在本論文中我們針對sigma-type環境穩定混合式鎖模摻鉺光纖雷射架構進行研究，在實驗與理論上探討高重複率鎖模脈衝產生之雷射動力學與雜訊特性，主要研究成果包括釐清10 GHz重複率光固子束縛態鎖模之雷射行為，以及進一步發展出100 GHz高重複率功率穩定鎖模光纖雷射系統、觀察其雷射品質並改善其特性。其中在理論上我們發展了一套新穎的鎖模雷射雜訊計算模型，係基於線性化master equation 模型的背向傳播方法所推導而得，與傳統的計算模型相比，此模型能用較少的計算求解複雜的鎖模雷射雜訊問題。透過一些計算範例的驗證我們證明了其計算的可靠度與準確性，同時我們也利用此方法在數值計算上預測了主動振幅調變鎖模雷射系統時序雜訊抵銷的新穎現象，透過在腔外將脈衝傳遞於一段與雷射相反色散之線性物質來抵銷一部分的脈衝時序雜訊。我們也進一步使用此雜訊計算模型來探討束縛態光固子鎖模之振幅雜訊特性，並在實驗上觀察與量測了10 GHz束縛態光固子雷射之行為，包含其鎖模態過渡區間、脈衝分裂與穩定機制、雷射參數相關性、以及振幅雜訊特性等。在數值上分別利用脈衝傳播解法與非線性特徵值方法來求解master equation 模型以進行分析，我們發現並證實一新穎的脈衝分裂程序，同時也證實束縛態光固子相較於單一光固子能具有較低的振幅雜訊。最後在實驗上我們調整雷射架構並加入一Fabry-Pérot etalon來輔助雷射達成100 GHz鎖模，透過一個Finesse=100之etalon的使用，我們能將雷射操作於100 GHz被動連續波鎖模並佐以一功率穩定回授系統來控制雷射，其功率穩定性能被控制在0.1%。若是透過Finesse=6之etalon的使用，我們能將雷射分別操作於100 GHz被動連續波鎖模與主被動混合式burst-mode鎖模狀態。在混合式burst-mode鎖模態下，透過振幅調變器的使用，我們發現脈衝的時域品質能獲得顯著改善。在理論模擬上我們也運用了脈衝傳播解法來模擬離散式雷射共振腔模型以驗證此高重複率鎖模雷射的實驗結果，良好的符合性驗證了理解的合理正確性。

In this thesis work we investigate experimentally and theoretically the laser dynamics of an environmentally stable hybrid mode-locked Er-doped fiber laser with a sigma-type laser cavity. We develop a new laser noise calculation model based on the linearized back-propagation approach for the master equation. Due to the deterministic computation nature, the developed model can calculate complicate noise problems with less computation. The reliability and accuracy of the model are verified through working out some examples for determining different kinds of noises. We find a novel timing jitter cancellation effect based on active amplitude modulation mode-locked lasers. It is observed that the timing jitter can be slightly reduced through propagating the pulses in a piece of extra-cavity opposite-sign dispersive medium. We then apply the noise calculation model to study the relative intensity noises (RIN) of the bound soliton mode-locking state. We have experimentally investigated the laser characteristics of single and bound soliton mode-locking states including the state transition behavior and the RINs. We find an interesting bound soliton formation process and also find that the bound soliton state can have a smaller RIN compare to the single soliton state. Finally we achieve 100 GHz mode-locking by incorporating an intra-cavity Fabry-Pérot etalon and a section of high nonlinearity fiber. A power control loop is employed to stabilize the laser power variation to only near 0.1%. We observe different mode-locking results by replacing different finesse etalons (finesse = 6 and 100) with the turning on/off of an intra-cavity active amplitude modulator. The laser can be operated under the 100 GHz continuous passive mode-locking state and the 100 GHz burst-mode hybrid mode-locking state with very good stability. Under the burst-mode hybrid mode-locking state, the pulse quality enhancement effect is observed with the use of an active amplitude modulator. Numerical simulation based on the discrete/lumped laser cavity model is carried out to verify the experimental results. Nice agreement has been achieved to support our understanding about the observed laser dynamics.

摘要......................................................I
Abstract..................................................II
Contents..................................................III
List of figures............................................V
List of tables............................................IX
Chapter 1. Introduction....................................1
1.1. Overview of mode-locked fiber laser technologies...1
1.2. Motivations of the research........................5
1.3. Organization of the thesis.........................7
1.4. References.........................................8
Chapter 2. Mode-locked fiber laser theory.................14
2.1. Principles of mode-locking........................14
2.1.1. Active mode-locking basis.........................14
2.1.2. The master equation model.........................21
2.1.3. Comb filters......................................24
2.1.4. Optical temporal soliton formation................26
2.2. Numerical simulation methods of mode-locked fiber lasers....................................................27
2.3. Numerical analysis methods of mode-locked fiber laser noises....................................................32
2.4. References........................................32
Chapter 3. A new noise calculation method for mode-locked lasers....................................................37
3.1. General theory of the back-propagation method.....37
3.2. Timing jitter reduction of amplitude modulation mode-locked lasers.............................................47
3.3. Chapter summary...................................54
3.4. References........................................55
Chapter 4. Bound soliton laser dynamics of a high repetition 10 GHz hybrid mode-locked fiber laser.....................58
4.1. Experimental setup and results....................58
4.2. Numerical simulation results......................69
4.3. Chapter summary...................................76
4.4. References........................................77
Chapter 5. 100 GHz ultrahigh repetition rate mode-locking...................................................81
5.1. 100 GHz passive mode-locking with output power stabilization.............................................81
5.1.1. Experimental configuration and results............82
5.1.2. Numerical simulations.............................86
5.2. 100 GHz burst/continuous dual-operation-mode mode-locking with enhanced auto-correlation contrast...........88
5.2.1. Experimental configurations and results...........91
5.2.2. Numerical simulation results......................93
5.3. Chapter summary...................................94
5.4. References........................................95
Chapter 6. Summary and future works.......................97
6.1. Thesis summary....................................97
6.2. Future works......................................99
6.3. References........................................102
Publication list..........................................105

Chapter 1.
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15. C. J. Luo, S. M. Wang, and Y. Lai, “Bound soliton fiber laser mode-locking without saturable absorption effect,” IEEE Photonics J., 8, 1502609 (2016).
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27. S. M. Wang, and Y. Lai, “Up to 400 GHz burst-mode pulse generation from a hybrid harmonic mode-locked Er-doped fibre laser,” Laser Phys. Lett., 14, 025102 (2017).
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30. W. W. Hsiang, H. C. Chang, and Y. Lai, “Laser dynamics of a 10 GHz 0.55 ps asynchronously harmonic modelocked Er-doped fiber soliton laser,” IEEE J. Quantum Electron., 46, 299n-299u (2010).
31. K. Xu, R.Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Super-mode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett., 10, 055108 (2013).
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37. D. Hou, B. Ning, S. Zhang, J. Wu, and J. Zhao, “Long-term stabilization of fiber laser using phase-locking technique with ultra-low phase noise and phase drift,” IEEE J. Sel. Topics Quantum Electron., 20, 1101308 (2014).
38. D. Hou, J. Wu, Q. Ren, and J. Zhao, “Analysis of long-term phase-locking technique for mode-locked laser with PID regulator,” IEEE J. Quantum Electron., 48, 839-846 (2012).
39. B. Ning, D. Hou, P. Du, and J. Zhao, “Long-term repetition frequency stabilization of passively mode-locked fiber lasers using high-frequency harmonic synchronization,” IEEE J. Quantum Electron., 49, 839-846 (2013).
40. K. Jung, and J. Kim, “Subfemtosecond synchronization of microwave oscillators with mode-locked Er-fiber lasers,” Opt. Lett., 37, 2958-2960 (2012).
41. D. Hou, B. Ning, P. Li, Z. Zhang, and J. Zhao, Q. Ren, and J. Zhao, “Modeling analysis for phase-locking of mode-locked laser,” IEEE J. Quantum Electron., 47, 891-898 (2011).
42. B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, M. F. Yan, and C. G. Jørgensen, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett., 29, 250-250 (2004).
43. K. Iwakuni, H. Inaba, Y. Nakajima, T. Kobayashi, K. Hosaka, A. Onae, and F. L. Hong, “Narrow linewidth comb realized with a modelocked fiber laser using an intra-cavity waveguide electro-optic modulator for highspeed control,” Opt. Express, 20, 13769-13776 (2012).
44. S. Zhang, J. Wu, J. Leng, S. Lai, and J. Zhao, “Highly precise stabilization of intra-cavity prism-based Er:fiber frequency comb using optical-microwave phase detector,” Opt. Lett., 39, 6454-6457 (2014).
45. F. Quinlan, C. Williams, S. Ozharar, S. Gee, and P. J. Delfyett, “Self-stabilization of the optical frequencies and the pulse repetition rate in a coupled optoelectronic oscillator,” J. Lightw. Technol., 26, 2571-2577 (2008).
46. M. Akbulut, J. D. Rodriguez, I. Ozdur, F. Quinlan, S. Ozharar, N. Hoghooghi, and P. J. Delfyett, “Measurement of carrier envelope offset frequency for a 10 GHz etalon-stabilized semiconductor optical frequency comb,” Opt. Express, 19, 16851-16865 (2011).
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48. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively modelocked lasers,” IEEE J. Quantum Electron., 40, 1458–1470 (2004).
49. C. R. Menyuk, and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics, 5, 332–350 (2016).
50. R. Paschotta, “Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations,” Appl. Phys. B, 79, 163–173 (2004).
51. Y. Song, C. Kim, K. Jung, H. Kim, and J. Kim, “Timing jitter optimization of mode-locked Yb-fiber lasers toward the attosecond regime,” Opt. Express, 19, 14518–14525 (2011).
52. J. Shin, K. Jung, Y. Song, and J. Kim, “Characterization and analysis of timing jitter in normal-dispersion mode-locked Er-fiber lasers with intra-cavity filtering,” Opt. Express, 23, 22898–22906 (2015).
53. D. Kim, S. Zhang, D. Kwon, R. Liao, Y. Cui, Z. Zhang, Y. Song, and J. Kim, “Intensity noise suppression in mode-locked fiber lasers by double optical bandpass filtering,” Opt. Lett., 42, 4095–4098 (2017).
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58. D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, and H. Y. Tam, “Bound-soliton fiber laser,” Phys. Rev. A., 66, 033806 (2002).
59. N. D. Nguyen and L. N. Binh, “Generation of high order multi-bound solitons and propagation in optical fibers,” Opt. Commun., 282, 2394–2406 (2009)

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3. M. O. Scully, and M. S. Zubairy, Quantum optics, Cambridge University Press (1997).
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6. M. A. Solodyankin, E. D. Obraztsova, A. S. Lobach, A. I. Chernov, A. V. Tausenev, V. I. Konov, and E. M. Dianov, “Mode-locked 1.93 um thulium fiber laser with a carbon nanotube absorber,” Opt. Lett., 33, 1336-1338 (2008).
7. F. X. Kärtner, D.M. Zumbühl, and N. Matuschek, “Turbulence in mode-locked lasers,” Phys. Rev. Lett., 82, 4428-4431 (1999).
8. H. A. Haus, and A. Mecozzi, “Long-term storage of a bit stream of solitons,” Opt. Lett., 17, 1500-1502 (1992).
9. D. J. Jones, H. A. Haus, and E. P. Ippen, “Subpicosecond solitons in an actively mode-locked fiber laser,” Opt. Lett., 21, 1818-1820 (1996).
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14. W. W. Hsiang, H. C. Chang, and Y. Lai, “Laser dynamics of a 10 GHz 0.55 ps asynchronously harmonic mode-locked Er-doped fiber soliton laser,” IEEE J. Quantum Electron., 46, 299n-299u (2010).
15. H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wong, “Theory of soliton stability in asynchronous mode-locking,” J. Lightwave Technol., 14, 622-627 (1996).
16. M. Yoshida, K. Yoshida, K. Kasai, and M. Nakazawa, “1.55 μm hydrogen cyanide optical frequency stabilized and 10 GHz repetition-rate stabilized mode-locked fiber laser,” Opt. Express, 24, 24287-24296 (2016).
17. K. Xu, R.Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, “Super-mode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett., 10, 055108 (2013).
18. M. Nakazawa, K. Tamura, and E. Yoshida, “Super-mode noise suppression in a harmonically modelocked fibre laser by self phase modulation and spectral filtering,” Electron. Lett., 32, 461-463 (1996).
19. C. J. Luo, S. M. Wang, and Y. Lai, “Bound soliton fiber laser mode-locking without saturable absorption effect,” IEEE Photonics J., 8, 1502609 (2016).
20. C. J. Luo, and Y. Lai, “Relative intensity noise of hybrid mode-locked bound soliton fiber laser: Theory and experiment,” Appl. Sci., 8, 1451 (2018).
21. D. Hou, B. Ning, S. Zhang, J. Wu, and J. Zhao, “Long-term stabilization of fiber laser using phase-locking technique with ultra-Low phase noise and phase drift,” IEEE J. Sel. Topics Quantum Electron., 20, 1101308 (2014).
22. K. Jung, and J. Kim, “Subfemtosecond synchronization of microwave oscillators with mode-locked Er-fiber lasers,” Opt. Lett., 37, 2958-2960 (2012).
23. B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, M. F. Yan, and C. G. Jørgensen, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett., 29, 250-250 (2004).
24. S. Zhang, J. Wu, J. Leng, S. Lai, and J. Zhao, “Highly precise stabilization of intra-cavity prism-based Er:fiber frequency comb using optical-microwave phase detector,” Opt. Lett., 39, 6454-6457 (2014).
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38. S. Balac, A. Fernandez, F. Mahé, F. Méhats, and R. T. Picard, “The interaction picture method for solving the generalized nonlinear Schrödinger equation in optics,” edp sciences, 50, 945-964 (2016).
39. J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett., 32, 3519–3521 (2007).
40. Y. Song, C. Kim, K. Jung, H. Kim, and J. Kim, “Timing jitter optimization of mode-locked Yb-fiber lasers toward the attosecond regime,” Opt. Express, 19, 14518–14525 (2011).
41. J. Shin, K. Jung, Y. Song, and J. Kim, “Characterization and analysis of timing jitter in normal-dispersion mode-locked Er-fiber lasers with intra-cavity filtering,” Opt. Express, 23, 22898–22906 (2015).
42. K. Tamura, and M. Nakazawa, “Timing jitter of solitons compressed in dispersion-decreasing fibers,” Opt. Lett., 23, 1360–1362 (1998).
43. W. Chen, Y. Song, K. Jung, M. Hu, C. Wang, and J. Kim, “Few-femtosecond timing jitter from a picosecond all-polarization-maintaining Yb-fiber laser,” Opt. Express, 24, 1347–1357 (2016).
44. H. A. Haus, and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron., 29, 983–996 (1993).
45. C. X. Yu, S. Namiki, and H. A. Haus, “Noise of the stretched pulse fiber laser: Part II—experiments,” IEEE J. Quantum Electron., 33, 660–668 (1997).
46. M. E. Grein, L. A. Jiang, H. A. Haus, E. P. Ippen, C. McNeilage, J. H. Searls, and R. S. Windeler, “Observation of quantum-limited timing jitter in an active, harmonically mode-locked fiber laser,” Opt. Lett., 27, 957–959 (2002).
47. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron., 40, 1458–1470 (2004).
48. R. Paschotta, “Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations,” Appl. Phys. B, 79, 163–173 (2004).

Chapter 3.
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2. R. K. Lee, Y. Lai, and B. A. Malomed, “Quantum correlations in bound-soliton pairs and trains in fiber lasers,” Phys. Rev. A, 70, 063817 (2004).
3. R. K. Lee, Y. Lai, and B. A. Malomed, “Photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers,” Opt. Lett., 30, 3084–3086 (2005).
4. J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett., 32, 3519–3521 (2007).
5. Y. Song, C. Kim, K. Jung, H. Kim, and J. Kim, “Timing jitter optimization of mode-locked Yb-fiber lasers toward the attosecond regime,” Opt. Express, 19, 14518–14525 (2011).
6. J. Shin, K. Jung, Y. Song, and J. Kim, “Characterization and analysis of timing jitter in normal-dispersion mode-locked Er-fiber lasers with intra-cavity filtering,” Opt. Express, 23, 22898–22906 (2015).
7. K. Tamura, and M. Nakazawa, “Timing jitter of solitons compressed in dispersion-decreasing fibers,” Opt. Lett., 23, 1360–1362 (1998).
8. W. Chen, Y. Song, K. Jung, M. Hu, C. Wang, and J. Kim, “Few-femtosecond timing jitter from a picosecond all-polarization-maintaining Yb-fiber laser,” Opt. Express, 24, 1347–1357 (2016).
9. C. R. Menyuk, and S. Wang, “Spectral methods for determining the stability and noise performance of passively mode-locked lasers,” Nanophotonics, 5, 332–350 (2016).
10. N. G. Usechak, and G. P. Agrawal, “Rate-equation approach for frequency-modulation mode locking using the moment method,” J. Opt. Soc. Am. B, 22, 2570–2580 (2005).
11. H. A. Haus, and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron., 29, 983–996 (1993).
12. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron., 40, 1458–1470 (2004).
13. C. X. Yu, S. Namiki, and H. A. Haus, “Noise of the stretched pulse fiber laser: Part II—Experiments,” IEEE J. Quantum Electron., 33, 660–668 (1997).
14. M. E. Grein, L. A. Jiang, H. A. Haus, E. P. Ippen, C. McNeilage, J. H. Searls, and R. S. Windeler, “Observation of quantum-limited timing jitter in an active, harmonically mode-locked fiber laser,” Opt. Lett., 27, 957–959 (2002).
15. I.L. Budunog˘lu, C. Ülgüdür, B. Oktem, and F. Ö. Ilday, “Intensity noise of mode-locked fiber lasers,” Opt. Lett., 34, 2516-2518 (2009).
16. K. Wu, P. P. Shum, S. Aditya, C. Ouyang, J. H. Wong, H. Q. Lam, and K. E. K. Lee, “Noise conversion from pump to the passively mode-locked fiber lasers at 1.5 μm,” Opt. Lett., 37, 1901-1903 (2012).
17. J. Chen, J. W. Sickler, E. P. Ippen, and F. X. Kärtner, “High repetition rate, low jitter, low intensity noise, fundamentally mode-locked 167 fs soliton Er-fiber laser,” Opt. Lett., 32, 1566–1568 (2007).
18. C. Kim, K. Jung, K. Kieu, and J. Kim, “Low timing jitter and intensity noise from a soliton Er-fiber laser mode-locked by a fiber taper carbon nanotube saturable absorber,” Opt. Express, 20, 29524–29530 (2012).
19. D. Kim, S. Zhang, D. Kwon, R. Liao, Y. Cui, Z. Zhang, Y. Song, and J. Kim, “Intensity noise suppression in mode-locked fiber lasers by double optical bandpass filtering,” Opt. Lett., 42, 4095–4098 (2017).
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Chapter 4.
1. F. X. K¨artner, J. A. D. Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers—What’s the difference?,” IEEE J. Sel. Top. Quantum Electron., 4, 159-168 (1998).
2. B. G. Bale1, K. Kieu, J. N. Kutz, and F. Wise, “Transition dynamics for multi-pulsing in mode-locked lasers,” Opt. Express, 17, 23137-23146 (2009).
3. R. Gumenyuk, and O. G. Okhotnikov, “Temporal control of vector soliton bunching by slow/fast saturable absorption,” J. Opt. Soc. Am. B, 29, 1-7 (2012).
4. R. Gumenyuk, and O. G. Okhotnikov, “Impact of gain medium dispersion on stability of soliton bound states in fiber laser,” IEEE photonic tech. Lett., 25, 133-135 (2013).
5. D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, and H. Y. Tam, “Bound-soliton fiber laser,” Phys. Rev. A., 66, 033806 (2002).
6. D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E., 72, 016616 (2005).
7. W. W. Hsiang, C. Y. Lin, and Y. Lai, “Stable new bound soliton pairs in a 10 GHz hybrid frequency modulation mode-locked Er-fiber laser,” Opt. Lett., 31, 1627-1629 (2006).
8. N. D. Nguyen and L. N. Binh, “Generation of high order multi-bound solitons and propagation in optical fibers,” Opt. Commun., 282, 2394–2406 (2009).
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11. C. J. Luo, S. M. Wang, and Y. Lai, “Bound soliton fiber laser mode-locking without saturable absorption effect,” IEEE Photonics J., 8, 1502609 (2016).
12. L. Gui, and C. Yang, “Soliton molecules with ±π/2, 0, and π phase differences in a graphene-based mode-locked erbium-doped fiber laser,” IEEE Photonics J., 10, 1502609 (2018).
13. C. J. Luo, and Y. Lai, “Relative intensity noise of hybrid mode-locked bound soliton fiber laser: Theory and experiment,” Appl. Sci., 8, 1451 (2018).
14. T. F. Carruthers, I. N. Duling III, and M. L. Dennis, “Active-passive mode-locking in a single- polarisation erbium fibre laser,” Electronics Letters, 30, 1051-1052 (1994).
15. T. F. Carruthers, and I. N. Duling III, “10-GHz, 1.3-ps erbium fiber laser employing soliton pulse shortening,” Opt. Lett., 21, 1927-1929 (1996).
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17. T. F. Carruthers, I. N. Duling III, M. Horowitz, and C. R. Menyuk “Dispersion management in a harmonically mode-locked fiber soliton laser,” Opt. Lett., 25, 153-155 (2000).
18. J. W. Lou, T. F. Carruthers, and M. Currie, “4 X 10 GHz mode-locked multiple-wavelength fiber laser,” IEEE photonic tech. Lett., 16, 51-53 (2004).
19. J. D. McKinney, S. Dongsun, D. E. Leaird ,and A. M. Weiner, “Photonically assisted generation of arbitrary millimeter-wave and microwave electromagnetic waveforms via direct space-to-time optical pulse shaping,” J. Lightwave Technol., 21, 3020-3028 (2003).
20. I.L. Budunog˘lu, C. Ülgüdür, B. Oktem, and F. Ö. Ilday, “Intensity noise of mode-locked fiber lasers,” Opt. Lett., 34, 2516-2518 (2009).
21. K. Wu, P. P. Shum, S. Aditya, C. Ouyang, J. H. Wong, H. Q. Lam, and K. E. K. Lee, “Noise conversion from pump to the passively mode-locked fiber lasers at 1.5 μm,” Opt. Lett., 37, 1901-1903 (2012).
22. J. Chen, J. W. Sickler, E. P. Ippen, and F. X. Kärtner, “High repetition rate, low jitter, low intensity noise, fundamentally mode-locked 167 fs soliton Er-fiber laser,” Opt. Lett., 32, 1566–1568 (2007).
23. R. Paschotta, “Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations,” Appl. Phys. B, 79, 163–173 (2004).
24. R. K. Lee, Y. Lai, and B. A. Malomed, “Quantum correlations in bound-soliton pairs and trains in fiber lasers,” Phys. Rev. A, 70, 063817 (2004).
25. R. K. Lee, Y. Lai, and B. A. Malomed, “Photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers,” Opt. Lett., 30, 3084–3086 (2005).
26. S. Y. Wu, W. W. Hsiang, and Y. Lai, “Synchronous-asynchronous laser mode-locking transition,” Phys. Rev. A, 92, 013848 (2015).
27. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron., 40, 1458–1470 (2004).

Chapter 5.
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2. H. G. Weber, R. Ludwig, S. Ferber, C. S. Langhorst, M. Kroh, V. Marembert, C. Boerner, and C. Schubert, “Ultrahigh-speed OTDM-transmission technology,” J. Lightwave Technol., 24, 4616-4627 (2006).
3. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature Letters 450, 1214-1217 (2007).
4. F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J., 2, 719-727 (2010).
5. J. Schröder, T. D. Vo, and B. J. Eggleton, “Repetition-rate-selective, wavelength-tunable mode-locked laser at up to 640 GHz,” Opt. Lett., 34, 3902-3904 (2009).
6. M. Peccianti, A. Pasquazi, Y. Park, B. Little, S.T. Chu, D. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature communications 3, 765 (2012).
7. S.-S. Jyu, L.-G. Yang, C.-Y. Wong, C.-H. Yeh, C.-W. Chow, H.-K. Tsang, and Y. Lai, “250-GHz passive harmonic mode-locked Er-doped fiber laser by dissipative four-wave mixing with silicon-based micro-ring,” IEEE Photonics Journal, 5, 1502107 (2013).
8. L. G. Yang, C. H. Yeh, C. Y. Wong, C. W. Chow, F. G. Tseng, and H. K. Tsang, “Stable and wavelength-tunable silicon-micro-ring-resonator based erbium-doped fiber laser,” Opt. Express, 21, 2869-2874 (2013).
9. S. M. Wang, and Y. Lai, “Up to 400 GHz burst-mode pulse generation from a hybrid harmonic mode-locked Er-doped fibre laser,” Laser Phys. Lett., 14, 025102 (2017).
10. X. M. Tan, H. J. Chen, H. Cui, Y. K. Lv, G. K. Zhao, Z. C. Luo, A. P. Luo, and W. C. Xu, “Tunable and switchable dual-waveband ultrafast fiber laser with 100 GHz repetition-rate,” Opt. Express, 25, 16291-16299 (2017).
11. Y. Liu, Y. Hsu, C. W. Chow, L. G. Yang, C. H. Yeh, Y. Lai, and H. K. Tsang, “110 GHz hybrid mode-locked fiber laser with enhanced extinction ratio based on nonlinear silicon-on-insulator micro-ring-resonator (SOI MRR),” Laser Phys. Lett., 13, 035101 (2016).
12. T. F. Carruthers, I. N. Duling III, M. Horowitz, and C. R. Menyuk, “Dispersion management in a harmonically mode-locked fiber soliton laser,” Opt. Lett., 25, 153-155 (2000).
13. C. J. Luo, S. M. Wang, and Y. Lai, “Bound soliton fiber laser mode-locking without saturable absorption effect,” IEEE Photonics Journal, 8, 1502609 (2016).
14. C. J. Luo, and Y. Lai, “Relative intensity noise of hybrid mode-locked bound soliton fiber laser: Theory and experiment,” Appl. Sci., 8, 1451 (2018).
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16. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Topics Quantum Electron., 6, 1173-1185 (2000).
17. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron., 40, 1458–1470 (2004).

Chapter 6.
1. H. A. Haus, and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron., 29, 983–996 (1993).
2. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron., 40, 1458–1470 (2004).
3. J. Shin, K. Jung, Y. Song, and J. Kim, “Characterization and analysis of timing jitter in normal-dispersion mode-locked Er-fiber lasers with intra-cavity filtering,” Opt. Express, 23, 22898–22906 (2015).
4. W. Chen, Y. Song, K. Jung, M. Hu, C. Wang, and J. Kim, “Few-femtosecond timing jitter from a picosecond all-polarization-maintaining Yb-fiber laser,” Opt. Express, 24, 1347–1357 (2016).
5. L. Gui, and C. Yang, “Soliton molecules with ±π/2, 0, and π phase differences in a graphene-based mode-locked erbium-doped fiber laser,” IEEE Photonics J., 10, 1502609 (2018).
6. R. K. Lee, Y. Lai, and B. A. Malomed, “Quantum correlations in bound-soliton pairs and trains in fiber lasers,” Phys. Rev. A, 70, 063817 (2004).
7. R. K. Lee, Y. Lai, and B. A. Malomed, “Photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers,” Opt. Lett., 30, 3084–3086 (2005).
8. M. Nakazawa, and M. Yoshida, “Scheme for independently stabilizing the repetition rate and optical frequency of a laser using a regenerative mode-locking technique,” Opt. Lett., 33, 1059-1061 (2008)
9. M. Yoshida, K. Yoshida, K. Kasai, and M. Nakazawa, “1.55 μm hydrogen cyanide optical frequency stabilized and 10 GHz repetition-rate stabilized mode-locked fiber laser,” Opt. Express, 24, 24287-24296 (2016).
10. C. H. Yeh , H. Y. Cheng, Y. C. Chang, C. W. Chow, and J. H. Chen, “Silicon-micro-ring resonator-based erbium fiber laser with single-longitudinal-mode oscillation,” IEEE Photonics J., 10, 7103107 (2018).
11. F. Quinlan, C. Williams, S. Ozharar, S. Gee, and P. J. Delfyett, “Self-stabilization of the optical frequencies and the pulse repetition rate in a coupled optoelectronic oscillator,” J. Lightw. Technol., 26, 2571-2577 (2008).
12. M. Akbulut, J. D. Rodriguez, I. Ozdur, F. Quinlan, S. Ozharar, N. Hoghooghi, and P. J. Delfyett, “Measurement of carrier envelope offset frequency for a 10 GHz etalon-stabilized semiconductor optical frequency comb,” Opt. Express, 19, 16851-16865 (2011).
13. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “A highly compact third-order silicon micro-ring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express, 15, 14765-14771 (2007).
14. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science, 332, 555-559 (2011).
15. M. Savanier, R. Kumar, and S. Mookherjea, “Optimizing photon-pair generation electronically using a p-i-n diode incorporated in a silicon micro-ring resonator,” Appl. Phys. Lett., 107, 131101 (2015).
16. P. Dong, R. Shafiiha, S. Liao, H. Liang, N. N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express, 18, 10941-10946 (2010).
17. J. Hong, F. Qiu, X. Cheng, A. M. Spring, and S. Yokoyama, “A high-speed electro-optic triple-micro-ring resonator modulator,” Scientific reports, 7, 4682 (2017).
18. Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express, 23, 3795-3808 (2015).
19. X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett., 37, 3483–3485 (2012).
20. Y. Ding, H. Ou, and C. Peucheret, “Ultrahigh-efficiency apodized grating coupler using fully etched photonic crystals,” Opt. Lett., 38, 2732–2734 (2013).
21. Y. Ding, C. Peucheret, H. Ou, and K. Yvind, “Fully etched apodized grating coupler on the SOI platform with −0.58 dB coupling efficiency,” Opt. Lett., 39, 5348–5350 (2014).
22. L. G. Yang, S. S. Jyu, C. W. Chow, C. H. Yeh, C. Y. Wong, H. K. Tsang, and Y. Lai, “A 110 GHz passive mode-locked fiber laser based on a nonlinear silicon-micro-ring-resonator,” Laser Phys. Lett., 11, 065101 (2014).
23. Y. Liu, Y. Hsu, C. W. Chow, L. G. Yang, C. H. Yeh, Y. Lai, and H. K. Tsang, “110 GHz hybrid mode-locked fiber laser with enhanced extinction ratio based on nonlinear silicon-on-insulator micro-ring-resonator (SOI MRR),” Laser Phys. Lett., 13, 035101 (2016).
24. M. Kues, C. Reimer, B. Wetzel, P. Roztocki, B. E. Little, S. T. Chu, T. Hansson, E. A. Viktorov, D. J. Moss, and R. Morandotti, “Passively mode-locked laser with an ultra-narrow spectral width,” nature photonics, 11, 159-164 (2017).
25. O. A. Egorov, and D. V. Skryabin, “Frequency comb generation in a resonantly pumped exciton-polariton micro-ring resonator,” Opt. Express, 26, 24003-24009 (2018).