本論文中我們在10 GHz非同步諧波鎖模摻鉺光纖雷射下透過改變調變頻率大小成功演示非同步諧波鎖模與頻率調變震盪態之過渡，同時也利用數值模型模擬在不同調變頻率下雷射的狀態，此外也針對在頻率調變震盪狀態下進行腔外脈衝壓縮的實驗與模擬，結果有很好的吻合性。

In this thesis, we successfully demonstrate the asynchronous harmonic mode-locking and frequency modulation (FM) oscillation transition with increasing detuning frequencies in a 10 GHz hybrid mode-locked Er-doped fiber laser. We also simulate the states of lasing under different detuning frequencies as well as the external pulse compression results under the FM oscillation state. The experimental and simulation results are in good agreement.

摘要 i
Abstract ii
致謝 iii
Contents iv
List of figures and tables vii
List of tables x

Chapter 1　Introduction
1.1　Overview 1
1.2　Motivation of the research 4
1.3　Organization of the thesis 4
Chapter 2　Theories of Mode-locked Fiber Lasers
2.1　Techniques of mode-locking 6
2.2　Active mode-locking 6
2.2.1　Amplitude modulation mode-locking 8
2.2.2　Phase modulation mode-locking and FM oscillation 12
2.3　Passive mode-locking by P-APM mechanism 15
2.4　Asynchronous mode-locking 17
2.5　FM oscillation 21
Chapter 3　Experimental Setup and Results
3.1　Experimental setup 25
3.2　Experimental results 28
3.2.1　Results of synchronous mode-locking 29
3.2.2　Results of asynchronous mode-locking 32
3.2.3　Results of FM oscillation 34
Chapter 4　Theoretical Simulation
4.1　The master equation and numerical method 37
4.2　Simulation of different laser operation regions 41
4.3　Simulation of external chirp compensation 49
Chapter 5　Conclusions
5.1　Summary 52
5.2　Future work 53
Reference 55

[1] A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett., vol. 23, no. 3, pp. 142-144, Aug., 1973.
[2] T. Miya, Y. Terunuma, T. Hosaka and T. Miyashita, “ULTIMATE LOW-LOSS SINGLE-MODE FIBRE AT 1.55 μm,” Electron. Lett., vol. 15, no. 4, pp. 106-108, Feb., 1979.
[3] L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers,” PRL, vol. 45, no. 13, pp. 1095-1098, Sep., 1980.
[4] P. L. Kelley, I. P. Kaminow, G. P. Agrawal, Nonlinear Fiber Optics, 3th ed. San Diego, California: Academic Press, 2001.
[5] E. Desurvire, C. R. Giles, J. R. Simpson and J. L. Zyskind, “ERBIUM-DOPED FIBER AMPLIFIER,” U.S. Patent 5,005,175, Apr. 2, 1991.
[6] R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-Doped Fiber Amplifiers,” IEEE J. Quantum Electron., vol. 33, no. 7, pp. 1049-1056, Jul., 1997.
[7] M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Theoretical and experimental study of harmonically modelocked fiber lasers for optical communication systems,” J. Lightwave Technol., vol. 18, no. 11, pp. 1565-15174, Nov., 2000.
[8] J. Lee, J. Koo, Y. M. Chang, P. Debnath, Y. W. Song, and J. H. Lee, “Experimental investigation on a Q-switched, mode-locked fiber laser based on the combination of active mode locking and passive Q switching,” J. Opt. Soc. Am. B, vol. 29, no.6, pp. 1479-1485, Jun., 2012.
[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, vol. 24, no. 21, pp. 24287-24296, Oct., 2016.
[10] A. M. Weiner, ULTRAFAST OPTICS, Hoboken, NJ: Wiley, 2009.
[11] W.-W. Hsiang, C.-Y. Lin, M.-F. Tien, and Y. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett., vol. 30, no. 18, pp. 2493-2495, Sep., 2005.
[12] L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B, vol. 65, no. 2, pp. 277-294, Aug., 1997.
[13] S.-M Wang, S.-S. Jyu, W.-W. Hsiang, and Y. Lai, “Asynchronous Harmonic Mode Locking in an All-Normal Dispersion Yb-Doped Fiber Laser,” IEEE Photon. J., vol. 5, no. 1, pp. 1500207, Feb., 2013.
[14] 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., vol. 46, no. 3, pp. 299n-299u, Mar., 2010.
[15] W.-W. Hsiang, C.-Y. Lin, N. K. Sooi, and Y. Lai, “Long-term stabilization of a 10 GHz 0.8 ps asynchronously mode-locked Er-fiber soliton laser by deviation-frequency locking,” Opt. Express, vol. 14, no. 5, pp. 1822-1828, Mar., 2006.
[16] S. Yang, E. A. Ponomarev, and X. Bao “40-GHz Transform-Limited Pulse Generation From FM Oscillation Fiber Laser With External Cavity Chirp Compensation,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1631-1633, Jul., 2004.
[17] C.-C. Wen, “Scaling of an Asynchronous Harmonic Mode locked Er-doped Fiber Laser up to 40 GHz Repetition Rate,” M.S. thesis, Inst. EO Eng., NCTU, Hsinchu, Taiwan, 2017.
[18] S.-Y. Wu, W.-W. Hsiang, and Y. Lai, “Synchronous-asynchronous laser mode-locking transition,” Phys. Rev. A, vol. 92, no. 1, pp. 013848, Jul., 2015.
[19] S. Yang and X. Bao, “Experimental observation of excess noise in a detuned phase-modulation,” Phys. Rev. A, vol. 74, no. 3, pp. 033805, Sep., 2006.
[20] S. Longhi, and P. Laporta, “Time-domain analysis of frequency modulation laser oscillation,” Appl. Phys. Lett., vol. 73, no. 6, pp. 720-722, Aug., 1998.
[21] S. Longhi and P. Laporta, “Floquet theory of intracavity laser frequency modulation,” Phys. Rev. A, vol. 60, no. 5, pp. 4016-4028, Nov., 1999.
[22] H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B, vol. 8, no. 10, pp. 2068-2076, Oct., 1991.
[23] H. A. Haus, “Mode-Locking of Lasers,” ‎IEEE J. Sel. Top. Quantum Electron., vol. 6, no. 6, pp. 1173-1185, Nov., 2000.
[24] H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-Pulse Modelocking in Fiber Lasers,” IEEE J. Quantum Electron., vol. 30, no. 1, pp. 200-208, Jan., 1994.
[25] H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wong, “Theory of Soliton Stability in Asynchronous Modelocking,” ‎J. Light. Technol., vol. 14, no. 4, pp. 622-627, Apr., 1996.
[26] C. R. Doerr, H. A. Haus, and E. P. Ippen, “Asynchronous soliton mode locking,” Opt. Lett., vol. 19, no. 23, pp. 1958-1960, Dec., 1994.
[27] S. Longhi, “Experimental observation of spectral oscillations in frequency modulation laser operation,” Phys. Rev. E, vol. 6, no. 4, pp. 047201, Sep., 2001.
[28] S. Longhi, “Spectral oscillations in a frequency-modulation laser operation,” Phys. Rev. E, vol. 63, no. 3, pp. 037201, Feb., 2001.
[29] G. H. Weiss and A. A. Maradudin, “The Baker‐Hausdorff Formula and a Problem in Crystal Physics,” J. Math. Phys., vol. 3, no. 4, pp. 771-777, Jul., 1962.
[30] S.-S. Jyu and Y. Lai, “Repetition frequency pulling effects in asynchronous mode-locking,” Opt. Lett., vol. 38, no. 3, pp. 347-349, Feb., 2013.
[31] S. E. Harris and O. P. McDuff, “Theory of FM Laser Oscillation,” IEEE J. Quantum Electron., vol. 1, no. 6, pp. 245-262, Sep., 1965.