掺杂光纤中Peregrine孤子的产生和传输
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摘要
基于光脉冲在掺杂光纤中的传输模型,采用分步傅里叶方法对Peregrine孤子在掺杂光纤中的产生和传输进行数值研究。基于Peregrine孤子解,讨论Peregrine孤子在掺杂光纤中的产生和传输;提取Peregrine孤子的峰值脉冲,消去背景波,研究高峰值脉冲的传输特性。结果表明,Peregrine孤子在掺杂光纤中传输时,会激发产生一个在时间和空间上都局域化的高峰值单脉冲,随后迅速分裂产生多个子脉冲;小信号增益越大,饱和能量越高,脉冲峰值强度越强,脉宽越小,激发产生的子脉冲空间间隔也不断减小;消去高峰值脉冲的背景波后,脉冲在掺杂光纤中可以稳定传输,脉宽呈呼吸式周期变化,脉冲强度呈周期性振荡,且脉冲强度的平均值不断增加。
Based on the propagation model of optical pulse in doped fiber,the split-step Fourier method is used to numerically study the generation and the transmission of Peregrine soliton in doped fiber.Based on the Peregrine soliton solution,the generation and the transmission of Peregrine soliton in doped fiber are discussed.The peak pulses of Peregrine soliton are extracted,the background waves are eliminated,and the transmission characteristics of high peak pulses are discussed.The results show that,when it is transmitted in doped fiber,the Peregrine soliton generates a high peak single pulse that is localized temporally and spatially,and then the high peak pulse splits rapidly to produce multiple sub-pulses.The saturated energy and the pulse peak intensity increase with the increasing small signal gain,the pulse width declines with the increasing gain,and the spatial separations of the excited sub-pulses are gradually reduced.When the background wave of the high peak pulse is eliminated,the pulse can be transmitted stably in doped fiber,the pulse width presents breath-type periodic change with periodic oscillation of the pulse intensity,and the average value of the pulse intensity is gradually increasing.
Based on the propagation model of optical pulse in doped fiber,the split-step Fourier method is used to numerically study the generation and the transmission of Peregrine soliton in doped fiber.Based on the Peregrine soliton solution,the generation and the transmission of Peregrine soliton in doped fiber are discussed.The peak pulses of Peregrine soliton are extracted,the background waves are eliminated,and the transmission characteristics of high peak pulses are discussed.The results show that,when it is transmitted in doped fiber,the Peregrine soliton generates a high peak single pulse that is localized temporally and spatially,and then the high peak pulse splits rapidly to produce multiple sub-pulses.The saturated energy and the pulse peak intensity increase with the increasing small signal gain,the pulse width declines with the increasing gain,and the spatial separations of the excited sub-pulses are gradually reduced.When the background wave of the high peak pulse is eliminated,the pulse can be transmitted stably in doped fiber,the pulse width presents breath-type periodic change with periodic oscillation of the pulse intensity,and the average value of the pulse intensity is gradually increasing.
引文
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[30]Yang Guangye,Li Lu,Tian Jinping.Study on transformation of Kuznetsov-Ma soliton to quasi-fundamental soliton based on spectral-filtering method[J].Acta Optica Sinica,2016,36(6):0619002.杨光晔,李禄,田晋平.基于谱过滤方法的Kuznetsov-Ma孤子向准基态孤子转化研究[J].光学学报,2016,36(6):0619002.
[31]Fatome J,Kibler B,Finot C.High quality optical pulse train generator based on solitons on finite background[J].Opt Lett,2013,38(10):1663-1665.
[2]Akhmediev N,Ankiewicz A,Taki M.Waves that appear from nowhere and disappear without a trace[J].Phys Lett A,2008,373(6):675-678.
[3]Chabchoub A,Hoffmann N P,Akhmediev N.Rogue wave observation in a water wave tank[J].Phys Rev Lett,2011,106(20):204502.
[4]Kharif C,Pelinovsky E.Physical mechanisms of the rogue wave phenomenon[J].Eur J Mech B,2003,22(6):603-634.
[5]Solli D R,Ropers C,Koonath P,et al.Optical rogue waves[J].Nat Lett,2007,450(7172):1054-1057.
[6]Arecchi F T,Bortolozzo U,Montina A,et al.Granularity and inhomogeneity are the joint generators of optical rogue waves[J].Phys Rev Lett,2011,106(15):153901.
[7]Bonatto C,Feyereisen M,Barland S,et al.Deterministic optical rogue waves[J].Phys Rev Lett,2011,107(5):053901.
[8]Solli D R,Ropers C,Jalali B.Active control of rogue waves for stimulated supercontinuum generation[J].Phys Rev Lett,2008,101(23):233902.
[9]Zaviyalov A,Egorov O,Iliew R,et al.Rogue waves in mode-locked fiber lasers[J].Phys Rev A,2012,85(1):013828.
[10]Soto-Crespo J M,Grelu P,Akhmediev N.Dissipative rogue waves:Extreme pulses generated by passively mode-locked lasers[J].Phys Rev E,2011,84(1):016604.
[11]Lecaplain C,Grelu P,Soto-Crespo J M,et al.Dissipative rogue waves generated by chaotic pulse bunching in a modelocked laser[J].Phys Rev Lett,2012,108(23):233901.
[12]Runge A F J,Aguergaray C,Broderick N G R,et al.Raman rogue waves in a partially mode-locked fiber laser[J].Opt Lett,2014,39(2):319-322.
[13]Solli D R,Herink G,Jalali B,et al.Fluctuations and correlations in modulation instability[J].Nat Photonics,2012,6(7):463-468.
[14]Dudley J M,Genty G,Dias F,et al.Modulation instability,Akhmediev breathers and continuous wave supercontinuum generation[J].Opt Express,2009,17(24):21497.
[15]Genty G,Dudley J M,Eggleton B J.Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime[J].Appl Phys B,2009,94(2):187-194.
[16]Zhang Jiefang,Lou Jihui.Line optical rogue wave and transmission controlling in inhomogeneous nonlinear wave guides[J].Acta Optica Sinica,2013,33(9):0919001.张解放,楼吉辉.非均匀非线性波导中线光学畸形波及其传输控制[J].光学学报,2013,33(9):0919001.
[17]Dudley J M,Dias F,Erkintalo M,et al.Instabilities,breathers and rogue waves in optics[J].Nat Photonics,2014,8(10):755-764.
[18]Akhmediev N,Korneev V I.Modulation instability and periodic solutions of the nonlinear Schrodinger equation[J].Theor Math Phys,1986,69(2):1089-1093.
[19]Akhmediev N,Eleonskii V M,Kulagin N E.Exact first-order solution of the nonlinear Schrodinger equation[J].Theor Math Phys,1987,72(2):809-818.
[20]Kuznetsov E A.Solitons in a parametrically unstable plasma[J].Sov Phys Dokl,1977,22(9):507-508.
[21]Ma Y C.The perturbed plane-wave solutions of the cubic Schrodinger equation[J].Stud Appl Math,1979,60(1):43-58.
[22]Peregrine D H.Water waves,nonlinear Schrodinger equations and their solutions[J].Soc Ser B Appl Math,1983,25(1):16-43.
[23]Kibler B,Fatome J,Finot C,et al.The Peregrine soliton in nonlinear fibre optics[J].Nat Phys,2010,6(10):790-795.
[24]Hammani K,Kibler B,Finot C,et al.Peregrine soliton generation and breakup in standard telecommunications fiber[J].Opt Lett,2011,36(2):112-114.
[25]Yang G Y,Li L,Jia S T.Peregrine rogue waves induced by the interaction between a continuous wave and a soliton[J].Phys Rev E,2012,85(4):046608.
[26]Yang G Y,Li L,Jia S T,et al.High power pulses extracted from the Peregrine rogue wave[J].Physics,2013,65(2):391-400.
[27]Song Y F,Guo J,Zhao L M,et al.280GHz dark soliton fiber laser[J].Opt Lett,2014,39(2):3484-3487.
[28]Agrawal G.Nonlinear fiber optics[M].Jia Dongfang,Ge Chunfeng,Transl.Beijing:Publishing House of Electronics Industry,2013:31-33.阿戈沃.非线性光纤光学[M].贾东方,葛春风,译.北京:电子工业出版社,2013:31-33.
[29]Duan L,Yang Z Y,Liu C,et al.Optical rogue wave excitation and modulation on a bright soliton background[J].Chin Phys Lett,2016,33(1):010501.
[30]Yang Guangye,Li Lu,Tian Jinping.Study on transformation of Kuznetsov-Ma soliton to quasi-fundamental soliton based on spectral-filtering method[J].Acta Optica Sinica,2016,36(6):0619002.杨光晔,李禄,田晋平.基于谱过滤方法的Kuznetsov-Ma孤子向准基态孤子转化研究[J].光学学报,2016,36(6):0619002.
[31]Fatome J,Kibler B,Finot C.High quality optical pulse train generator based on solitons on finite background[J].Opt Lett,2013,38(10):1663-1665.