臺灣博碩士論文加值系統

在本論文中我們從實驗和理論上研究三種腔內梳狀濾波器輔助之高重複率鎖模光纖雷射，包含雙折射光纖濾波器輔助混合鎖模摻鉺光纖雷射、低Q值Fabry-Pérot etalon輔助混合鎖模摻鉺光纖雷射和高Q值Fabry-Pérot etalon輔助混合鎖模摻鉺光纖雷射，利用適當長度之非線性光纖以及梳狀濾波器，透過四波混頻效應和非線性偏振旋轉效應可以達成100 GHz以上之脈衝重複頻率。

在雙折射光纖濾波器輔助混合鎖模摻鉺光纖雷射的部分，我們成功利用7.7公尺之偏振保持光纖產生100 GHz之梳狀濾波效應，配合10 GHz - 25 GHz之相位調變產生重複率高達100 GHz - 400 GHz的burst-mode主被動混合鎖模，並且發現一種類似約分諧波鎖模之現象可以僅僅透過改變200 kHz左右之相位調變頻率，即可使burst-mode主被動混合鎖模之重複頻率在100 GHz和300 GHz之間轉換。在理論上我們利用distributed master equation來模擬此雷射在一般主被動混合鎖模操作態和倍頻鎖模操作態。

在低Q值Fabry-Pérot etalon輔助混合鎖模摻鉺光纖雷射的部分，我們在雷射共振腔內加入finesse = 6之Fabry-Pérot etalon成功在被動鎖模之下產生100 GHz均勻脈衝序列，在主被動混合鎖模之下產生100 GHz burst-mode鎖模，並在此狀態之下研究相位調變強度對於burst pulse的波包寬度之影響，發現burst pulse的波包寬度與相位調變強度二次根號成反比。在理論上利用distributed master equation來驗證實驗結果，在波包寬度對相位調變強度之關係、光譜寬度、雷射頻率分量線寬、脈衝寬度上皆得到與實驗一樣的趨勢，並發現相位調變訊號須加上線性延遲(頻率微調)才能產生穩定鎖模狀態。

在高Q值Fabry-Pérot etalon輔助混合鎖模摻鉺光纖雷射的部分，使用finesse = 100之Fabry-Pérot etalon成功在被動鎖模以及主被動混和鎖模之下產生100 GHz的脈衝序列，並發現在此雷射中相位調變可以提升脈衝序列自相關的對比度。實驗上利用適當強度的相位調變成功提升3.4 dB 的脈衝序列自相關對比度，有助於產生較高品質的高重複率光源。

In this dissertation we have experimentally and theoretically investigated 3 kinds of intra-cavity comb filter assisted high repetition rate mode-locked lasers. The inserted comb filters include the birefringence filter, the low-Q Fabry-Pérot etalon, and the high-Q Fabry-Pérot etalon. By utilizing the highly nonlinear fiber and comb filter, stable mode-locking with the repetition rate up to 100 GHz can be achieved along with the induced four wave mixing effect and the nonlinear polarization rotation effect.

In the birefringence filter assisted hybrid mode-locked Er-doped fiber laser, 100 GHz - 400 GHz burst-mode hybrid mode-locking has been successfully demonstrated by using 10 GHz - 25 GHz phase modulation and a section of 7.7 m polarization-maintaining fiber that acts as a 100 GHz birefringence filter. A new effect analogous to rational harmonic mode-locking has also been discovered, with which the operation state of the laser can be switched between the 100 GHz and 300 GHz burst-mode mode-locking states by merely detuning the modulation frequency around 200 kHz. In simulation, the distributed master equation model is used to investigate the operation of the laser under the hybrid mode-locking state and the repetition rate multiplied mode-locking state.

In the low-Q Fabry-Pérot etalon assisted hybrid mode-locked Er-doped fiber laser, 100 GHz passive mode-locking and 100 GHz burst-mode hybrid mode-locking have been generated by inserting an etalon with the finesse of 6. The dependence of the burst envelope width and the phase modulation depth is found to follow the relationship of inverse square root. The distributed master equation model is used to reveal the underlying physical mechanisms and confirm the observed experimental results. The tendency of most laser characteristics are consistent with the experimental results. In particular, the requirement of modulation frequency detuning for achieving stable burst-mode hybrid mode-locking is clarified.

In the high-Q Fabry-Pérot etalon assisted hybrid mode-locked Er-doped fiber laser, 100 GHz pulse trains are generated under pure passive mode-locking and hybrid mode-locking by using a high-Q etalon with the finesse of 100. It is found that the phase modulation can enhance the auto-correlation contrast of the pulse train by 3.4 dB compared with the pure passive mode-locking case. Better mode-locked pulse trains at high repetition rates can be generated.

摘要 I
ABSTRACT II
CONTENTS III
LIST OF FIGURES V
LIST OF TABLES X
CHAPTER 1. INTRODUCTION 1
1.1. OVERVIEW OF HIGH REPETITION RATE FIBER LASERS 1
1.2. MOTIVATION OF THE RESEARCH 3
1.3. ORGANIZATION OF THE DISSERTATION 4
1.4. REFERENCES 5
CHAPTER 2. THEORY OF HYBRID MODE-LOCKED FIBER LASERS WITH COMB FILTERING 9
2.1. ACTIVE MODE-LOCKING WITH PHASE MODULATION 9
2.2. COMB FILTERS 13
2.2.1. Birefringence filter 13
2.2.2. Etalon 17
2.3. RATIONAL HARMONIC MODE-LOCKING AND REPETITION RATE MULTIPLICATION 19
2.4. NUMERICAL MODEL AND SIMULATION 24
2.4.1. Master equation 24
2.4.2. Split-step Fourier method 26
2.5. REFERENCES 29
CHAPTER 3. CHARACTERISTICS OF HYBRID MODE-LOCKED FIBER LASERS WITH COMB FILTERING 33
3.1. HYBRID MODE-LOCKED ER-DOPED FIBER LASER WITH A BIREFRINGENCE FILTER 33
3.1.1. Laser setup 33
3.1.2. Laser operation states 36
3.1.3. Operation state transition 41
3.1.4. Numerical simulation 43
3.2. HYBRID MODE-LOCKED ER-DOPED FIBER LASER WITH AN AIR-SPACED LOW-Q ETALON 50
3.2.1. Laser setup 50
3.2.2. Laser operation states 52
3.2.3. Numerical simulation 56
3.3. HYBRID MODE-LOCKED ER-DOPED FIBER LASER WITH AN AIR-SPACED HIGH-Q ETALON 65
3.3.1. Laser setup 66
3.3.2. Laser operation states 68
3.3.3. Numerical simulation 74
3.4. REFERENCES 80
CHAPTER 4. CONCLUSION AND FUTURE WORK 81
4.1. UNIQUE CHARACTERISTICS OF HYBRID MODE-LOCKED FIBER LASERS WITH COMB FILTERING 81
4.1.1. Hybrid mode-locking with birefringence filter 81
4.1.2. Hybrid mode-locking with low-Q etalon 82
4.1.3. Hybrid mode-locking with high-Q etalon 83
4.1.4. Summary of the studied lasers with different comb filters 84
4.2. FUTURE WORK 84
4.3. REFERENCES 87
PUBLICATION LIST 89

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