由於光通訊的快速成長與需求，傳輸資訊量每年皆以倍數成長，加上消除OH－離子光纖的技術突破，使得低損耗波段可傳輸的波長擴展為1.3 μm~1.6 μm。伴隨著光纖通訊的頻寬需求急速增加，亦發展出分波多工技術，但仍要有光放大器加以搭配，才能充分發揮這項新技術。Cr4+:YAG晶體，其自發輻射光譜涵蓋了1.3 μm ~1.6 μm的範圍，且其吸收頻譜在0.9 μm~1.2 μm波長範圍內，與目前摻鉺光纖放大器0.98 μm激發光源相容，故非常適合於晶體光纖放大器之應用。

本論文以雷射加熱基座生長法製備的超寬頻雙纖衣Cr4+:YAG晶體光纖放大器的研發進一步分析與討論。目前以端面對接耦合方式在SMF28-Cr4+:YAG DCF-SMF28 (Cr4+:YAG DCF即雙纖衣Cr4+:YAG晶體光纖)架構，雙向各輸入1.3 W激發光功率時，可產生增益4.0 dB，系統淨損耗最低為0.7 dB。本論文亦對雙纖衣Cr4+:YAG晶體光纖做完整的數值模擬分析，並與實驗結果比對，進而找出實驗上的改善方向。此外，本論文也對Cr4+:YAG晶體光纖作系統量測，得知此系統的誤碼率。藉數值模擬分析可知泵浦光的激發態吸收是目前雙纖衣Cr4+:YAG晶體光纖放大器增益不夠高的主因。

未來我們將試著藉由cladding pump取代core pump架構，用波長925 nm取代波長1064 nm作為泵浦光源、用CuO側鍍和Cr2O3側鍍來減少內纖衣的吸收和增加纖心的吸收；以及使用Yb2O3側鍍在Cr4+:YAG晶體光纖，使Yb:YAG的螢光沿著inner cladding傳播，並泵浦core裡的Cr4+:YAG。同時我們將嘗試生長纖心直徑更小的光纖並拉長其長度，以改善元件的增益，並以雙向泵浦及兩次訊號傳輸來繼續提升系統增益。

The maximum capacity of an optical fiber transmission system is more than doubled every year to cater the fast-growing communication need. The technology breakthrough in dry fiber fabrication opens the possibility for fiber bandwidth from 1.3 μm to 1.6 μm. The fast increasing demand of communication capacity results in the emergence of wavelength division multiplexing (WDM) technology, which results in the need for ultra-broadband optical amplifier. Cr4+:YAG has a strong spontaneous emission spectrum covers from 1.3 μm to 1.6 μm. In addition, its absorption spectrum is between 0.9 μm to 1.2 μm, which matches with the pumping source in current erbium doped optical amplifier. Such fiber is, therefore, eminently suitable for optical amplifier applications.

In this thesis, we introduce the development of ultra-broadband optical amplifier using the double-clad Cr4+:YAG crystal fiber, which is grown by the laser heated pedestal growth (LHPG) technique. With the butt-coupling method, a gross gain of 4.0 dB is demonstrated at 1.3W bi-directional pump power at present. Moreover, theoretical models and numerical simulations have been developed to find out a better method for experiments. Numerical simulation indicates that the pump ESA will seriously impede the development of optical amplifier using the double-clad Cr4+:YAG crystal fiber.

In the future, in order to reduce pump ESA we attempt to use clad-pump scheme instead of core-pump scheme, to choose pumping wavelength at 925 nm instead of 1064 nm and to use side deposition of Yb2O3. At the same time, we will also try to grow crystal fiber of smaller core diameter and to extend its length to improve gain performance.

中文摘要 i
英文摘要 ii
致謝 iii
目錄 iv
圖目錄 vi
表目錄 x
第一章 緒論 1
第二章 雙纖衣Cr4+:YAG晶體光纖的特性 9
2.1 Cr4+:YAG晶體之結構與特性 9
2.2 Cr4+:YAG的能階模型與吸收及放射頻譜 15
2.3雙纖衣Cr4+:YAG晶體光纖之生長方法 18
2.4雙纖衣Cr4+:YAG晶體光纖之成份分析 26
2.5雙纖衣Cr4+:YAG晶體光纖中之信號傳輸 29
第三章 理論分析與數值模擬 39
3.1 理論模型 39
3.1.1速率方程式 39
3.1.2泵浦光源、訊號光源與ASE之光強度變化 41
3.2 數值模擬分析 42
第四章 雙纖衣Cr4+:YAG晶體光纖放大器樣品製備 51
4.1雙纖衣Cr4+:YAG晶體光纖之散熱封裝 51
4.2元件之研磨與拋光 53
第五章 雙纖衣Cr4+:YAG晶體光纖放大器之特性量測 59
5.1雙纖衣Cr4+:YAG晶體光纖之耦光 59
5.2插入損耗量測 62
5.2.1輸入端插入損耗 63
5.2.2雙邊插入損耗 64
5.3 增益實驗量測架構與結果 68
5.3.1 系統增益 68
5.3.2 雙向泵浦雙纖衣Cr4+:YAG晶體光纖 70
5.3.3 雙向泵浦且雙次傳輸量測 74
5.4 纖衣泵浦實驗 78
5.4.1 纖衣泵浦實驗架構 78
5.4.2 銅離子擴散實驗及量測結果 79
5.5誤碼率及眼形圖量測 83
5.5.1 位元錯誤率及眼形圖 83
5.5.2量測架構與結果 84
第六章 結論和未來展望 87
參考文獻 91
中英對照表 95
附錄：CDFA之模擬程式 98

[1]山下真司，“圖解光纖通信原理與散新應用技術”，建興文化，2003年。
[2]D. W. Hewak, “Progress towards a 1300 nm fiber amplifier,” IEEE Colloquium, vol. 26, pp. 12/1-12/5, 1998.
[3]S. Q. Man, H. W. Liu, Y. H. Wong, E. Y. B. Pun, and P. S. Chung, “Tellurite glasses for 1.3 μm optical amplifiers,” Lasers and Electro-Optics Society (LEOS) Annual Meeting, vol. 1, pp. 196-197, 1998.
[4]S. Aozasa, H. Masuda, H. Ono, T. Sakamoto, T. Kanamori, Y. Ohishi, and M. Shimizu, “1480-1510 nm-band Tm doped fiber amplifier (TDFA) with a high power conversion efficiency of 42%,” Optical Fiber Communication (OFC) Conference, vol. 4, pp. PD1, 2001.
[5]Y. Miyajima, T. Kamukai, and T. Sugawa, “1.31-1.36 μm optical amplification in Nd3+-doped fluorozirconate fiber,” Electron. Lett., vol. 26, pp. 194-195, 1990.
[6]G. P. Agrawal and N. K. Dutta, “Long-wavelength Semiconductor Lasers,” New York: Van Nostrand Reinhold, 1986, Ch. 3.
[7]A. Mecozzi and J. M. Wiesenfeld, “The roles of semiconductor optical networks,” Opti. & Photon. News, pp. 37-42, March 2001.
[8]E. Desurvire, “Erbium-doped Fiber Amplifiers: Principles and Applications,” New York: Wiley, 1994, Ch. 4.
[9]S. Shimada and H. Ishio, “Optical Amplifiers and their Applications,” New York: Wiley, 1994, Ch. 2.
[10]Y. Shi and O. Poulsen, “High-power broadband single mode Pr3+-doped fiber superfluorescence light source,” Electron. Lett., vol. 29, pp. 1945-1946, 1993.
[11]N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Quant. Electron., vol. 8, pp. 548-559, 2002.
[12]R. S. Feigelson, W. L. Kway, and R. K. Route, “Single crystal fibers by the laser-heated pedestal growth method,” Opt. Eng., vol. 24, pp. 1102-1107, 1985.
[13]J. S. Haggerty, “Production of fibers by a floating zone fiber drawing technique,” Final Report NASA-CR-120948, 1972.
[14]C. A. Burrus and J. Stone, “Single-crystal fiber optical devices: A Nd:YAG fiber laser,” Appl. Phys. Lett., vol. 26, pp. 318-320, 1975.
[15]M. M. Fejer, G. A. Magel, and R. L. Byer, “High-speed high-resolution fiber diameter variation measurement system,” Appl. Opt., vol. 24, pp. 2362-2368, 1985.
[16]S. Sudo, A. Cordova-Plaza, R. L. Byer, and H. J. Shaw, “MgO:LiNbO3 single-crystal fiber with magnesium-ion in-diffused cladding,” Opt. Lett., vol. 12, pp. 938-940, 1987.
[17]S. Ishibashi, K. Naganuma, and I. Yokohama, “Cr,Ca:Y3Al5O12 laser crystal grown by the laser-heated pedestal growth method,” J. Crys. Growth, vol. 183, pp. 614-621, 1998.
[18]S. Ishibashi and K. Naganuma, “Diode-pumped Cr4+:YAG single-crystal fiber laser,” in Advanced Solid State Lasers, OSA Technical Digest Series (Optical Society of America, 2000), paper MD4.
[19]M. A. Gulgun, W. Y. Ching, Y. N. Xu, and M. Ruhle, “Electron states of YAG probed by energy-loss near-edge spectrometry and ab initio calculations,” Phil. Mag. B, vol. 79, pp. 921-940, 1999.
[20]H. Eilers, W. M. Dennis, W. M. Yen, S. Kuck, K. Peterman, G. Huber, and W. Jia, “Performance of a Cr:YAG laser,” IEEE J. Quant. Electron., vol. 29, pp. 2508-2512, 1993.
[21]S. Kuck, K. Petermann, and G. Huber, “Spectroscopic investigation of the Cr4+-center in YAG,” OSA Proceedings on Advanced Solid-State Lasers, vol. 10, pp. 92-94, 1991.
[22]B. M. Tissue, W. Jia, L. Lu, and W. M. Yen, “Coloration of chromium-doped yttrium aluminum garnet single-crystal fibers using a divalent codopant,” J. Appl. Phys., vol. 70, pp. 3775-3777, 1991.
[23]G. Keiser, “Optical Fiber Communications,” 3rd ed. McGraw-Hill, 2000, Ch. 2 and Ch. 3.
[24]A. Sennaroglu, “Analysis and optimization of lifetime thermal loading in continuous-wave Cr4+-doped solid-state lasers,” J. Opt. Soc. Am., vol. 18, pp. 1578-1586, 2001.
[25]G. A. Magel, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched second harmonic generation of blue light in periodically poled LiNbO3,” Appl. Phys. Lett., vol. 56, pp. 108-110, 1990.
[26]L. Hesseling and S. Redfield, “Photorefractive holographic recording in strontium barium niobate fiber,” Opt. Lett., vol. 13, pp. 877-879, 1988.
[27]R. S. Feigelson, D. Gazit, and D. K. Fork, “Superconducting Bi-Ca-Sr-Cu-O fibers grown by the laser-heated pedestal growth method,” Science, vol. 240, pp. 1642-1645, 1988.
[28]張金倉，霍玉晶，何豫生，“激光加熱浮區生長強織構高溫超導晶纖的研究”，中國激光，第20卷，第8期，1993年。
[29]B. E. A. Saleh and M. C. Teich, “Fundamentals of Photonics,” 1st ed. John Wiley & Sons, 1991, Ch. 6 and Ch. 7.
[30]J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibers and devices Part 1: Adiabaticity criteria,” IEE Proc., vol. 138, pp. 343-354, 1991.
[31]N. I. Borodin, V. A. Zhitnyuk, A. G. Okhrimchuk, and A. V. Shestakov, “Oscillation of a Y3Al5O12 : Cr4+ laser in wavelength region of 1.34-1.6 μm,” Bull. Acad. Sci. USSR, Phys. Ser., vol. 54, pp. 54-60, 1990.
[32]I. J. Miller, A. J. Alcock, and J. E. Bernard, “Experimental investigation of Cr4+ in YAG as a passive Q-switch,” in OSA Proceedings on Advanced Solid-state Lasers, vol. 13, pp. 322-325, 1992.
[33]H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, “Saturation of 1.064 μm absorption in Cr,Ca:Y3Al5O12 crystals,” Appl. Phys. Lett., vol. 61, pp. 2958-2960, 1992.
[34]K. Spariosu, W. Chen, R. Stultz, M. Birnbaum, and A. V. Shestakov, “Dual Q switching and laser action at 1.06 and 1.44 μm in a Nd3+:YAG-Cr4+:YAG oscillator at 300 K,” Opt. Lett. vol. 18, pp. 814-816, 1993.
[35]E. Eilers, U. Hommerich, S. M. Jacobsen, and W. M. Yen, “Spectroscopy and dynamics of Cr4+:Y3Al5O12,” Phys. Rev. B, vol. 49, No. 22, pp. 15505-15513, 1994.
[36]Y. Shimony, Z. Burshtein, and Y. Kalisky, “Cr4+:YAG as passive Q-switch and Brewster plate in a pulsed Nd:YAG laser,” IEEE J. Quant. Electron., vol. 31, pp. 1738-1741, 1995.
[37]S. Kuck, K. Petermann, U. Pholmann, and G. Huber, “Near-infrared emission of Cr4+-doped garnets: lifetimes, quantum efficiencies, and emission cross sections,” Phys. Rev. B, vol. 51, pp. 17323-17331, 1995.
[38]S. C. Lopez, R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Intensity-induced birefringence in Cr4+:YAG,” J. Mod. Opt., vol. 44, pp. 209-219, 1997.
[39]A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, “Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a doubled-pulse pumping technique,” IEEE. J. Quant. Electron., vol. 35, pp. 1548-1553, 1999.
[40]J. C. Diettrich, I. T. McKinnie, and D. M. Warringtion, “The influence of active ion concentration and crystal parameters on pulsed Cr:YAG laser performance,” Opt. Commun., vol. 167, pp. 133-140, 1999.
[41]R. Feldman, Y. Shimony, and Z. Burshtein, “Dynamics of chromium ion valence transformations in Cr,Ca:YAG crystals used as laser gain and passive Q-switching media,” Opt. Mater., vol. 24, pp. 333-344, 2003.
[42]Taylor Lyman, “Metallography, structures and phase diagrams” , American society for metals, Vol. 8, 8th Edition, 1973.
[43]D. Derickson Ed.,“Fiber Optic Test and Measurement”, Hewlett Packard 1998.
[44]S. M. Yeh, D. J. Feng, Y. C. Huang, T. S. Lay, S. L. Huang, P. Yeh, and W. H. Cheng, “Mode matching and insertion loss in ultra-broadband Cr-doped multimode fibers,” Opt. Lett., vol. 33, pp. 785-787, 2008.