新型高能量超短脉冲光纤光源的研究
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摘要
高能量光纤飞秒光源已被广泛应用于光纤通信、生物科学和激光技术等研究领域。目前获得飞秒光脉冲的主要方法是实现激光器锁模输出。根据谐振腔内不同的色散分布,光纤锁模激光器可分为孤子光脉冲、加宽脉冲和正色散激光器等不同种类。其中,利用正色散的耗散孤子整形技术所得光脉冲的能量最高。为了得到更高能量的飞秒光脉冲,研究人员常利用光放大和压缩相结合的技术,即在压缩前利用光纤放大器对种子光脉冲进行放大及自相似传输。本论文对新型高能量飞秒光源进行了理论和实验研究,主要内容如下:
1.理论推导了超短光脉冲在光纤中传输时所满足的广义非线性薛定谔方程;阐述了求解非线性薛定谔方程的基本方法——快速分步傅里叶变换方法。
2.实验研究了正色散光纤激光器,得到了脉冲宽度为3.29ps、3dB谱宽为60.0nm、中心波长在1550nm、时间带宽积为24.6、具有较大啁啾的抛物线形脉冲。通过增加泵浦功率和调节偏振控制器,得到了脉冲间隔为6.5nm的两个束缚态抛物线光脉冲。通过改变泵浦功率和调整偏振控制器的状态,实验同时得到了脉冲间隔不变的3个4个、5个束缚态自相似光脉冲。
3.理论研究了利用正色散、增益随光纤长度按不同分布函数变化、含三阶色散的光纤放大器产生自相似光脉冲的全过程,利用分离变量方法,得到了同时考虑非线性相移和三阶色散的共同作用时的相位、啁啾和振幅的表达式。结果表明,由于三阶色散的存在,脉冲将失去其自相似特性和线性啁啾频率。
4.利用数值模拟方法,通过非线性相移和三阶色散之间的补偿作用,对发生畸变的脉冲进行压缩,获得了具有较好压缩质量的光脉冲。研究发现,对于较小的三阶色散,存在一个最优的非线性相移与之对应。利用这个最佳值,我们获得了具有最高峰值功率的压缩脉冲。
High energy femtosecond light fiber pulse sources have been extensively applied in optical communication, bioscience, and laser technology and so on. Nowadays, mode-locking technology is the main way to obtain femtosecond pulse. According to cavity dispersion, mode-lock fiber laser can be divided into siliton pulse fiber laser, stretched pulse fiber laser, normal dispersion fiber laser and so on. One can obtain the pulse with highest energy by using the technology of reshape dissipative soliton in normal dispersion regime. In order to produce femtosecond pulse with higher energy, people often need amplify the seed pulse in a fiber amplifier system, then they should compress the pulse in a grating. Using this method one need propagate the seed pulse self-similarly in amplifier before into the compressor. In recent years, it was found that highly chirped parabolic pulse can be produced in a self-similar laser. In this thesis, we theoretically and experimentally study research on new high energy fiber ultrashort pulse light sources. The main contents are as follows:
1. We have theoretically obtained the generalized nonlinear Schr?dinger equation that governs propagation of optical pulse in fiber. We also introduced the standard split-step Fourier method used to solve the pulse propagation equations.
2. We have experimentally observed parabolic pulses with large chirp in a normal dispersion fiber laser. The pulse duration is 3.29 ps, the 3 dB spectrum width is ~ 60.0 nm and the center wavelength is about 1550 nm, so the time bandwidth product is 24.6. By increasing the pump power and carefully adjusting the intra-cavity PCs, we have obtained bound states of two parabolic pulses. These bound states of parabolic pulses are separated by 6.5 ps. Through changing pump power and orienting the polarization controllers, our laser can operate in different states with three, four and five bound pulse operation.
3. We have developed a theoretical treatment for the normal-dispersion optical cubicon fiber amplifier with an arbitrary longitudinal gain profile and with constant gain profile. The expressions of phaseφ( z ,τ), chirpδωand amplitude A( z,τ) of such amplifier are found analytically when the nonlinear phase shifts and the third order dispersion (TOD) are all included. The results showed that the characteristics of self-similarity and linear chirp are lost due to third order dispersion.
4. Using the standard split-step Fourier method, we have also simulated the asymmetric pulse propagation in the compression fiber, and have found that for a definite TOD, there exists an optimal nonlinear phase, in which value, the optimal compression pulse can has a higher peak power.
1.理论推导了超短光脉冲在光纤中传输时所满足的广义非线性薛定谔方程;阐述了求解非线性薛定谔方程的基本方法——快速分步傅里叶变换方法。
2.实验研究了正色散光纤激光器,得到了脉冲宽度为3.29ps、3dB谱宽为60.0nm、中心波长在1550nm、时间带宽积为24.6、具有较大啁啾的抛物线形脉冲。通过增加泵浦功率和调节偏振控制器,得到了脉冲间隔为6.5nm的两个束缚态抛物线光脉冲。通过改变泵浦功率和调整偏振控制器的状态,实验同时得到了脉冲间隔不变的3个4个、5个束缚态自相似光脉冲。
3.理论研究了利用正色散、增益随光纤长度按不同分布函数变化、含三阶色散的光纤放大器产生自相似光脉冲的全过程,利用分离变量方法,得到了同时考虑非线性相移和三阶色散的共同作用时的相位、啁啾和振幅的表达式。结果表明,由于三阶色散的存在,脉冲将失去其自相似特性和线性啁啾频率。
4.利用数值模拟方法,通过非线性相移和三阶色散之间的补偿作用,对发生畸变的脉冲进行压缩,获得了具有较好压缩质量的光脉冲。研究发现,对于较小的三阶色散,存在一个最优的非线性相移与之对应。利用这个最佳值,我们获得了具有最高峰值功率的压缩脉冲。
High energy femtosecond light fiber pulse sources have been extensively applied in optical communication, bioscience, and laser technology and so on. Nowadays, mode-locking technology is the main way to obtain femtosecond pulse. According to cavity dispersion, mode-lock fiber laser can be divided into siliton pulse fiber laser, stretched pulse fiber laser, normal dispersion fiber laser and so on. One can obtain the pulse with highest energy by using the technology of reshape dissipative soliton in normal dispersion regime. In order to produce femtosecond pulse with higher energy, people often need amplify the seed pulse in a fiber amplifier system, then they should compress the pulse in a grating. Using this method one need propagate the seed pulse self-similarly in amplifier before into the compressor. In recent years, it was found that highly chirped parabolic pulse can be produced in a self-similar laser. In this thesis, we theoretically and experimentally study research on new high energy fiber ultrashort pulse light sources. The main contents are as follows:
1. We have theoretically obtained the generalized nonlinear Schr?dinger equation that governs propagation of optical pulse in fiber. We also introduced the standard split-step Fourier method used to solve the pulse propagation equations.
2. We have experimentally observed parabolic pulses with large chirp in a normal dispersion fiber laser. The pulse duration is 3.29 ps, the 3 dB spectrum width is ~ 60.0 nm and the center wavelength is about 1550 nm, so the time bandwidth product is 24.6. By increasing the pump power and carefully adjusting the intra-cavity PCs, we have obtained bound states of two parabolic pulses. These bound states of parabolic pulses are separated by 6.5 ps. Through changing pump power and orienting the polarization controllers, our laser can operate in different states with three, four and five bound pulse operation.
3. We have developed a theoretical treatment for the normal-dispersion optical cubicon fiber amplifier with an arbitrary longitudinal gain profile and with constant gain profile. The expressions of phaseφ( z ,τ), chirpδωand amplitude A( z,τ) of such amplifier are found analytically when the nonlinear phase shifts and the third order dispersion (TOD) are all included. The results showed that the characteristics of self-similarity and linear chirp are lost due to third order dispersion.
4. Using the standard split-step Fourier method, we have also simulated the asymmetric pulse propagation in the compression fiber, and have found that for a definite TOD, there exists an optimal nonlinear phase, in which value, the optimal compression pulse can has a higher peak power.
引文
[1] Tamura K, Haus H A, Ippen E P. Self-starting additive pulse mode-locked erbium fibre ring laser[J]. Electron. Lett., 1992, 28(24), 2226-2228.
[2] Fermann M E, Andrejco M J, Silberberg Y, et al. Generation of pulses shorter than 200 fs from a passively mode-locked Er fiber laser[J]. Opt. Lett., 1993, 18(1): 48-50.
[3] Andy C, William H R, and Frank W W. All-normal-dispersion femtosecond fiber laser with pulse energyabove 20 nJ[J]. Opt. Lett., 2007, 32(16):2408-2410.
[4] McFerran J J, Nenadovic L, Swann W C, et al. A passively mode-locked fiber laser at 1.54μm with a fundamental repetition frequency reaching 2 GHz[J]. Opt. Exp., 2007, 15(20):13155-13166.
[5]王肇颖,王永强,林冉等.亚皮秒自起振被动锁模掺铒光纤激光器[J].光电子·激光,2004,15(3):295-298.
[6]赵德双,刘永智,王秉中等.飞秒被动锁模环形腔掺Er 3+光纤激光器[J].应用光学,2006,27(3):220-224.
[7] Tu C H, Guo W G, Li Y N, et al. Stable multiwavelength and passively mode- locked Yb-doped fiber laser based on nonlinear polarization rotation[J]. Optics Communications, 2007, 280(2):448–452.
[8] Souza E A D,Soccolich C E,Pleibel W,et al. Saturable absorber Mode-locked polarisation maintaining erbium-doped fibre laser [J]. Electron. Lett.,1992, 29(5):447-449.
[9] Duling I N. Sub-picosecond all-fiber erbium laser[J]. Electron. Lett., 1991, 27(6): 544-545.
[10] Richardson D J, Laming R I, Payne D N, et al. 320 fs soliton generation with passively modelocked erbium fiber laser[J]. Electron. Lett., 1991, 27(9): 730-732.
[11] Yoshida E, Kimura Y, and Nakazawa M. Laser diode-pumped femtosecond erbium-doped fiber laser with a sub-ring cavity for repetition rate control[J]. Appl. Phys. Lett., 1992, 60(8): 932-934.
[12] Fermann M, and Weiner A. Poster paper at the Ultrafast Phenomena Conference, June 6-12 , 1992, Antibes, France.
[13] Stolen R H, Botineau J, and Ashkin A. Intensity discrimination of optical pulses with birefringent filters[J]. Opt. Lett., 1982, 7(10): 512-514.
[14] Hofer M, Fermann M E, F. Haberl, et al. Mode locking with cross-phase and self-phase modulation[J]. Opt. Lett., 1991, 16(7): 502-504.
[15] Kafka J D, Baer T, and Hall D W. Modelocked erbium-doped fiber laser with soliton pulse shaping[J]. Opt. Lett., 1989, 14(22): 1269-1271.
[16] Fermann M E, Andrejco M J, Stock M L, Silberberg Y, Weiner A M. In OSA Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington DC, 1992), Paper PD 16
[17] Tomlinson W J, Stolen R J, Shank C V J. Compression of optical pulses chirped by self-phase modulation in fibers[J]. Opt. Soc. Am. B, 1984, 1(2):139-149.
[18] Tamura K, Nelson L E, Haus H A, et al. Soliton versus nonsoliton operation of fiber ring lasers[J]. Appl. Phys. Lett., 1994, 64(2), 149-159.
[19] Menyuk C R, Levi D, and Winternitz P. Self-similarity in transient stimulated Raman scattering[J]. Phys. Rev. Lett., 1992, 69(21): 3048-3051.
[20] Sunghyuck A and Sipe J E. Universality in the dynamics of phase grating formation in optical fibers[J]. Opt. Lett.,1991,16(19):1478-1480.
[21] Monro T M,Millar P D,Poladian L et al. Self-similar and evolution of self-written waveguides[J]. Opt. Lett.,1998,23(4):268-270.
[22] Marin S, Mordechai S, and Curtis R M. Self-similar and fractals in soliton-supporting systems[J]. Pys. Rev. E.,2000,61(2):1048-1051.
[23] Anderson D, Desaix M, Karlsson M, et al. Wave-breaking-free pulses in nonlinear-optical fibers[J]. J. Opt. Soc. Am. B 1993, 10(7): 1185-1190.
[24] Ilday F ? ,Buckley J R,Clark W G,et al. Self-Similar Evolution of Parabolic Pulses in a Laser[J]. Phy. Rev. Lett.,2004,92(21):213902-1-4.
[25] Billet C, Dudley J M, Joly N, et al. Intermediate asymptotic evolution and photonic bandgap fiber compression of optical similaritons around 1550 nm[J]. Opt. Exp., 2005, 13(9): 3236–3241.
[26] Dudley J M, Finot C, Richardson D J, et al. Self-similarity in ultrafast nonlinear optics[J]. Nature Physics, 2007, 3, 597–603.
[27] Fermann M E, Kruglov V I, Thomsen B C, et al. Self-similar propagation and amplification of parabolic in optical fibers[J]. Phys. Rev. Lett., 2000, 84(26): 6010–6013.
[28] Kruglov V I, Peacock A C, Dudley J M, et al. Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers[J]. Opt. Lett. 2000, 25(24): 1753–1755.
[29] Logvin Y, Kalosha V P, and Anis H. Third-order dispersion impact on mode-locking regimes of By-doped fiber laser with photonic band gap fiber for dispersion compensation[J]. Opt. Exp., 2007, 15(3): 985–991.
[30] Zhou S, Kuznetsova L, Chong A, et al. Compensation of nonlinear-phase shifts with third-order dispersion in short-pulse fiber amplifiers[J]. Opt. Exp., 2005, 13(13): 4869-4877.
[31] Shah L, Liu Z, Hartl I, et al. High energy femtosecond Yb cubicon fiber amplifier[J]. Opt. Exp., 2005, 13(12): 4717–4722.
[32] Chong A, Kuznetsova L, and Wise F W. Theoretical optimization of nonlinear chirped-pulse fiber amplifiers[J]. J. Opt. Soc. Am. B, 2007, 24(8), 1815-1823.
[33] Fork R L, Martinez O E, and Gordon J P. Negative dispersion using pairs of prisms[J]. Opt. Lett., 1984, 9(5): 150-152.
[34] E. B. Treacy. Optical pulse compression with diffraction gratings[J]. J. Quantum Electron. 1969, 5(9): 454-458.
[35] Szipocs R, Ferencz K, Spielmann C, et al. Chirped multilayer coatings for broadband dispersion control in femtosecond lasers[J]. Opt. Lett., 1994, 19(3): 201-203.
[36] Martinez O E, Fork R L, and Gordon J P. Theory of passively mode-locked laser including self-phase modulation and group-velocity dispersion[J]. Opt. Lett., 1984, 9(5): 156-158.
[37] Haus H A, Fujimoto J G, and Ippen E P. Analytic theory of additive pulse and Kerr lens mode locking[J]. J. Quantum Electron. 1992, 28(10): 2086-2096.
[38] Proctor B, Westwig E, and Wise F. Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion[J]. Opt. Lett., 1993, 18(19): 1654-1656.
[39] Kelly S M J. Characteristic sideband instability of periodically amplified average soliton[J]. Electron. Lett., 1992, 28(8): 806-807.
[40] Buckley J R, Wise F W, Ilday F O, et al. Femtosecond fiber lasers with pulse energiesabove 10nJ[J]. Opt. Lett., 2005, 30(14): 1888-1890.
[41] Lim H, Ilday F O, and Wise F W. Femtosecond ytterbium fiber laser with photonic crystal fiber for dispersion control[J]. Opt. Exp. 2002, 10(25): 1497-1502.
[42] Avdkhin A V, Popov S W, and Taylor J R, Totally fiber integrated, figure-of-eight, femtosecond source at 1065 nm[J]. Opt. Exp. 2003, 11(3): 265-269.
[43] Hartl I, Imeshev G, Dong L. Ultra-compact dispersion compensated fem-tosecond fiber oscillators and amplifiers[J]. Conference on Lasers and Electro-Optics 2005, Baltimore, MD, paper CThG1.
[44] Buckley J, Chong A, Zhou S, et al. Stabilization of high-energy femtosecond ytterbium fiber lasers by use of a frequency filter[J]. J. Opt. Soc. Am. B, 2007, 24(8):1803-1806
[45] Chong A, Buckley J, Renninger W, et al. All-normal-dispersion femtosecond fiber laser[J]. Opt. Exp., 2006, 14(21): 10095–10100.
[46] Andy C, William H R, and Frank W W. All-normal-dispersion femtosecond fiber laser with pulse energyabove 20 nJ[J]. Opt. Lett.,2007,32(16):2408-2410
[47] Andy C, William H R, and Frank W W. Properties of normal-dispersion femtosecond fiber lasers[J]. Opt. Soc. Am. B,2008,25(2):140-148.
[48] Lei T,Tu C H,Lu F Y, Deng Y X and Li E B. Numerical study on self-similar pulses in mode-locking fiber laser by coupled Ginzburg- Landau equation model[J]. Opt. Exp., 2009,17(2):585-591.
[49] Bale B G , NathanKutz J , and Frank W. Analytic theory of self-similar mode-locking[J]. Opt. Lett., 2009, 33(9): 911-913.
[50] Agrawal G P著,贾东方,余震虹等译.非线性光纤光学原理及应用[M].北京,电子工业出版社,2002.
[51] Mamyshev P V and Chernikov S V. Ultra-short pusle propagation in optical fiber[J]. J. Opt. Soc. Am.B, 1990, 15(19): 1076-1078.
[52] Fleck J A, Morris J R, and Feit M D. Time-dependent propagation of high energy laser beams through the atomsphere[J]. Appl. Phys., 1976, 10(2): 129-160.
[53] Grelu Ph, and Akhmediev N. Group interactions of dissipative solitons in a laser cavity: the case 2+1[J]. Opt. Exp. 2004, 12(14): 3184-3189.
[2] Fermann M E, Andrejco M J, Silberberg Y, et al. Generation of pulses shorter than 200 fs from a passively mode-locked Er fiber laser[J]. Opt. Lett., 1993, 18(1): 48-50.
[3] Andy C, William H R, and Frank W W. All-normal-dispersion femtosecond fiber laser with pulse energyabove 20 nJ[J]. Opt. Lett., 2007, 32(16):2408-2410.
[4] McFerran J J, Nenadovic L, Swann W C, et al. A passively mode-locked fiber laser at 1.54μm with a fundamental repetition frequency reaching 2 GHz[J]. Opt. Exp., 2007, 15(20):13155-13166.
[5]王肇颖,王永强,林冉等.亚皮秒自起振被动锁模掺铒光纤激光器[J].光电子·激光,2004,15(3):295-298.
[6]赵德双,刘永智,王秉中等.飞秒被动锁模环形腔掺Er 3+光纤激光器[J].应用光学,2006,27(3):220-224.
[7] Tu C H, Guo W G, Li Y N, et al. Stable multiwavelength and passively mode- locked Yb-doped fiber laser based on nonlinear polarization rotation[J]. Optics Communications, 2007, 280(2):448–452.
[8] Souza E A D,Soccolich C E,Pleibel W,et al. Saturable absorber Mode-locked polarisation maintaining erbium-doped fibre laser [J]. Electron. Lett.,1992, 29(5):447-449.
[9] Duling I N. Sub-picosecond all-fiber erbium laser[J]. Electron. Lett., 1991, 27(6): 544-545.
[10] Richardson D J, Laming R I, Payne D N, et al. 320 fs soliton generation with passively modelocked erbium fiber laser[J]. Electron. Lett., 1991, 27(9): 730-732.
[11] Yoshida E, Kimura Y, and Nakazawa M. Laser diode-pumped femtosecond erbium-doped fiber laser with a sub-ring cavity for repetition rate control[J]. Appl. Phys. Lett., 1992, 60(8): 932-934.
[12] Fermann M, and Weiner A. Poster paper at the Ultrafast Phenomena Conference, June 6-12 , 1992, Antibes, France.
[13] Stolen R H, Botineau J, and Ashkin A. Intensity discrimination of optical pulses with birefringent filters[J]. Opt. Lett., 1982, 7(10): 512-514.
[14] Hofer M, Fermann M E, F. Haberl, et al. Mode locking with cross-phase and self-phase modulation[J]. Opt. Lett., 1991, 16(7): 502-504.
[15] Kafka J D, Baer T, and Hall D W. Modelocked erbium-doped fiber laser with soliton pulse shaping[J]. Opt. Lett., 1989, 14(22): 1269-1271.
[16] Fermann M E, Andrejco M J, Stock M L, Silberberg Y, Weiner A M. In OSA Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington DC, 1992), Paper PD 16
[17] Tomlinson W J, Stolen R J, Shank C V J. Compression of optical pulses chirped by self-phase modulation in fibers[J]. Opt. Soc. Am. B, 1984, 1(2):139-149.
[18] Tamura K, Nelson L E, Haus H A, et al. Soliton versus nonsoliton operation of fiber ring lasers[J]. Appl. Phys. Lett., 1994, 64(2), 149-159.
[19] Menyuk C R, Levi D, and Winternitz P. Self-similarity in transient stimulated Raman scattering[J]. Phys. Rev. Lett., 1992, 69(21): 3048-3051.
[20] Sunghyuck A and Sipe J E. Universality in the dynamics of phase grating formation in optical fibers[J]. Opt. Lett.,1991,16(19):1478-1480.
[21] Monro T M,Millar P D,Poladian L et al. Self-similar and evolution of self-written waveguides[J]. Opt. Lett.,1998,23(4):268-270.
[22] Marin S, Mordechai S, and Curtis R M. Self-similar and fractals in soliton-supporting systems[J]. Pys. Rev. E.,2000,61(2):1048-1051.
[23] Anderson D, Desaix M, Karlsson M, et al. Wave-breaking-free pulses in nonlinear-optical fibers[J]. J. Opt. Soc. Am. B 1993, 10(7): 1185-1190.
[24] Ilday F ? ,Buckley J R,Clark W G,et al. Self-Similar Evolution of Parabolic Pulses in a Laser[J]. Phy. Rev. Lett.,2004,92(21):213902-1-4.
[25] Billet C, Dudley J M, Joly N, et al. Intermediate asymptotic evolution and photonic bandgap fiber compression of optical similaritons around 1550 nm[J]. Opt. Exp., 2005, 13(9): 3236–3241.
[26] Dudley J M, Finot C, Richardson D J, et al. Self-similarity in ultrafast nonlinear optics[J]. Nature Physics, 2007, 3, 597–603.
[27] Fermann M E, Kruglov V I, Thomsen B C, et al. Self-similar propagation and amplification of parabolic in optical fibers[J]. Phys. Rev. Lett., 2000, 84(26): 6010–6013.
[28] Kruglov V I, Peacock A C, Dudley J M, et al. Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers[J]. Opt. Lett. 2000, 25(24): 1753–1755.
[29] Logvin Y, Kalosha V P, and Anis H. Third-order dispersion impact on mode-locking regimes of By-doped fiber laser with photonic band gap fiber for dispersion compensation[J]. Opt. Exp., 2007, 15(3): 985–991.
[30] Zhou S, Kuznetsova L, Chong A, et al. Compensation of nonlinear-phase shifts with third-order dispersion in short-pulse fiber amplifiers[J]. Opt. Exp., 2005, 13(13): 4869-4877.
[31] Shah L, Liu Z, Hartl I, et al. High energy femtosecond Yb cubicon fiber amplifier[J]. Opt. Exp., 2005, 13(12): 4717–4722.
[32] Chong A, Kuznetsova L, and Wise F W. Theoretical optimization of nonlinear chirped-pulse fiber amplifiers[J]. J. Opt. Soc. Am. B, 2007, 24(8), 1815-1823.
[33] Fork R L, Martinez O E, and Gordon J P. Negative dispersion using pairs of prisms[J]. Opt. Lett., 1984, 9(5): 150-152.
[34] E. B. Treacy. Optical pulse compression with diffraction gratings[J]. J. Quantum Electron. 1969, 5(9): 454-458.
[35] Szipocs R, Ferencz K, Spielmann C, et al. Chirped multilayer coatings for broadband dispersion control in femtosecond lasers[J]. Opt. Lett., 1994, 19(3): 201-203.
[36] Martinez O E, Fork R L, and Gordon J P. Theory of passively mode-locked laser including self-phase modulation and group-velocity dispersion[J]. Opt. Lett., 1984, 9(5): 156-158.
[37] Haus H A, Fujimoto J G, and Ippen E P. Analytic theory of additive pulse and Kerr lens mode locking[J]. J. Quantum Electron. 1992, 28(10): 2086-2096.
[38] Proctor B, Westwig E, and Wise F. Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion[J]. Opt. Lett., 1993, 18(19): 1654-1656.
[39] Kelly S M J. Characteristic sideband instability of periodically amplified average soliton[J]. Electron. Lett., 1992, 28(8): 806-807.
[40] Buckley J R, Wise F W, Ilday F O, et al. Femtosecond fiber lasers with pulse energiesabove 10nJ[J]. Opt. Lett., 2005, 30(14): 1888-1890.
[41] Lim H, Ilday F O, and Wise F W. Femtosecond ytterbium fiber laser with photonic crystal fiber for dispersion control[J]. Opt. Exp. 2002, 10(25): 1497-1502.
[42] Avdkhin A V, Popov S W, and Taylor J R, Totally fiber integrated, figure-of-eight, femtosecond source at 1065 nm[J]. Opt. Exp. 2003, 11(3): 265-269.
[43] Hartl I, Imeshev G, Dong L. Ultra-compact dispersion compensated fem-tosecond fiber oscillators and amplifiers[J]. Conference on Lasers and Electro-Optics 2005, Baltimore, MD, paper CThG1.
[44] Buckley J, Chong A, Zhou S, et al. Stabilization of high-energy femtosecond ytterbium fiber lasers by use of a frequency filter[J]. J. Opt. Soc. Am. B, 2007, 24(8):1803-1806
[45] Chong A, Buckley J, Renninger W, et al. All-normal-dispersion femtosecond fiber laser[J]. Opt. Exp., 2006, 14(21): 10095–10100.
[46] Andy C, William H R, and Frank W W. All-normal-dispersion femtosecond fiber laser with pulse energyabove 20 nJ[J]. Opt. Lett.,2007,32(16):2408-2410
[47] Andy C, William H R, and Frank W W. Properties of normal-dispersion femtosecond fiber lasers[J]. Opt. Soc. Am. B,2008,25(2):140-148.
[48] Lei T,Tu C H,Lu F Y, Deng Y X and Li E B. Numerical study on self-similar pulses in mode-locking fiber laser by coupled Ginzburg- Landau equation model[J]. Opt. Exp., 2009,17(2):585-591.
[49] Bale B G , NathanKutz J , and Frank W. Analytic theory of self-similar mode-locking[J]. Opt. Lett., 2009, 33(9): 911-913.
[50] Agrawal G P著,贾东方,余震虹等译.非线性光纤光学原理及应用[M].北京,电子工业出版社,2002.
[51] Mamyshev P V and Chernikov S V. Ultra-short pusle propagation in optical fiber[J]. J. Opt. Soc. Am.B, 1990, 15(19): 1076-1078.
[52] Fleck J A, Morris J R, and Feit M D. Time-dependent propagation of high energy laser beams through the atomsphere[J]. Appl. Phys., 1976, 10(2): 129-160.
[53] Grelu Ph, and Akhmediev N. Group interactions of dissipative solitons in a laser cavity: the case 2+1[J]. Opt. Exp. 2004, 12(14): 3184-3189.