲率半徑控制困難。因此，在提高良率之前提下，僅需將光纖微透鏡偏心量控制小於0.6μm，並使其短軸曲率半徑控制於2.4~2.9μm時，而藉此技術研製所得之光纖微透鏡，其耦光效率均大於80%。

A study of double-variable-curvature microlenses (DVCM) for promoting coupling efficiency between the high-power 980-nm pumping laser diodes and the single-mode fibers has been proposed. In comparison with the previous works on asymmetric fiber microlenses fabricated by the multi-step processes with complicated fabrication, the advantages of the DVCM structure for achieving high coupling are a single-step fabrication, a reproducible process, and a high-yield output. In the fusing procedure, the slight arc fusion was mainly applied for fine polishing merely instead of reshaping for the reason that the fabricated double-variable-curvature fiber endface (DVCFE) was very close to the ideal shape. Hence, the fabrication time was reduced and the yield was promoted due to the withdrawn step of tip elimination.
In this study, the geometric center of the fiber was defined through, the cladding diameter and the core diameter, for comparison to measure the offset. The offset measured by the core diameter was more accurate and coincidence with the coupling efficiency in the experiment.
In the fabricated 45 DVCMs, to achieve the average coupling efficiencies higher than 84%, the offsets were ought to be controlled in merely less than 0.6μm with the curvature radii in the minor axis ranged from 2.4 to 2.9μm (with tolerance of 0.5μm). Alternatively, the offsets were ought to be controlled in less than 0.3μm though the curvature radii in the minor axis ranged from 2.4 to 3.7μm (with larger tolerance of 1.3μm). However, it was more difficult to control over the offsets than the curvature radii in the minor axis while fabricating the DVCMs.
In conclusion, to achieve higher yield, it was relatively practical to control the offsets of fiber microlenses to be less than 0.6μm with 2.4 to 2.9μm curvature radius. As a result, the coupling efficiencies were all higher than 80%.

中文摘要 I
Abstract II
誌謝 IV
目錄 V
圖目錄 VII
表目錄 X
第一章 緒論 1
1.1 前言 1
1.2 研究動機 2
1.3 文獻回顧 3
1.4 論文架構 11
1.5 參考文獻 12
第二章 理論分析 15
2.1 雷射特性簡介 15
2.2 高斯光束與模態耦合理論 16
2.2.1 高斯光束 16
2.2.2 模態匹配 18
2.3 雙變曲率光纖微透鏡 21
2.3.1 雙變曲率光纖微透鏡曲率之設計 21
2.3.2 雙變曲率光纖微透鏡研製方式原理 24
2.4 參考文獻 28
第三章 雙變曲率光纖微透鏡之製作 30
3.1 雙變曲率光纖微透鏡研磨系統 30
3.2 雙變曲率光纖微透鏡之製程 31
3.2.1 光纖特性簡介 32
3.2.2 雙變曲率光纖微透鏡端面之成型 32
3.2.3 雙變曲率光纖微透鏡之製作步驟 36
3.3 參考文獻 48
第四章 雙變曲率光纖微透鏡之量測 49
4.1 雙變曲率光纖微透鏡外型量測 49
4.1.1 以光纖微透鏡之外徑量測偏心量 53
4.1.2 以光纖微透鏡之核心內緣邊界量測偏心量 54
4.1.3 光纖微透鏡曲率半徑量測 55
4.2 雙變曲率光纖微透鏡耦光效率量測 61
4.2.1 雙變曲率光纖微透鏡容忍度之分析 62
4.2.2 偏心量與短軸曲率半徑對於耦光效率之影響 65
4.2.3 耦光效率之重複性 69
第五章 結論與未來工作 73
5.1 結論 73
5.2 未來工作 74
圖目錄
圖 1.1 EDFA在光通訊網路上之架構示意圖 2
圖 1.2 外徑漸擴式楔型光纖微透鏡 3
圖 1.3 非軸對稱雙曲線型光纖微透鏡 4
圖 1.4 雙楔型光纖微透鏡 4
圖 1.5 楔型漸變折射率式光纖微透鏡 5
圖 1.6 雙曲線型光纖微透鏡製作方式 7
圖 1.7 雙曲線型光纖微透鏡 7
圖 1.8 四角錐型光纖微透鏡 8
圖 1.9 錐式楔型光纖微透鏡 9
圖 1.10 非軸對稱橢圓錐光纖微透鏡 10
圖 2.1 980nm單模雷射光之垂直發散角與水平發散角示意圖 16
圖 2.2 高斯光束之各參數 17
圖 2.3 980nm單模雷射與單模光纖內之分佈圖 18
圖 2.4 光場模態轉換示意圖 19
圖 2.5 980nm雷射模場變化 22
圖 2.6 長軸曲率半徑與耦光效率之關係 23
圖 2.7 短軸曲率半徑與耦光效率之關係 24
圖 2.8 正壓力變化與光纖旋轉角度關係圖 26
圖 2.9 光纖端面示意圖 27
圖 3.1 雙變曲率光纖研磨機台 30
圖 3.2 雙變曲率光纖研磨機台控制參數 31
圖 3.3 雙變曲率光纖微透鏡之製作流程 31
圖 3.4 雙變曲率光纖微透鏡研磨過程示意圖 33
圖 3.5 雙變曲率光纖端面之短軸剛接觸研磨片時 34
圖 3.6 雙變曲率光纖端面之短軸最大壓力時 34
圖 3.7 雙變曲率光纖端面之長軸彎曲時 35
圖 3.8 雙變曲率光纖端面之長軸最小壓力時 35
圖 3.9 雙變曲率光纖端面研磨參數輸入 37
圖 3.10 雙變曲率光纖端面研磨進給方式 38
圖 3.11 雙變曲率光纖端面 40
圖 3.12 雙變曲率光纖端面SEM圖 42
圖 3.13 熔燒前之未磨尖雙變曲率光纖端面SEM圖 42
圖 3.14 雙變曲率光纖微透鏡 44
圖 3.15 雙變曲率光纖微透鏡SEM圖 46
圖 3.16 熔燒後之雙變曲率光纖微透鏡SEM圖 46
圖 4.1 光纖微透鏡偏心量與曲率半徑示意圖 49
圖 4.2 將光纖微透鏡照片載入ImageJ量測 50
圖 4.3 光纖微透鏡照片轉換後之灰階圖像 51
圖 4.4 光纖微透鏡灰階圖像增加對比度調整 51
圖 4.5 設定光纖微透鏡臨界亮度取得其外廓 52
圖 4.6 邊界判定後之光纖微透鏡圖片 52
圖 4.7 光纖微透鏡之偏心量量測 53
圖 4.8 光纖微透鏡核心內緣邊界之定義 54
圖 4.9 光纖微透鏡短軸之曲率半徑量測 55
圖 4.10 光纖微透鏡長軸之曲率半徑量測 56
圖 4.11 不同量測方式之偏心量與耦光效率關係圖 59
圖 4.12 0.3~0.6μm之偏心量與耦光效率關係圖 61
圖 4.13 耦光效率80%以上之短軸曲率半徑與偏心分布圖 63
圖 4.14 短軸曲率半徑與耦光效率分布 68
表目錄
表 1.1 各種適用於980nm雷射的光纖微透鏡特性比較 6
表 2.1 雷射參數以及光纖微透鏡設計之計算 21
表 3.1 康寧HI-980單模光纖參數 32
表 3.2 雙變曲率光纖端面研磨進給方式 38
表 4.1 雙變曲率光纖微透鏡尺寸與耦光效率 56
表 4.2 不同量測方式之平均耦光效率 58
表 4.3 0.3~0.6μm偏心量與平均耦光效率 60
表 4.4 較小短軸曲率半徑與較小的偏心量 64
表 4.5 理論之短軸曲率半徑與較大的偏心量 64
表 4.6 不同偏心量對於短軸曲率半徑最大容忍度 65
表 4.7 最佳短軸曲率半徑在偏心量不同之耦光效率 65
表 4.8 短軸曲率半徑離理想值較遠或偏心量較大 65
表 4.9 偏心量0~0.3μm與短軸曲率半徑2.7~2.9μm 66
表 4.10 偏心量0.5~0.8μm與短軸曲率半徑2.7~2.9μm 66
表 4.11 偏心量0~0.3μm與短軸曲率半徑3.5~3.7μm 67
表 4.12 偏心量0.5~0.8μm與短軸曲率半徑3.5~3.7μm 67
表 4.13 四組平均耦光效率比較 68
表 4.14 30次耦光效率與其參數 71

第一章
1.S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. I. Laming, “Fabrication and Characterization of Low-Loss Optical Fibers Containing Rare-Earth Ions,” Journal of Lightwave Technology, Vol.LT-4, pp. 870-876, 1986.
2.E. Desurvire, J. R. Simpson, and P. C. Becker, “High-Gain Erbium-Doped Traveling-Wave Fiber Amplifier,” Optics Letters, Vol.12, pp. 888-890, 1987.
3.W. J. Miniscalco, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” Journal of Lightwave Technology, Vol.9, pp.234-250, 1991.
4.M. Yamada, M. Shimizu, T. Takeshita, M. Okayasu, M. Horiguchi, S. Uehara, and E. Sugita, “Er3+-Doped Fiber Amplifier Pumped by 0.98μm Laser Diodes, “IEEE Photonics Technology Letters, Vol.1, pp.422-424, 1989.
5.M. Yamada, M. Shimizu, M. Okayasu, T. Takeshita, M. Horiguchi, S. Uehara, Y. Tachikawa, and E. Sugita, “Noise Characteristics of Er3+-Doped Fiber Amplifiers Pumped by 0.98 and 1.48μm Laser Diodes,” IEEE Photonics Technology Letters, Vol.2, pp.205-207, 1990.
6.R. E. Smith, C. T. Sullivan, G. A. Vawter, G. R. Hadley, J. R. Wendt, M. B. Snipes, and J. F. Klem, “Reduced Coupling Loss Using a Tapered-Rib Adiabatic-Following Fiber Coupler,” IEEE Photonics Technology Letters, Vol.8, pp.1052-1054, 1996.
7.Y. Fu, N. K. A. Bryan, and O. N. Shing “Integrated Micro-Cylindrical Lens with Laser Diode for Single-Mode Fiber Coupling,” IEEE Photonics Technology Letters, Vol.12, pp.1213-1215, 2000.
8.J. C. Livas, S. R. Chinn, E. S. Kintzer, J. N. Walpole, C. A. Wang, and L. J. Missaggia, “High-Power Erbium-Doped Fibre Amplifier with 975nm Tapered-Gain-Region Laser Pumps,” Electronics Letters, Vol.30, pp.1054-1055, 1994.
9.S. Y. Huang, C. E. Gaebe, K. A. Miller, G. T. Wiand, and T. S. Stakelon, “High Coupling Optical Design for Laser Diodes with Large Aspect Ratio,” IEEE Transactions on Advanced Packaging, Vol.23, pp.165-169, 2000.
10.V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bour, and W. C. Young, “Efficient Power Coupling from a 980-nm, Broad-Area Laser to a Single-Mode Fiber Using a Wedge-Shaped Fiber Endface,” Journal of Lightwave Technology, Vol.8, pp. 1313-1318, 1990.
11.H. M. Presby and C. A. Edwards, “Efficient Coupling of Polarization-Maintaining Fiber to Laser Diodes,” IEEE Photonics Technology Letters, Vol. 4, pp. 897-899, 1992.
12.H. M. Presby and C. R. Giles, “Asymmetric Fiber Microlenses for Efficient Coupling to Elliptical Laser Beams,” IEEE Photonics Technology Letters, Vol. 5, pp. 184-186, 1993.
13.R. A. Modavis and T. W. Webb, “Anamorphic Microlens for Laser Diode to Single-Mode Fiber Coupling,” IEEE Photonics Technology Letters, Vol.7, pp. 798-800, 1995.
14.H. Yoda and K. Shiraishi, “A New Scheme of a Lensed Fiber Employing a Wedge-Shaped Graded-Index Fiber Tip for the Coupling Between High-Power Laser Diodes and Single-Mode Fibers,” Journal of Lightwave Technology, Vol.19, pp. 1910-1917, 2001.
15.H. M. Yang, S. Y. Huang, C. W. Lee, T. S. Lay, and W. H. Cheng, “High-Coupling Tapered Hyperbolic Fiber Microlens and Taper Asymmetry Effect,” Journal of Lightwave Technology, Vol.22, pp.1395-1401, 2004.
16.S. M. Yeh, Y. K. Lu, S. Y. Huang, H. H. Lin, C. H. Hsieh, and W. H. Cheng, “A Novel Scheme of Lensed Fiber Employing a Quadrangular-Pyramid-Shaped Fiber Endface for Coupling Between High-Power Laser Diodes and Single-Mode Fibers,” Journal of Lightwave Technology, Vol.22, pp. 1374-1379, 2004.
17.S. M. Yeh, S. Y. Huang, and W. H. Cheng, “A New Scheme of Conical-Wedge-Shaped Fiber Endface for Coupling Between High-Power Laser Diodes and Single-Mode Fibers,” Journal of Lightwave Technology, Vol.23, pp. 1781-1786, 2005.
18.Y. K. Lu, Y. C. Tsai, Y. D. Liu, S. M. Yeh, C. C. Lin, and W. H. Cheng, “Asymmetric elliptic-cone-shaped microlens for efficient coupling to high-power laser diodes,” Optics Express, Vol. 15, pp.1434-1442, 2007.
19.葉斯銘，“橢圓光纖微透鏡之研究,”國立中山大學光電工程研究所，博士論文國立中山大學光電工程研究所, 2006.
第二章
1.林啟中, “非軸對稱橢圓錐光纖透鏡之研製與特性,” 碩士論文, 國立中山大學光電工程研究所, 2007.
2.葉斯銘, “橢圓光纖微透鏡之研究,” 博士論文, 國立中山大學光電工程研究所, 2006.
3.呂昱寬, “波前量測應用於雷射與光纖耦合之研究,” 博士論文, 國立中山大學光電工程研究所, 2008.
4.B. E. A. Saleh, M. C. Teich, “Fundamentals of Photonics,” John Wiley & Sons, pp. 83, 1991.
5.V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bour, and W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” Journal of Lightwave Technology, vol.8, pp. 1313-1318, 1990.
6.C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” Journal of Lightwave Technology, Vol. 11, pp. 252 -257, 1993.
7.劉育達, “雙變曲率光纖微透鏡之研究,” 博士論文, 國立中山大學光電工程研究所, 2011.
8.Y. D. Liu, Y. C. Tsai, L. J. Wang, Y. K. Lu, M. C. Hsieh, S. M. Yeh, and W. H. Cheng, “New scheme of double-variable-curvature microlens for efficient coupling high-power lasers to single-mode fibers,” Journal of Lightwave Technology, Vol. 29, pp898-904, 2011.
9.F. W. Preston, “The theory and design of plate glass polishing machines,” Journal of the Society of Glass Technology, Vol. 11, pp. 214-256, 1927.
10.劉育達, “非對稱型光纖端面研磨機構設計之研究,” 碩士論文, 中山大學機械與機電工程學系, 2006.
11.Y. K. Lu, Y. C. Tsai, Y. D. Liu, S. M. Yeh, C. C. Lin, and W. H. Cheng, “Asymmetric elliptic-cone-shaped microlens for efficient coupling to high-power laser diodes,” Optics Express, Vol. 15, pp.1434-1442, 2007.
12.S. Teich, Fundamentals of Photonics, Canada, Wiley Interscience, Ch. 1-2, 1991.
第三章
1.謝銘駿, “雙變曲率光纖端面研磨機構設計與製造之研究,” 碩士論文, 國立中山大學機械與機電工程學系, 2008.
2.Axcel Photonics Data Sheets, 45 Bartlett St., Marborough, MA 01752, 2009.
3.Y. D. Liu, Y. C. Tsai, L. J. Wang, Y. K. Lu, M. C. Hsieh, S. M. Yeh, and W. H. Cheng, “New scheme of double-variable-curvature microlens for efficient coupling high-power lasers to single-mode fibers,” Journal of Lightwave Technology, Vol. 29, pp898-904, 2011.
4.劉育達, “雙變曲率光纖微透鏡之研究,” 博士論文, 國立中山大學光電工程研究所, 2011.