雷射模組經常使用於光纖通訊及感測系統上，一般雷射模組包括半導體雷射光源與單模光纖，其中雷射與光纖耦光會有模態不匹配情形，因為雷射光場為橢圓型而光纖光場為圓型，及雷射波前為曲面而光纖波前為平面，導致二者之間耦合效率不佳。因此在單模光纖端面研磨為非對稱，可使光纖端面成為非對稱透鏡光纖，因此光纖光場大小及相位與雷射匹配，提升雷射與光纖耦光效率。
本論文提出雷射與光纖模態匹配及極化保持光纖研製之研究，其中雷射與光纖模態匹配研究包括單模態光纖光場大小及相位之量測與雷射匹配，而極化保持光纖之研究包括極化保持光纖透鏡研製及耦光效率與消光比之量測。
第一部分研究為平端光纖和光纖透鏡的波前相位和光場光束的量測與匹配。光纖透鏡在z軸小於5μm時具有水平橢圓形的光場，與980nm雷射曲面相同。而在近場的相位測量，光纖透鏡波前相位在空間中分佈也與980nm雷射互相匹配。因此在這光場形狀與波前相位匹配，才能夠使光纖透鏡與雷射之間的高耦合效率到80%以上。相對的平端光纖，波前相位為平面波，且光場形狀在空間中的分佈狀況為圓形也與雷射橢圓狀不匹配，導致耦合效率低於40％。
第二部分研究為利用第一部分研究結果研製光纖方向性透鏡(OHM)，使保偏光纖與雷射具有高耦合的光學特性。利用自動研磨和CCD準確定位，使OHM短軸與極化保持光纖的快軸在同一水平方向上，在極化保持光纖透鏡研磨後，經過光纖熔接機熔燒，使OHM短軸曲率半徑在4.23μm，偏移小於0.7μm, 機器研磨公差為± 1度。而在極化保持光纖透鏡與980nm雷射之間傳輸的保偏特性量測，平均消光比為31.7 dB，並同時具有高平均耦合效率83.4％。機器研磨公差為± 1度，於極化保持光纖量測誤差容忍度± 2度內，消光比可達30 dB，且耦合效率同時達到80%以上，表示OHM可視為被動對準雷射。因此極化保持光纖微透鏡可應用於高精準度的光纖陀螺儀模組及許多和低成本的光學通訊的傳輸上之模組。

A laser module, which consists of laser diode and single-mode fiber, is often used in optical-fiber communications and sensor systems. Generally there is mode mismatch between laser and optical fibers, because the mode field of laser source is elliptical while that of fiber is circle. Also, the wavefront of laser is a curve wave, while the wavefront of fiber is plane wave. This mode mismatch causes a low coupling efficiency between two components. By grinding the endface of fiber to make asymmetric endface and then fusing to form asymmetric microlens which enables to spot size and wavefront match to laser diode. Therefore, the coupling efficiency of laser to fiber will significantly improve due to mode match between laser and fiber.
There are two research parts in this study. The first study is the mode matching between laser and fiber. The second study is the microlens fabrication of polarization maintaining fiber (PMF). The mode matching study includes the spot size and wavefront measurements of the SMF. The microlens fabrication of PMF includes the grinding the endface of PMF and performance measurements, such as coupling efficiency and polarization extinction ratio (PER).
In the spot-size measurement of lensed fibers the results showed that lensed fiber exhibited a horizontally elliptical field when z < 5 μm, which was spot size matched to as 980 nm laser diode. However, the spot-size of the cleaved showed a circle field. For the wavefront measurement of lensed fibers, the distribution of wavefront of lensed exhibited a curve wave which was matched to 980 nm laser diode of a Gussian beam. However, the wavefront of the cleaved showed a plane wave. Therefore, the mode match of spot-size and wavefront between laser and lensed fiber resulting in high coupling efficiency of 80 % between lensed fiber and laser. On the contrary, the mode mismatching between cleaved fiber and laser resulting a low coupling efficiency of 40 %.
In the second parts of study, we demonstrated an oriented-hyperboloid microlens (OHM) for high coupling efficiency and high polarized extinction ratio (PER) form high-power 980 nm pump laser to polarization maintaining fiber (PMF). Using an automatic grinding machine and a charge-coupled-device (CCD) to precisely control and attain the required minor radius of curvature 4.23 μm, offset within 0.7μm, and axis orientation accuracy of ±1o, the OHM exhibited a high-average coupling efficiency of 83.4 % and a high-average PER of 31.7-dB. For a 30-dB PER and 80% coupling efficiency, the angular misalignment tolerance of the OHM was measured to be ±2o. This indicates that the OHM endface of the fast axis can be visually observed and then passively aligned to the axis of the laser polarization direction. Therefore, the proposed OHM is beneficial for the fabrications of laser/PMF modules where mode polarization and high coupling are required for use in high-precision fiber optic gyroscopes and many high-performance and low-cost lightwave interconnections.

中文摘要 ------------------------------------------------------------------------------- ⅰ
英文摘要 -------------------------------------------------------------------------- ⅱ
目錄 ------------------------------------------------------------------------------- ⅳ
圖目錄 -------------------------------------------------------------------------- ⅴ
表目錄 --------------------------------------------------------------------------- ⅵ
第一章 緒論 ------------------------------------------------------------------------------------ 1
1.1 前言---------------------------------------------------------------------------------------- 1
1.2 研究動機 -------------------------------------------------------------------------------- 3
1.3 文獻回顧 -------------------------------------------------------------------------------- 4
1.3.1 近場量測原理---------------------------------------------------------------------- 4
1.3.2 光纖微透鏡製作理---------------------------------------------------------------- 5
1.4 論文架構 -------------------------------------------------------------------------------10
第二章 理論基礎 ---------------------------------------------------------------------------- 11
2.1 雷射原理 -------------------------------------------------------------------------------11
2.2 單模光纖干涉儀之原理---------------------------------------------------------------13
2.3 傅立葉分析------------------------------------------------------------------------------14
2.4 高斯光束-------------------------------------------------------------------------------- 16
2.5 模態匹配-------------------------------------------------------------------------------- 20
2.6 雙曲線光纖微透鏡曲率設計-------------------------------------------------------- 23
第三章 光纖微透鏡近場光場與波前相位量測------------------------------------------ 26
3.1 光纖透鏡近場光場量測---------------------------------------------------------------30
3.1.1 近場光場量測架構--------------------------------------------------------------- 30
3.1.2 光纖透鏡近場光場量測--------------------------------------------------------- 33
3.1.3 平端光纖近場光場量測--------------------------------------------------------- 40
3.2 光纖透鏡近場相位量測---------------------------------------------------------------47
3.2.1 近場相位量測架構--------------------------------------------------------------- 47
3.2.2 光纖透鏡近場相位量測--------------------------------------------------------- 52
3.2.3 平端光纖近場相位量測--------------------------------------------------------- 55
3.3 結論與討論------------------------------------------------------------------------------58
第四章 極化保持光纖透鏡研製及分析--------------------------------------------------- 60
4.1 極化保持光纖特性---------------------------------------------------------------------60
4.2 雷射極化量測---------------------------------------------------------------------------64
4.3 極化保持光纖定位研磨---------------------------------------------------------------68
4.4 極化保持光纖透鏡量測---------------------------------------------------------------73
4.5.1光纖微透鏡偏心量測------------------------------------------------------------- 79
4.5.2光纖微透鏡曲率半徑量測------------------------------------------------------- 80
4.6 極化保持光纖透鏡---------------------------------------------------------------------83
4.7 極化保持光纖透鏡量測---------------------------------------------------------------85
4.8 極化保持光纖透鏡研磨誤差---------------------------------------------------------87
4.9極化保持光纖透鏡被動對準量測----------------------------------------------------90
4.10.1極化保持光纖透鏡角度偏差耦合效率量測-------------------------------- 93
4.10.2極化保持光纖透鏡角度偏差消光比量測----------------------------------- 94
第五章 討論與未來展望--------------------------------------------------------------------- 95
5.1 結論---------------------------------------------------------------------------------------95
5.2 未來研究方向---------------------------------------------------------------------------98
5.2.1極化保持光纖透鏡製作---------------------------------------------------------- 98
5.2.2極化保持光纖透鏡封裝測------------------------------------------------------- 99
參考文獻-----------------------------------------------------------------------------------------101

[1] 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.
[2] 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.
[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 0.98 µm 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 1.48 µm Laser Diodes,” IEEE Photonics Technology Letters, vol. 2, pp. 205-207, 1990.
[6] 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.
[7] 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.
[8] 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.
[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. Yang, “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. R. Giles, “Asymmetric Fiber Microlenses for Efficient　Coupling to Elliptical Laser Beams,” IEEE Photonics Technology Letter, vol. 5, pp. 184-186, 1993.
[12] C. A. Edwards, H. M. Presby, and C. Dragone, “Ideal Microlens for Laser to Fiber Coupling,” Journal of Lightwave Technology, vol. 11, pp. 252-257, 1993.
[13] H. Yoda and K. Shiraishi, “A New Scheme of Lensed Fiber Employing A Wedge-Shaped Graded-Index Fiber Tip for the Coupling Between High-Power Laser Diodes and Single-Mode Fiber,” Journal of Lightwave Technology, vol. 19, pp. 1910-1917, 2001.
[14] H. Yoda and K. Shiraishi, “Cascaded GI-fiber Chips with A Wedge- Shaped End for the Coupling between An SMF and A High-Power LD with Large Astigmatism,” Journal of Lightwave Technology, vol. 20, pp. 1545-1548, 2002.
[15] Y. Irie, J. Miyokawa, A. Mugino, and T. Shimizu, “Over 200 mW 980 nm Pump Laser Diode Module Using Optimized High-Coupling Lensed Fiber,” in Tech. Dig. OFC/IOOC'99, San Diego, CA, pp. 238-240, 1999.
[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 Wood-Hi 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. 14, pp. 1434-1442, 2006.
[19] 林啟中, “非軸對稱橢圓錐光纖透鏡之研製與特性,” 碩士論文, 2007.
[20] 林詠弦, “雙曲線光纖微透鏡曲率半徑熔燒製程及提高耦光效率之研究,” 碩士論文, 2011.
[21] W. D. Herzog, M. S. Unlu, B. B. Goldberg, G. H. Rhodes, and C. Harder, “Beam Divergence and Waist Measurements of Laser Diodes by Near-Field Scanning Optical Microscopy,” Appl. Phys. Lett., vol. 70, pp. 688-690, February 1997.
[22] 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.
[23] 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.
[24] 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.
[25] 盧廷昌、王興宗, “半導體雷射導論,” 初版, 台灣：五南, 第四章, 2010.
[26] J. W. Goodman, “Introduction to Fourier Optics,” McGraw-Hill Inc., 1995.
[27] A. W. Lohmann, “Wavefront Reconstruction for Incoherent Object,” J. Opt. Soc. Am., 55:1555, 1965.
[28] J. S. Walker, “Fast Fourier transforms,” 2nd ed., Boca Raton, Fla. : CRC Press, 1996.
[29] B. E. A. Saleh and M. C. Teich, “Fundamentals of Photonics,” New York, NY, John Wiley and Sons, pp. 81-83, 1991.
[30] 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.
[31] 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.
[32] C. A. Edwards, H. M. Presby, and C. Dragone, “Ideal Microlenses for Laser to Fiber Coupling,” Journal of Lightwave Technology, vol. 11, pp. 252 -257, 1993.
[33] S. Teich, Fundamentals of Photonics, Canada, Wiley Interscience, Ch. 1-2, 1991.
[34] 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.
[35] 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.
[36] Y. K. Lu, P. H. Yeh, and W. H. Cheng, “Direct near-field phase measurement of laser diodes employing a single-mode fiber interferometer”, Opt. Lett., 35, pp. 3643-3645, 2010.
[37] J. N. Katsunari Okamoto, and Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications”, Journal of Lightwave Technology, vol. 4, pp. 1071-1089, 1986.
[38] 許正安,“熊貓光纖端面研磨機設計與製造,”碩士論文,正修科技大學機電工程研究所, 2014.
[39] Y.C. Hsu, Y.C. Tsai, J.H. Kuang, M.T. Sheen, A.D. Lin, P.H. Hsu, and W.H. Cheng, "A Notch-Saddle-Compensation Technique in Butterfly-Type Laser Module Packages," J. Lightwave Technol. vol.25, pp.1594 - 1601, 2007.
[40] Y.D. Liu, M.T. Sheen, Y.C. Hsu, H.K. Hsu, Y.C. Tsai, and W.H. Cheng, “Online postweld shift measurement of butterfly-type laser module employing high-resolution capacitance displacement measurement system,” IEEE Tran. Electron. Pack. Manuf. vol 33, pp. 91-97, 2010.