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研究生:呂昱寬
研究生(外文):Yu-Kuan Lu
論文名稱:波前量測應用於雷射與光纖耦合之研究
論文名稱(外文):A Study of Wavefront Measurement Applied to the Coupling between Lasers and Fibers
指導教授:鄭木海
指導教授(外文):Wood-Hi Cheng
學位類別:博士
校院名稱:國立中山大學
系所名稱:光電工程研究所
學門:工程學門
學類:材料工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:131
中文關鍵詞:耦合波前雷射光纖透鏡
外文關鍵詞:Hartmannwavefrontphase retrieval
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本論文係提出大發散角雷射波前的量測技術,此波前量測技術是改良Hartmann和Shack-Hartmann波前量測儀所建構出來的,相對於Hartmann和Shack-Hartmann波前量測儀僅能量小角度波前,本研究所提波前量測技術具有180度的動態量測範圍且量測精密度可達 0.02度,由於儀器本身是利用孔徑對待測波前進行取樣,使得所量測到的波前標準差受限於繞射極限下(~λ/d)。
透過此波前量測技術,將所測得的相位分佈以及能量分佈透過光學傅立葉轉換計算,可建構出雷射光束在任何一個位置的電場分佈,包括近場以及遠場,而這些電場資料將有助於雷射與光纖耦合的分析及研究。實驗證實所建構出的波前量測儀可以提供一個可靠的波前量測方式,不過在進行近場電場的計算時,因本身儀器固有的量測誤差,使得近場的計算值與實驗值的誤差高達150%。
因此我們改以利用顯微物鏡、CCD攝影機直接量測雷射近場的能量分佈,在距離雷射出光口8μm的位置,光模場為圓對稱分佈、模場直徑為4.75μm,透過相位補償演算法計算出近場垂直軸的波前曲率半徑為8μm、水平軸的波前曲率半徑為41μm,利用幾何光學可計算出對於模場直徑4.75μm的光纖,其最佳橢圓光纖透鏡的曲率半徑垂直軸為4μm、水平軸為20.5μm,當知道最佳透鏡曲率半徑後即可利用研磨及熔燒方式製作出高耦合效率的光纖透鏡。
We have proposed and demonstrated a technique for the measurement of the wavefront of a diode laser beam with a large dynamic range. Our technique is a modified version of Hartmann and Shack-Hartmann wavefront sensor. The modified version is capable of providing a large dynamic range (180 degrees). The wavefront measurement exhibits a precision of ( 0.02 degrees), subject to a standard deviation governed by the diffraction limit (~λ/d).
Using the physical measurement of the wavefront, we are able to reconstruct the electric fields of a diode laser beam at any location, including the far-field and near-field. The reconstructed electric fields were computed form the data of the intensity and the phase distribution by means of Fourier transform. The information about the electric field can be very useful in the design of microlens for the efficient coupling of light source into optical components. The results indicate that the wavefront sensor with large dynamic range can provide a reliable method for measuring the wavefront distributions of diode lasers with large divergence angles. However, the numerical near-field intensity is 150% deviated from the measured near-field intensity because of the inherent inaccuracy in the wavefront measurement.
In this study, we have measured the near field intensity distribution directly with an objective and a CCD camera. We found that the distribution of the mode field was symmetric at a distance of 8μm from a diode laser and the mode field diameter was 4.75μm. Using the phase retrieval algorithms, the radii of the near-field wavefront in the vertical axis and the horizontal axis were 8μm and 41μm, respectively. Through the geometrical optics, the optimum curvatures of elliptic-cone-shaped lensed fiber for efficient coupling in the vertical axis and the horizontal axis were 4μm and 20.5μm individually. Once we know the optimum curvatures of elliptic-cone- shaped lensed fiber, we can fabricate it using grinding and fusing.
目錄
中文摘要 ------------------------------------------------------------------------Ⅰ
英文摘要 ----------------------------------------------------------------------- Ⅱ
誌謝 ----------------------------------------------------------------------------- Ⅲ
目錄 ----------------------------------------------------------------------------- Ⅳ
圖目錄 -------------------------------------------------------------------------- Ⅷ
表目錄 ----------------------------------------------------------------------- ⅩⅢ
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 高斯光束 ------------------------------------------------------- 5
1.3.2 繞射理論 ------------------------------------------------------ 11
1.4 論文架構 -------------------------------------------------------------- 13
1.5 參考文獻 -------------------------------------------------------------- 14

第二章 波前量測技術 ------------------------------------------------------- 17
2.1波前剪切干涉術 ------------------------------------------------------ 17
2.1.2 側向剪切干涉術 --------------------------------------------- 18
2.1.2 側向剪切干涉的操作原理 --------------------------------- 19
2.1.3 側向剪切干涉波前建構 ------------------------------------ 21
2.1.4 大發散角雷射波前的量測 --------------------------------- 22
2.2 Hartmann波前量測系統 -------------------------------------------- 24
2.2.1 Hartmann波前量測系統介紹 ------------------------------- 24
2.2.2 波前量測裝置及量測原理 --------------------------------- 25
2.2.3 波前斜率 ------------------------------------------------------ 28
2.2.4 波前相位還原 ------------------------------------------------ 29
2.2.5 總結 ------------------------------------------------------------ 30
2.3 參考文獻 -------------------------------------------------------------- 31

第三章 具大動態量測範圍波前量測系統 ------------------------------ 32
3.1具大動態範圍之波前量測儀 --------------------------------------- 32
3.2 波前量測的量測操作 ----------------------------------------------- 35
3.3建構空間中雷射光束場型分佈 ------------------------------------ 40
3.4 雷射波前行進角度的量測 ----------------------------------------- 42
3.5 雷射光束相位分佈的建構 ----------------------------------------- 44
3.6 計算空間中光束光場 ----------------------------------------------- 47
3.7 近場光束還原 -------------------------------------------------------- 51
3.8 誤差可能原因 -------------------------------------------------------- 52
3.9 參考文獻 -------------------------------------------------------------- 56

第四章 近場能量分佈量測及波前建構術 ------------------------------ 57
4.1 相位補償演算法 ----------------------------------------------------- 57
4.2 雷射近場能量量測 -------------------------------------------------- 60
4.3 雷射近場相位的重建 ----------------------------------------------- 65
4.4 模態耦合與光纖透鏡 ----------------------------------------------- 69
4.5 總結 -------------------------------------------------------------------- 74
4.6 參考文獻 -------------------------------------------------------------- 74

第五章 橢圓光纖透鏡 ------------------------------------------------------ 76
5.1橢圓光纖透鏡的設計 ----------------------------------------------- 76
5.1.1橢圓光纖透鏡研製方式 ------------------------------------ 76
5.1.2 橢圓錐形光纖成型原理 ----------------------------------- 77
5.2 光纖研磨系統 ------------------------------------------------------- 82
5.2.1光纖研磨機台簡介 ------------------------------------------ 82
5.2.2週期性變動扭矩系統 --------------------------------------- 84
5.3 橢圓光纖透鏡製程 ------------------------------------------------- 88
5.3.1光纖簡介 ------------------------------------------------------ 88
5.3.2橢圓光纖透鏡之製程 --------------------------------------- 88
5.3.3橢圓光纖透鏡之研製 --------------------------------------- 91
5.4 橢圓光纖透鏡兩軸曲率半徑之控制 ---------------------------- 96
5.5 橢圓光纖透鏡研製結果 -------------------------------------------- 96
5.6 橢圓錐光纖透鏡外型量測 --------------------------------------- 101
5.7 耦合效率實驗與模擬的分析 ------------------------------------ 106
5.8 參考文獻 ------------------------------------------------------------ 109

第六章 結果與討論 ------------------------------------------------------ 110
第一章
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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. 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 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. R. A. Modavis and T. W. Webb, “Anamorphic microlens for laser diode to single-mode fiber coupling” IEEE Photonics Technology Letter, Vol. 7, pp. 798-800 (1995)
14. 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)
15. 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)
16. 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)
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18. 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)
19. 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).
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24. R. W. H. Engelmann, D. Kerps, G. Hom, D.E. Ackley, “A gain-guided- stripe diode laser with a single longitudinal mode, high kink power, and minimal beam distortion,” Electron Devices Meeting, 1982 International, Vol. 28, pp. 350-353 (1982)
25. F. H. Peters and D. T. Cassidy, “Model of the spectral output of gain-guided and index-guided semiconductor diode lasers,” J. Opt. Soc. Am. B, Vol. 8, pp. 99-105 (1991)
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27. H. Kogelink, “Coupling and conversion coefficients for optical modes in quasi-optics,” in Microwave Research Institute Symposia Series , New York Polytechnic Press, Vol. 14, pp. 333-347 (1964)
28. J. W. Goodman, “Introduction to Fourier optics,” McGraw-Hill, Ch.4 (1968)
29. “Real Beam Propagation,” http://www.mellesgriot.com/.

第二章
1. I. Ghozeil, "Optical shop testing," D.Malacara, ed., John Wiley & Sons, Ch. 4 (1978)
2. I. Ghozeil, "Optical Shop Testing," D.Malacara, ed., John Wiley & Sons, Ch. 10 (1978)
3. A. F. Brooks, T. L. Kelly, Peter J. Veitch, and Jesper Munch, “Ultra-sensitive wavefront measurement using a Hartmann sensor,” Optics Express, Vol. 15, pp. 10370-10375 (2007)
4. M. Rocktaschel and H. J. Tiziani,”Limitations of the Shack–Hartmann sensor for testing optical aspherics,” Optics & Laser Technology, Vol. 34, pp. 631-637 (2002)
5. I. Ghozeil, "Optical Shop Testing," D.Malacara, ed., John Wiley & Sons, Ch. 3 (1978)
6. P. Hariharan, B. F. Oreb and T. Eiju, “Digital phase shifting interferometry: a simple error compensating calculation algorithm,” Applied Optics, Vol. 26, pp. 2504-2505 (1987)
7. J. Schwiegerling, D. R. Neal, “Historical Development of the Shack-Hartmann Wavefront Sensor,” www.wavefrontsciences.com.

第三章
1. A. F. Brooks, T. L. Kelly, P. J. Veitch, and J. Munch, “Ultra-sensitive wavefront measurement using a Hartmann sensor,” Optics Express, Vol. 15, pp. 10370-10375 (2007)
2. D. W. de Lima Monteiro, T. Nirmaier, G. V. Vdovin, and A. J. P. Theuwissen, “Fast Shack-Hartmann wavefront sensors manufactured in standard CMOS technology,” IEEE Sensors Journal, Vol. 5, pp. 976-982 (2005)
3. S. K. Park, S. H. Baik, C. J. Kim, and S. W. Rab, “A study on a fast measuring technique of wavefront using a Shack-Hartmann sensor,” Optics & Laser Technology, Vol. 34, pp. 687-694 (2002)
4. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am., 70, pp. 998-1066 (1980)
5. B. E. A. Saleh and M. C. Teich, “Fundamentals of photonics,” New York, NY, John Wiley and Sons, Inc., Ch.2 (1991)
6. Copyright © 1989-2007. INRIA ENPC." and "Scilab is a trademark of INRIA

第四章
1. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, pp. 237-246 (1972)
2. J. R. Fienup, "Phase retrieval algorithms: a comparison," Applied Optics, vol. 21, pp. 2758-2769 (1982)
3. S. Matsuoka and K. Yamakawa, “Wavefront reconstruction from intensity measurements using fresnell phase retrieval method,” Japanese Journal of Applied Physics, vol.38 , pp. 1183-1185 (1999)
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5. W. D. Herzog, M. S. U Unlu, B. B. Goldberg, and G. H. Rhodes, “Beam divergence and waist measurements of laser diodes by near-field scanning optical microscopy” Applied Physics Letter, Vol. 70, pp. 688-690 (1997)
6. B. E. A. Saleh, M. C. Teich, “Fundamentals of Photonics,” John Wiley & Sons, pp. 83 (1991)
7. 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)
8. 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)
9. 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)

第五章
1. 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)
2. 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)
3. Y. C. Tsai, Y. D. Liu, C. L. Cao, Y. K. Lu and W. H. Cheng, “A new scheme of fiber end-face fabrication employing a variable torque technique,” Journal of Micromechanics and Microengineering, Vol. 18, 055003 (2008).
4. User Guide for ULTRAPOL 1200 Series Polishing Bases.
5. W. S. Rasband, ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA, http://rsb.info.nih.gov/ij/, 1997-2007.
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