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High peak power, single frequency nanosecond fiber lasers have aroused the intense interest in their applications such as nonlinear frequency generation, LIDAR, and remote sensing. However, self-phase modulation (SPM) will induce a temporally dependent phase shift φNL (L, t)=|Ap (0, t)|2γLeff, where Ap is the amplitude of pump wave, γ is the nonlinear parameter, and Leff is the effective fiber length. The nonlinear phase shift will broaden the spectral linewidth of pulsed laser, which degrades the coherence of the laser and influences the performance of the laser. In order to obtain laser pulses with narrower linewidth, we can phase-modulate the pulsed laser with a value of-φNL(L,t). Thus, the SPM induced the nonlinear phase shift can be eliminated, and the spectra of pulsed laser can remain during the amplification and transmission in the fiber. Stimulated Brillouin scattering (SBS) has very low threshold and should be taken into consideration in narrow linewidth fiber lasers. The SBS threshold, which is dependent on the linewidth of laser, will be changed at the same time when the SPM is pre-compensated for. Because the SPM pre-compensation will change the linewidth of the pulsed laser. According to three coupled amplitude equations, we numerically analyze the influence of SPM pre-compensation on SBS threshold and spectral characteristics. The stimulation results show that in a master oscillator power amplifier structured fiber laser system, when SPM is completely compensated for (φM(t)=φNL(L,t)), the spectrum of the output pulsed laser can be maintained as that of the laser seed, but the SBS threshold usually decreases. When the SPM is compensated for incompletely (φM(t) φNL(L,t)), the spectral linewidth of the output laser cannot be compressed to that of the laser seed, and the SBS threshold in this situation is lower than the SBS threshold obtained when φM(t)=φNL(L,t). When the SPM is overcompensated for (φM(t) > φNL(L, t)), the spectral linewidth of the output laser cannot be compressed to that of the laser seed either, but the the SBS threshold in this situation is higher than the SBS threshold when φM(t)=φNL(L,t). We also build an experimental setup to verify the feasibility of SPM compensation. In our experiment, the linewidth of the pulsed laser is reduced from 1.4 GHz to 120 MHz when SPM is compensated for by phase modulation. The SBS threshold of the system are measured before and after SPM pre-compensation, and correctness of theoretical simulation is experimentally verified. This analysis method can provide the design guidelines for narrow-linewidth pulsed fiber laser systems.
[1] Liu Y, Liu J, Chen W 2011 Chin. Opt. Lett. 9 090604
[2] Liu A, Norsen M A, Mead R D 2005 Opt. Lett. 30 67
[3] Shi W, Leigh M A, Zong J, Yao Z, Nguyen D T, Chavez-Pirson A, Peyghambarian N 2009 IEEE J. Sel. Top. Quantum Electron. 15 377
[4] Zhu X, Liu J, Bi D, Zhou J, Diao W, Chen W 2012 Chin. Opt. Lett. 10 012801
[5] Zhang X, Diao W, Liu Y, Liu J, Hou X, Chen W 2015 Proc. SPIE 9255 925503
[6] Jiang J, Chang J H, Feng S J, Mao Q H 2010 Acta Phys. Sin. 59 7892 (in Chinese) [蒋建, 常建华, 冯素娟, 毛庆和 2010 59 7892]
[7] Su R, Zhou P, Wang X, Zhang H, Xu X 2012 Opt. Lett. 37 3978
[8] Geng J, Wang Q, Jiang Z, Luo T, Jiang S, Czarnecki G 2011 Opt. Lett. 36 2293
[9] Shi W, Petersen E B, Nguyen D T, Yao Z, Chavez-Pirson A, Peyghambarian N, Yu J 2011 Opt. Lett. 36 3575
[10] Fang Q, Shi W, Petersen E, Khanh K, Chavez-Pirson A, Peyghambarian N 2012 IEEE Photon. Technol. Lett. 24 353
[11] Wu W, Ren T, Zhou J, Du S, Liu X 2012 Chin. Opt. Lett. 10 050604
[12] Li P, Hu H, Yao Y, Chi J, Yang C, Zhao Z, Zhang G, Zhang M, Liang B, Ma C 2015 Proc. SPIE 9656 96560B
[13] Wang X, Jin X, Zhou P, Wang X, Xiao H, Liu Z 2015 Opt. Express 23 4233
[14] Su R, Zhou P, Wang X, Ma Y, Ma P, Xu X, Liu Z 2014 IEEE J. Sel. Top. Quantum Electron. 20 0903913
[15] Kobyakov A, Sauer M, Chowdhury D 2010 Adv. Opt. Photon. 2 1
[16] Zhang L, Zhang D, Shi J, Shi J, Gong W, Liu D 2012 Appl. Phys. B 109 137
[17] Chang L P, Guo S Q, Fan W, Xu H, Ren H L, Wang X C, Chen B 2010 Acta Opt. Sin. 30 1112 (in Chinese) [常丽萍, 郭淑琴, 范薇, 徐红, 任宏亮, 汪小超, 陈柏 2010 光学学报 30 1112]
[18] Liu Y K, Wang X L, Su R T, Ma P F, Zhang H W, Zhou P, Si L 2017 Acta Phys. Sin. 66 234203 (in Chinese) [刘雅坤, 王小林, 粟荣涛, 马鹏飞, 张汉伟, 周朴, 司磊 2017 66 234203]
[19] Wang X, Jin X, Wu W, Zhou P, Wang X, Xiao H, Liu Z 2015 IEEE Photon. Technol. Lett. 27 677
[20] Perry M D, Ditmire T, Stuart B C 1994 Opt. Lett. 19 2149
[21] Bao H, Gu M 2009 Opt. Lett. 34 148
[22] Shi W, Petersen E B, Yao Z, Nguyen D T, Zong J, Stephen M A, Chavez-Pirson A, Peyghambarian N 2010 Opt. Lett. 35 2418
[23] Su R T, Wang X L, Zhou P, Xu X J 2013 Laser Phys. Lett. 10 015105
[24] Washburn B R, Buck J A, Ralph S E 2000 Opt. Lett. 25 445
[25] Zaouter Y, Cormier E, Rigail P, Al E 2007 Proc. SPIE 6453 64530O
[26] Munroe M J, Hamamoto M Y, Dutton D A 2009 Proc. SPIE 7195 71952N
[27] Su R, Zhou P, Ma P, L H, Xu X 2013 Appl. Opt. 52 7331
[28] Xu C, Mollenauer L, Liu X 2002 Electron. Lett. 38 1578
[29] Agrawal G P 2013 Nonlinear Fiber Optics (Fifth Edition) (New York: Academic) pp370-372
[30] Boyd R W, Rzyzewski K, Narum P 1990 Phys. Rev. A 49 5514
[31] Hollenbeck D, Cantrell C D 2009 J. Lightwave Technol. 27 2140
[32] Xu S, Li C, Zhang W, Mo S, Yang C, Wei X, Feng Z, Qian Q, Shen S, Peng M, Zhang Q, Yang Z 2013 Opt. Lett. 38 501
[33] Xu S, Yang Z, Zhang W, Wei X, Qian Q, Chen D, Zhang Q, Shen S, Peng M, Qiu J 2011 Opt. Lett. 36 3708
[34] Su R, Zhou P, Wang X, Xiao H, Xu X 2012 Chin. Opt. Lett. 10 111402
[35] Su R, Zhou P, Wang X, L H, Xu X 2014 Opt. Commun. 316 86
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[1] Liu Y, Liu J, Chen W 2011 Chin. Opt. Lett. 9 090604
[2] Liu A, Norsen M A, Mead R D 2005 Opt. Lett. 30 67
[3] Shi W, Leigh M A, Zong J, Yao Z, Nguyen D T, Chavez-Pirson A, Peyghambarian N 2009 IEEE J. Sel. Top. Quantum Electron. 15 377
[4] Zhu X, Liu J, Bi D, Zhou J, Diao W, Chen W 2012 Chin. Opt. Lett. 10 012801
[5] Zhang X, Diao W, Liu Y, Liu J, Hou X, Chen W 2015 Proc. SPIE 9255 925503
[6] Jiang J, Chang J H, Feng S J, Mao Q H 2010 Acta Phys. Sin. 59 7892 (in Chinese) [蒋建, 常建华, 冯素娟, 毛庆和 2010 59 7892]
[7] Su R, Zhou P, Wang X, Zhang H, Xu X 2012 Opt. Lett. 37 3978
[8] Geng J, Wang Q, Jiang Z, Luo T, Jiang S, Czarnecki G 2011 Opt. Lett. 36 2293
[9] Shi W, Petersen E B, Nguyen D T, Yao Z, Chavez-Pirson A, Peyghambarian N, Yu J 2011 Opt. Lett. 36 3575
[10] Fang Q, Shi W, Petersen E, Khanh K, Chavez-Pirson A, Peyghambarian N 2012 IEEE Photon. Technol. Lett. 24 353
[11] Wu W, Ren T, Zhou J, Du S, Liu X 2012 Chin. Opt. Lett. 10 050604
[12] Li P, Hu H, Yao Y, Chi J, Yang C, Zhao Z, Zhang G, Zhang M, Liang B, Ma C 2015 Proc. SPIE 9656 96560B
[13] Wang X, Jin X, Zhou P, Wang X, Xiao H, Liu Z 2015 Opt. Express 23 4233
[14] Su R, Zhou P, Wang X, Ma Y, Ma P, Xu X, Liu Z 2014 IEEE J. Sel. Top. Quantum Electron. 20 0903913
[15] Kobyakov A, Sauer M, Chowdhury D 2010 Adv. Opt. Photon. 2 1
[16] Zhang L, Zhang D, Shi J, Shi J, Gong W, Liu D 2012 Appl. Phys. B 109 137
[17] Chang L P, Guo S Q, Fan W, Xu H, Ren H L, Wang X C, Chen B 2010 Acta Opt. Sin. 30 1112 (in Chinese) [常丽萍, 郭淑琴, 范薇, 徐红, 任宏亮, 汪小超, 陈柏 2010 光学学报 30 1112]
[18] Liu Y K, Wang X L, Su R T, Ma P F, Zhang H W, Zhou P, Si L 2017 Acta Phys. Sin. 66 234203 (in Chinese) [刘雅坤, 王小林, 粟荣涛, 马鹏飞, 张汉伟, 周朴, 司磊 2017 66 234203]
[19] Wang X, Jin X, Wu W, Zhou P, Wang X, Xiao H, Liu Z 2015 IEEE Photon. Technol. Lett. 27 677
[20] Perry M D, Ditmire T, Stuart B C 1994 Opt. Lett. 19 2149
[21] Bao H, Gu M 2009 Opt. Lett. 34 148
[22] Shi W, Petersen E B, Yao Z, Nguyen D T, Zong J, Stephen M A, Chavez-Pirson A, Peyghambarian N 2010 Opt. Lett. 35 2418
[23] Su R T, Wang X L, Zhou P, Xu X J 2013 Laser Phys. Lett. 10 015105
[24] Washburn B R, Buck J A, Ralph S E 2000 Opt. Lett. 25 445
[25] Zaouter Y, Cormier E, Rigail P, Al E 2007 Proc. SPIE 6453 64530O
[26] Munroe M J, Hamamoto M Y, Dutton D A 2009 Proc. SPIE 7195 71952N
[27] Su R, Zhou P, Ma P, L H, Xu X 2013 Appl. Opt. 52 7331
[28] Xu C, Mollenauer L, Liu X 2002 Electron. Lett. 38 1578
[29] Agrawal G P 2013 Nonlinear Fiber Optics (Fifth Edition) (New York: Academic) pp370-372
[30] Boyd R W, Rzyzewski K, Narum P 1990 Phys. Rev. A 49 5514
[31] Hollenbeck D, Cantrell C D 2009 J. Lightwave Technol. 27 2140
[32] Xu S, Li C, Zhang W, Mo S, Yang C, Wei X, Feng Z, Qian Q, Shen S, Peng M, Zhang Q, Yang Z 2013 Opt. Lett. 38 501
[33] Xu S, Yang Z, Zhang W, Wei X, Qian Q, Chen D, Zhang Q, Shen S, Peng M, Qiu J 2011 Opt. Lett. 36 3708
[34] Su R, Zhou P, Wang X, Xiao H, Xu X 2012 Chin. Opt. Lett. 10 111402
[35] Su R, Zhou P, Wang X, L H, Xu X 2014 Opt. Commun. 316 86
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