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Stimulated Brillouin scattering (SBS) currently limits the power scaling of narrow-linewidth amplifiers. To date, several techniques have been employed to suppress SBS. Within these SBS suppressing techniques, the phase modulation technique is a preferable approach to obtaining kilowatt-level narrow-linewidth laser sources. In this manuscript, we numerically investigate the influence of phase modulation signals on linewidth and SBS threshold, and discuss how to choose an appropriate modulation signal for suppressing SBS with less linewidth broadening. Three types of signals are studied, including sinusoidal signal, white noise signal (WNS), and pseudo-random binary sequence signal (PRBS). Signal parameters such as modulation frequency and modulation depth are also optimized. It is found that the linewidth increases linearly with the modulation frequency, and the linewidth is largest for WNS modulation for the same modulation frequency. Specially, the linewidth is approximate to the modulation frequency for PRBS modulation. In the case of sinusoidal modulation, the spectra exhibit a series of discrete sidebands at integer multiples of the modulation frequency while the spectral power density is almost continuous for WNS modulation. In the case of PRBS modulation, the spectra contain periodic features that are distributed as a function of modulation frequency and pattern length. The SBS threshold grows to a maximum at~100 MHz modulation frequency for the case of sinusoidal signal modulation, which can be further increased by increasing the modulation depth. The SBS threshold can be further increased by implementing the cascade sinusoidal signal modulation. When WNS modulation is employed, the SBS threshold increases almost linearly with the modulation frequency and has an S-shaped increase with the modulation depth. For the PRBS modulation, the pattern length has an optimal value for SBS suppressing:the SBS threshold increases almost linearly below a frequency, but keeps stable above that frequency. The PRBSs with longer pattern lengths tend to suppress SBS more effectively in higher modulation frequency regime than those with the shorter ones. In the commonly used 1-2 GHz frequency regimes, the PRBS with a pattern length of 7 provides the best SBS mitigation, and the pattern length should be longer when the frequency is higher than 2 GHz. It should also be noted that the SBS threshold is highest when the modulation depth is close to the half-wave voltage (π). From the aspect of SBS suppression, the PRBS is superior to other two modulation signals, which can achieve higher SBS threshold with less linewidth broadening. The investigation can present a reference for the phase modulation signal designing in the power scaling of the narrow-linewidth fiber amplifiers.
[1] Richardson D J, Nilsson J, Clarkson W A 2010 J. Opt. Soc. Am. B 27 11
[2] Andrés M V, Cruz J L, Díez A, Pérez M P, Delgado P M 2008 Laser Phys. Lett. 5 2
[3] Bufetov I A, Dianov E M 2009 Laser Phys. Lett. 6 6
[4] Kobyakov A, Sauer M, Chowdhury D 2010 Adv. Opt. Photonics 2 1
[5] Wei S Y, Jin D C, Sun R Y, Cao Y, Hou Y B, Wang J, Liu J, Wang P (in Chinese)[魏守宇, 金东臣, 孙若愚, 曹镱, 侯玉斌, 王静, 刘江, 王璞 2016 中国激光 43 0402005]
[6] Bowers M S 2015 SPIE Defense+Security, Maryland, United States, April 20-24, 2015 p0J
[7] Ran Y, Tao R M, Ma P F, Wang X L, Su R T, Zhou P, Si L 2015 Appl. Opt. 54 24
[8] Liao S Y, Gong M L 2007 Laser Optoelectron. Prog. 44 6 (in Chinese)[廖素英, 巩马理 2007 激光与光电子学进展 44 6]
[9] Gray S 2006 In Optical Amplifiers and Their Applications Whistler, Canada, June 25, 2006 pOSuB1
[10] Naderi N A, Flores A, Anderson B M, Dajani I 2016 Opt. Lett. 41 17
[11] Flores A, Dajani I 2014 Conference on Lasers and Electro-Optics California, United States, June 813, 2014 p1
[12] Beier F, Hupel C, Nold J, Kuhn S, Hein S, Ihring J, Sattler B, Haarlammert N, Schreiber T, Eberhardt R, Tnnermann A 2016 Opt. Express 24 6011
[13] Yu C X, Shatrovoy O, Fan T Y 2016 SPIE LASE, San Francisco, United States, March 9, 2016 p972806
[14] Nold J, Strecker M, Liem A, Eberhardt R, Schreiber T, Tnnermann A 2015 European Conference on Lasers and Electro-Optics Munich, Germany, June 21-25, 2015 pCJ114
[15] Anderson B, Flores A, Holten R, Dajani I 2015 Opt. Express 23 27046
[16] Sun Y H, Feng Y J, Li T L, Wang Y S, Ma Y, Tang C, Zhang K (in Chinese)[孙殷宏, 冯昱骏, 李腾龙, 王岩山, 马毅, 唐淳, 张凯 2015 强激光与粒子束 27 071013]
[17] Naderi N A, Dajani I, Flores A 2016 Opt. Lett. 41 1018
[18] Harish A V, Nilsson J 2015 Opt. Express 23 6988
[19] Zeringue C, Dajani I, Naderi S, Moore G T, Robin C 2012 Opt. Express 20 21196
[20] Du W B, Wang X L, Zhu J J, Zhou P, Xu X J, Shu B H 2013 High Power Laser and Particle Beams 25 598 (in Chinese)[杜文博, 王小林, 朱家健, 周朴, 许晓军, 舒博宏 2013 强激光与粒子束 25 598]
[21] Jenkins R B, Sova R M, Joseph R I 2007 J. Lightwave Technol. 25 763
[22] Boyd R W, Rzaewski K, Narum P 1990 Phys. Rev. A. 42 5514
[23] Mungan C E, Rogers S D, Satyan N, White J O 2012 IEEE J. Quant. Electron. 48 1542
[24] Tang C K, Reed G T 1995 Electron. Lett. 31 451
[25] Shimotsu S, Oikawa S, Saitou T, Mitsugi N, Kubodera K, Kawanishi T, Izutsu M 2001 IEEE Photonics Technol. Lett. 13 364
[26] Xie S P, Xu G L (in Chinese)[谢淑平, 许国良 2013 光学学报 33 0206003]
[27] Liu Y F 2008 Ph. D. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese)[刘英繁 2008 博士学位论文(哈尔滨:哈尔滨工业大学)]
[28] Zeringue C, Dajani I, Naderi S, Moore G, Robin C 2012 Opt. Express. 20 21196
[29] Salhi M, Hideur A, Chartier T, Brunel M, Martel G, Ozkul C, Sanches F 2002 Opt. Lett. 27 1294
[30] Ran Y 2015 M. D. Dissertation (Changsha:National University of Defense Technology) (in Chinese)[冉阳 2015 硕士学位论文(长沙:国防科学技术大学)]
[31] Hollenbeck D, Cantrell C 2009 J. Lightwave Technol. 27 2140
[32] Ran Y, Su R T, Ma P F, Wang X L, Zhou P, Si L 2016 Appl. Opt. 55 3809
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[1] Richardson D J, Nilsson J, Clarkson W A 2010 J. Opt. Soc. Am. B 27 11
[2] Andrés M V, Cruz J L, Díez A, Pérez M P, Delgado P M 2008 Laser Phys. Lett. 5 2
[3] Bufetov I A, Dianov E M 2009 Laser Phys. Lett. 6 6
[4] Kobyakov A, Sauer M, Chowdhury D 2010 Adv. Opt. Photonics 2 1
[5] Wei S Y, Jin D C, Sun R Y, Cao Y, Hou Y B, Wang J, Liu J, Wang P (in Chinese)[魏守宇, 金东臣, 孙若愚, 曹镱, 侯玉斌, 王静, 刘江, 王璞 2016 中国激光 43 0402005]
[6] Bowers M S 2015 SPIE Defense+Security, Maryland, United States, April 20-24, 2015 p0J
[7] Ran Y, Tao R M, Ma P F, Wang X L, Su R T, Zhou P, Si L 2015 Appl. Opt. 54 24
[8] Liao S Y, Gong M L 2007 Laser Optoelectron. Prog. 44 6 (in Chinese)[廖素英, 巩马理 2007 激光与光电子学进展 44 6]
[9] Gray S 2006 In Optical Amplifiers and Their Applications Whistler, Canada, June 25, 2006 pOSuB1
[10] Naderi N A, Flores A, Anderson B M, Dajani I 2016 Opt. Lett. 41 17
[11] Flores A, Dajani I 2014 Conference on Lasers and Electro-Optics California, United States, June 813, 2014 p1
[12] Beier F, Hupel C, Nold J, Kuhn S, Hein S, Ihring J, Sattler B, Haarlammert N, Schreiber T, Eberhardt R, Tnnermann A 2016 Opt. Express 24 6011
[13] Yu C X, Shatrovoy O, Fan T Y 2016 SPIE LASE, San Francisco, United States, March 9, 2016 p972806
[14] Nold J, Strecker M, Liem A, Eberhardt R, Schreiber T, Tnnermann A 2015 European Conference on Lasers and Electro-Optics Munich, Germany, June 21-25, 2015 pCJ114
[15] Anderson B, Flores A, Holten R, Dajani I 2015 Opt. Express 23 27046
[16] Sun Y H, Feng Y J, Li T L, Wang Y S, Ma Y, Tang C, Zhang K (in Chinese)[孙殷宏, 冯昱骏, 李腾龙, 王岩山, 马毅, 唐淳, 张凯 2015 强激光与粒子束 27 071013]
[17] Naderi N A, Dajani I, Flores A 2016 Opt. Lett. 41 1018
[18] Harish A V, Nilsson J 2015 Opt. Express 23 6988
[19] Zeringue C, Dajani I, Naderi S, Moore G T, Robin C 2012 Opt. Express 20 21196
[20] Du W B, Wang X L, Zhu J J, Zhou P, Xu X J, Shu B H 2013 High Power Laser and Particle Beams 25 598 (in Chinese)[杜文博, 王小林, 朱家健, 周朴, 许晓军, 舒博宏 2013 强激光与粒子束 25 598]
[21] Jenkins R B, Sova R M, Joseph R I 2007 J. Lightwave Technol. 25 763
[22] Boyd R W, Rzaewski K, Narum P 1990 Phys. Rev. A. 42 5514
[23] Mungan C E, Rogers S D, Satyan N, White J O 2012 IEEE J. Quant. Electron. 48 1542
[24] Tang C K, Reed G T 1995 Electron. Lett. 31 451
[25] Shimotsu S, Oikawa S, Saitou T, Mitsugi N, Kubodera K, Kawanishi T, Izutsu M 2001 IEEE Photonics Technol. Lett. 13 364
[26] Xie S P, Xu G L (in Chinese)[谢淑平, 许国良 2013 光学学报 33 0206003]
[27] Liu Y F 2008 Ph. D. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese)[刘英繁 2008 博士学位论文(哈尔滨:哈尔滨工业大学)]
[28] Zeringue C, Dajani I, Naderi S, Moore G, Robin C 2012 Opt. Express. 20 21196
[29] Salhi M, Hideur A, Chartier T, Brunel M, Martel G, Ozkul C, Sanches F 2002 Opt. Lett. 27 1294
[30] Ran Y 2015 M. D. Dissertation (Changsha:National University of Defense Technology) (in Chinese)[冉阳 2015 硕士学位论文(长沙:国防科学技术大学)]
[31] Hollenbeck D, Cantrell C 2009 J. Lightwave Technol. 27 2140
[32] Ran Y, Su R T, Ma P F, Wang X L, Zhou P, Si L 2016 Appl. Opt. 55 3809
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