本論文利用Z掃描技術量測不同層數堆疊石墨烯飽和吸收體之非線性光學特性，並以摻鉺光纖(Erbium-doped Fiber; EDF)作為增益介質之環形共振腔進行被動鎖模實驗產生穩定超短脈衝。石墨烯薄膜樣品採化學氣相沉積法(Chemical Vapor Deposition; CVD)製備，及以聚乙烯醇(polyvinyl alcohol; PVA)溶液製成高分子薄膜置入共振腔內進行鎖模。
Z掃描技術的實驗光源為皮秒級、波長532 nm的Nd:YAG雷射，藉由改變入射光強度來研究石墨烯薄膜的非線性光學特性。實驗結果石墨烯薄膜的非線性吸收係數與折射率隨著樣品層數堆疊的增加而上升，並隨著入射光強度的增加而衰減。對於層數較低(1、8層)的樣品，非線性吸收效應主要源自於單光子吸收達到飽和。而較高層數的樣品在高能量入射的時候開始出現反飽和效應，表示雙光子吸收機制的介入，推測為石墨烯材料的層數堆疊造成能隙變寬所導致。
被動鎖模實驗量測研究包括：(1)達成穩定鎖模的起始激發功率、(2)可穩定鎖模的能量區間以及(3)最佳化輸出的脈衝寬度。第一部份量測的結果5層薄膜樣品達成穩定鎖模的起始激發功率為62.8 mW、8層62.8 mW、12層72.1 mW，而17層則為86.0 mW。而第二部分，在穩定鎖模的能量區間方面，以5層樣品的範圍最廣，可達到107.7 mW，其次為8層100.2 mW、12層81.3 mW，17層則為55.0 mW。結果顯示起始激發功率隨著層數堆疊的增加而上升，而穩定鎖模區間則隨著層數的增加而縮減。原因在於高層數的樣品在入射光強較高的強況下會產生反飽和吸收效應，不利於鎖模脈衝陣列的輸出。第三部分的量測結果，在最佳化輸出的脈衝寬度方面，5層薄膜樣品為603 fs、8層584 fs、12層543 fs，17層的表現最佳，可達到523 fs。顯示層數堆疊的增加有利於提升壓縮脈衝寬度。

This research employed Z-scan technique to investigate optical nonlinearities of graphene saturable absorber with different number of layer, and used Erbium-doped fiber as gain medium in passive mode-locking to generated stable ultrashort pulses. Graphene thin-film was fabricated by Chemical vapor deposition (CVD) methods, and used polyvinyl alcohol (PVA) solution to produce high polymer thin-film for mode-locking experiment.

Our light source for Z-scan experiment was pico-second scale Nd:YAG Laser of 532 nm wavelength. Nonlinearities of graphene thin-film was investigated by changing illuminating intensity. Our research showed that both nonlinear absorption coefficient and nonlinear refractive index increased as number of layer increased, and decreased with increasing intensity. For samples with fewer layer-stacking (1-,8-layer), nonlinear absorption was resulted from the saturation of single photon absorption. However, for samples with higher number of layer, reverse saturable absorption phenomenon started to show at high illuminating intensities, indicated the involvement of two-photon absorption. This might because of the bandgap widening induced by layer-stacking in graphene material.

Our research also used graphene of different number of layer to fabricate hi-polymer thin film for passive mode-locking experiment. The experiment included the investigation of the starting pumping power and the dynamic range of stable mode-locking, as well as the optimized output pulse-width. First, the starting pumping power for stable mode-locking was 62.8 mW for 5-layer graphene sample, 62.8 mW for 8-layer, 72.1 mW for 12-layer, and 86.0 mW for 17-layer one, respectively. Secondly, as for the dynamic range, 5-layer sample had the widest dynamic range of 107.7 mW. And it was 100.2 mW for 8-layer, 81.3 mW for 12-layer, and 55.0 mW for 17-layer. The results indicated that the starting pumping power for stable mode-locking increased with the number of layer, and the dynamic range became narrower with increasing layer-stacking. The reason was that for graphene with more number of layer, the reverse saturable absorption phenomenon would be induced at high intensity, which caused instability for passive mode-locking. Lastly, the optimized pulse-width was 603 fs for 5-layer graphene thin-film, 584 fs for 8-layer, 543 fs for 12-layer, and 523 for 17-layer, respectively. The 17-layer graphene sample showed that shortest output pulse-width, indicating that the increase of layer-stacking favored the compression of mode-locking pulse.

內容目錄
摘要 i
Abstract ii
目錄 iv
圖目錄 vi
表目錄 v

第一章 緒論 1
1.1研究目的 1
1.2 論文架構 2
第二章 研究相關理論概述 3
2.1 模態鎖定 3
2.2 被動鎖模原理 5
2.2.1 飽和吸收體於被動鎖模之應用 5
2.2.2 影響被動鎖模的因素 7
2.3 Z掃描技術 10
2.3.1 Z-scan 理論 10
2.3.2 以Z掃描技術研究石墨烯非線性光學特性 12
2.3.2.1 三階非線性吸收 14
2.3.2.1 三階非線性折射 16
第三章 石墨烯材料簡介與實驗方法 18
3.1 石墨烯材料的結構與特性 18
3.1.1 奈米石墨烯材料簡介與飽和吸收特性 18
3.1.2 石墨烯材料結構分析 21
3.2 Z掃描技術量測架構 25
3.2.1 Nd:YAG雷射系統 25
3.2.2 Z掃描量測架構 26
3.3 被動鎖模脈衝實驗 27
3.3.1 石墨烯-高分子薄膜製備 27
3.3.2 被動鎖模實驗架構 29
第四章 結果與討論 32
4.1 CVD製備石墨烯樣品之材料分析 32
4.2 Z掃描技術量測結果 35
4.3 結晶層狀石墨烯樣品之鎖模結果 43
4.3.1 不同層數CVD石墨烯樣品鎖模量測 43
4.3.2 鎖模雷射之穩定度測試結果 52
第五章 結論與未來展望 53
5.1 結論 53
5.2 未來展望 54
參考文獻 55

[1] A.M Weiner, Ultrafast Optics, Wiley, New Jersey (2009)
[2] Qiaoliang Bao, Han Zhang, Yu Wang, Zhenhua Ni, Yongli Yan, Ze Xiang Shen, Kian Ping Loh, and Ding Yuan Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers”, Adv. Funct. Mater. 2009, 19, pp.3077-3083 (2009)
[3] E. Garmire, “Resonant Optical Nonlinearities in Semiconductors”, IEEE J. Sel. Top. Quantum Electron, vol.6, pp. 1094-1110 (2000)
[4] C. Rulliere, Femtosecond Laser Pulses: Principles and Experiments, Springer, New York (1998)
[5] 邱金城, “奈米碳管飽和吸收體增強鎖模雷射非線性自相位調變之研究”, 國立中山大學博士論文 (2010)
[6] Franz X. Kaertner, “Mode-locked Laser Theory” physics.gatech.edu, ch.1 (2006)
[7] H. A. Haus, “Theory of Mode Locking with a Fast Saturable Absorber”, J. Appl. Phys., vol.46, pp. 3049-3058 (1975)
[8] E. W. Van Stryland and M. S. Bahae, “Z-scan measurement of Optical Nonlinearities”, Characterization Techniques and Tabulations for Organic Nonlinear Materials, pp. 655 (1998)
[9] R. A. Ganeev, A. I. Ryasnyansky, Sh. R. Kamalov, M. K. Kodirov and T. Usmanov, “Nonlinear Susceptibilities, Absorption Coefficients and Refractive Indices of Colloidal Metals” J. Phys. D: Appl. Phys. 34, pp.1602-1611 (2001)
[10] Mansoor Sheik-Bahae, Ali A. Said, Tai-Huei Wei, David J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam”, IEEE Journal of Quantum Electronics. vol. 26. no. 4 (1990)
[11] Alan D. Bristow, Nir Rotenberg, and Henry A. Van Driel, “Two-Photon Absorption and Kerr Coefficients of Silicon for 850-2200 nm”, Applied Physics Letters 90, 191104 (2007)
[12] Han Zhang, Stephane Virally, Qiaoling Bao, Kian Ping Loh, Serge Massar, Nicolas Godbout, and Pascal Kockaert, “Large Nonlinear Kerr Effect in Graphene ” physics optics, arXiv:1203.5527v1 (2012)
[13] A. K. Geim & K. S. Novoselov, “The Rise of Graphene ”, Nature Materials 6, pp.183 - 191 (2007)
[14] research.physics.berkeley.edu/crommie/research:carbon-nanostructures
[15] Yong-Won Song, Sung-Yeon Jang, Won-Suk Han, and Mi-Kyung Bae, ‘’Graphene Mode-Lockers for Fiber Lasers Functioned with Evanescent Field Interaction,” Appl. Phys. Lett., vol. 96, pp. 051122-051123 (2010)
[16] M. Freitag, “Trilayers Unraveled”, NATURE PHYSICS, vol.7 (2011)
[17] R. R. Nair, et al “Fine Structure Constant Defines Vvisual Transparency of Graphene,” Science, Vol. 320, pp.1308–1308, (2008)
[18] A. C. Ferrari, “Raman Spectrum of Graphene and Graphene Layers ”, Physical Review Letters, 97, 187401 (2006)
[19] A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large Area, Few-Layer Graphene Films on Arbitrary Substrates by Chemical Vapor Deposition,” Nano Lett., vol. 9, no. 1, pp. 30-35, 2009
[20] Zheng Yan and Andrew R. Barron, “Characterization of Graphene by Raman Spectrum”, OpenStax CNX module: m34667
[21] 陳琬淋, “以Z掃描技術研究石墨烯之非線性光學特性”, 國立中山大學碩士論文 (2014)
[22] Ching-Yuan Su, Ang-Yu Lu, Chih-Yu Wu, Yi-Te Li, Keng-Ku Liu, Wenjing Zhang, Shi-Yen Lin, Zheng-Yu Juang, Yuan-Liang Zhong, Fu-Rong Chen, and Lain-Jong Li, “Direct Formation of Wafer Scale Graphene Thin Layers on Insulating Substrates by Chemical Vapor Deposition ” Nano Lett., vol.11, pp.3612–3616 (2011)
[23] Meisam Rahmani, Razali Ismail, Mohammad Taghi Ahmadi, Mohammad Javad Kiani, Mehdi Saeidmanesh, F. A. Hediyeh Karimi, Elnaz Akbari and Komeil Rahmani, “The Effect of Bilayer Graphene Nanoribbon Geometry on Schottky-Barrier Diode Performance”, Journal of Nanomaterial, Article ID 636239 (2013)
[24] 林紹晴, “飽和吸收體摻雜石墨烯被動鎖模之研究”, 國立中山大學碩士論文 (2011)
[25] http://wshnt.kuas.edu.tw/network/s7/index.html
[26] Zhibo Liu, Yan Wang, Xiaoliang Zhang, Yanfei Xu, Yongsheng Chen, and Jianguo Tian, “Nonlinear Optical Properties of Graphene Oxide in Nanosecond and Picosecond Regimes” Applied Physics Letters, vol.94, issue.2 (2009)
[27] J. Wang, B. Gu, H. Wang, and X. Ni, “Z-scan Analytical Theory for Material with Saturable Absorption and Two-Photon Absorption”, Opt. Communications, vol.238, pp.3525-3528 (2010)
[28] Pi Ling Huang, Wan-Lin Chen, Ta-Wei Peng, Ching-Yuan Su, Chao-Yung Yeh, and Wood-Hi Cheng, “Investigation of Saturable and Reverse Saturable Absorption for Graphene by Z-scan Technique”, Photonics Technology Letters IEEE , vol.27, pp.1791-1794 (2015)
[29] Pi Ling Huang, Shau-Ching Lin, Chao-Yung Yeh, Hsin-Hui Kuo, Shr-Hau Huang, Gong-Ru Lin, Lain-Jong Li, Ching-Yuan Su, and Wood-Hi Cheng “Stable Mode-Locked Fiber Laser Based on CVD Fabricated Graphene Saturable Absorber”, Optics Express, Vol. 20, pp.2460 (2012).