二阶光纤孤子传输特性研究
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摘要
对于光纤孤子的相互作用问题,现有的研究主要集中于基阶孤子间相互作用,而针对高阶孤子间相互作用问题的研究相对较少。本文通过分步傅立叶方法进行数值计算,研究了二阶光孤子在光纤中的传输特性,在总结前人研究成果的基础上得出了一些有益的结论。
在色散位移光纤中,研究了三阶色散影响下,同相和反相二阶孤子之间的互作用,分析了同相和反相二阶孤子对衰变后时域波形和频域频移的变化,发现三阶色散使二阶孤子分裂出一大一小两个不同振幅的基阶孤子,并彼此分离,但孤子对中心频率频移量却减小。通过引入非线性增益控制可以有效抑制二阶孤子间互作用,使孤子保型传输而不发生衰变,但孤子对会偏离原来的时间槽。这种偏离主要是由于三阶色散的影响造成的。因此我们提出周期性改变三阶色散系数的方法,减小了三阶色散的不利影响,抑制了孤子中心频率的频移。
时域相位共轭技术(TPC)能够对群速度色散,自相位调制,脉冲内拉曼散射等效应进行补偿。但是当脉冲宽度较小,或者脉冲中心波长接近零散射波长时,三阶色散效应变得不可忽略。TPC由于无法补偿三阶色散,因此限制了其进一步的应用。在总结前人解析方法的基础上,因此我们提出了一种谱共轭技术(SPC)。它通过在传输距离的中点在频域对脉冲进行共轭变换,即可实现在传输距离的后半程对各阶色散,自相位调制,自陡效应的补偿。将SPC与非线性增益控制结合作用于二阶孤子脉冲序列,获得了较好的整形效果。
For the issue of the interaction of optical solitons, there have been many studies focusing on the interaction of fundamental solitons, but few is on the interaction of higher-order solitions. In this paper, the propagation of two neighboring second-order solitons in single-mode fiber is investigated with Split-step Fourier Algorithm. On the basis of summarizing the reported research results, some useful results were obtained.
Under the influence of third-order dispersion, the interaction of second order solitons in dispersion-shifted fibers is investigated numerically. The characteristics of second order solitions split is studied in the time and frequency domain. It is found that under the influence of third-order dispersion, tow second order solitons are both split and apart from each other. But the frequency shift is decreased. A nonlinear gain and periodical alternation of third-order dispersion can be used to effectively suppress soliton interactions and the effects of third-order dispersion, and stabilize the soliton propagation.
Temporal phase conjugation(TPC) was proposed to compensate for group-velocity dispersion, self-phase modulation, and intrapulse Raman scattering of an optical pulse. However, when the pulse width is sufficiently short or the center wavelength is near the zero-dispersion point, third-order dispersion becomes more prominent and limits the reshaping performance of TPC. We propose to use a spectral phase conjugation(SPC) method that conjugations of the optical pulse in the frequency domain. With this method dispersion of all orders, self-phase modulation, and self-steepening in a fiber are automatically compensated. A hybrid scheme combining SPC and nonlinear gain can offer superior performance.
在色散位移光纤中,研究了三阶色散影响下,同相和反相二阶孤子之间的互作用,分析了同相和反相二阶孤子对衰变后时域波形和频域频移的变化,发现三阶色散使二阶孤子分裂出一大一小两个不同振幅的基阶孤子,并彼此分离,但孤子对中心频率频移量却减小。通过引入非线性增益控制可以有效抑制二阶孤子间互作用,使孤子保型传输而不发生衰变,但孤子对会偏离原来的时间槽。这种偏离主要是由于三阶色散的影响造成的。因此我们提出周期性改变三阶色散系数的方法,减小了三阶色散的不利影响,抑制了孤子中心频率的频移。
时域相位共轭技术(TPC)能够对群速度色散,自相位调制,脉冲内拉曼散射等效应进行补偿。但是当脉冲宽度较小,或者脉冲中心波长接近零散射波长时,三阶色散效应变得不可忽略。TPC由于无法补偿三阶色散,因此限制了其进一步的应用。在总结前人解析方法的基础上,因此我们提出了一种谱共轭技术(SPC)。它通过在传输距离的中点在频域对脉冲进行共轭变换,即可实现在传输距离的后半程对各阶色散,自相位调制,自陡效应的补偿。将SPC与非线性增益控制结合作用于二阶孤子脉冲序列,获得了较好的整形效果。
For the issue of the interaction of optical solitons, there have been many studies focusing on the interaction of fundamental solitons, but few is on the interaction of higher-order solitions. In this paper, the propagation of two neighboring second-order solitons in single-mode fiber is investigated with Split-step Fourier Algorithm. On the basis of summarizing the reported research results, some useful results were obtained.
Under the influence of third-order dispersion, the interaction of second order solitons in dispersion-shifted fibers is investigated numerically. The characteristics of second order solitions split is studied in the time and frequency domain. It is found that under the influence of third-order dispersion, tow second order solitons are both split and apart from each other. But the frequency shift is decreased. A nonlinear gain and periodical alternation of third-order dispersion can be used to effectively suppress soliton interactions and the effects of third-order dispersion, and stabilize the soliton propagation.
Temporal phase conjugation(TPC) was proposed to compensate for group-velocity dispersion, self-phase modulation, and intrapulse Raman scattering of an optical pulse. However, when the pulse width is sufficiently short or the center wavelength is near the zero-dispersion point, third-order dispersion becomes more prominent and limits the reshaping performance of TPC. We propose to use a spectral phase conjugation(SPC) method that conjugations of the optical pulse in the frequency domain. With this method dispersion of all orders, self-phase modulation, and self-steepening in a fiber are automatically compensated. A hybrid scheme combining SPC and nonlinear gain can offer superior performance.
引文
[1] SARUWATARI M. All-optical signal processing for Terabit/second optical transmission[J]. IEEE J. Select. topics. Quantum Electron., 2000,6(6): 1363-1374
[2] LEE J, RYU U C, AHN S J, et al. Enhancement of power conversion efficiency for a L-band EDFA with a secondary pumpong effect in the unpumped EDF section[J]. IEEE Photon. Techonol. Lett., 1999,11(1): 42-44
[3] HASEGAWA A, TAPPERT F. Transmission of stationary nonlinear optical pulse in dispersive fiber[J]. Appl. Phys. Lett., 1973, 23(4): 142-144
[4] MOLLENAUER L F, STOLEN R H, GORDEN J P. Experiment observation of picosecond pulse narrowing solution in optical fiber[J]. Phys. Rev. Lett. , 1982, 3(13):890-894
[5] HASEGAWA A, KODAMA Y. Amplification and reshaping of optical solitons in a glass fiber[J]. Opt. Lett., 1982, 7(6): 285-287
[6] 吴紫标．光纤中的光孤子[J]．大学物理,2000,19(3)：37-42
[7] MOLLENAUER L F, LICHTMAN E, HARVEY G T, NEUBELT M J and NYMAN B M. Demonstration of error-free soliton transmission over more than 1500km at 5Gbit/s, single-channel, and over more than 11000km at 10Gbit/s in two-channel WDM[J]. Elec. Lett., 1992, 28(8): 792-794
[8] MOLLENAUER L F, LICHTMAN E, NEUBELT M J, and HARVE G T. Demonstration, using sliding-frequency guiding filtering, of error-free soliton transmission over more than 20Mm at 10 Gbit/s, single channel, and over more than 13Mm at 20 Gbit/s in a two-channel WDM[J]. Elec. Lett., 1993,29(10): 910-911
[9] NAKAZAWA M, SUZUKI K, YAMADA E, KUBOTA H, KIMURA Y and TAKAYA M. Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains[J]. Elec. Lett. , 1993, 9(9): 729-730
[10] MECOZZI A and HAUS H A. Effect of filters on soliton interactions in wavelength-division-multiplexing systems[J]. Opt. Lett., 1992,17(14): 988-990
[11] ANGELIS C D, WABNITZ S and HAELTERMAN M. Bandwidth limits due to polarization multiplexed soliton interactions[J]. Elec. Lett., 1993,29(17): 1568-1570
[12] EVANGELIDES S G, MOLLENAUER L F, GORDON J P and BERGANO N S. Polarization multiplexing with solitons[J]. Lightwave Technol., 1992,10(1): 28-35
[13] NAKAZAWA M and.KUBOTA H. Physical interpretation of reduction of soliton interaction forces by bandwidth limited amplification[J]. Electron. Lett., 1992,28(10):958-960
[14] AFANASJEV V V. Interpretation of the effect of reduction of soliton interaction by bandwidth-limited amplification[J]. Opt. Lett., 1993,18(10):790-792
[15] UZUNOV I M, MUSCHALL R,GOLLES M etc. Effect of nonlinear gain and filtering on soliton interaction[J].Opt.Commun.,1995,118(5-6):577-580
[16]张介秋,陈砚圃,冯大毅,梁昌洪.用正弦变频滤波器抑制孤子间的相互作用[J].光学学报,2002,22(2):148-152.
[17]DUNG J C,CHI S,and WEN S.Reduction of soliton interactions by zigzag-sliding-frequency guiding filters[J].Opt.Lett.,1995,20(18):1862-1864
[18]MAEDA S,KASHIWA T and FUKAI I.Experimental observation of interaction forces between solitons in optical fibers[J].Opt.Lett.,1986,11(3):174-176
[19]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].天津:天津大学出版社
[20]HASEGAWA A.Eigenvalue Communication[J].J.Lightwave Technol.,1993,11(3):395-399
[21]蔡炬,杨祥林.光孤子通信技术的现状与未来[J].半导体光电,2003,24(1):67-70
[22]殷德京.三阶色散效应下的二阶光孤子裂变分析与控制[J].光电子 激光,2001,12(12):1305-1309
[23]OZYAZICI M S.Interaction of high order solitons[J].Journal of Optoelectronics And Advanced Materials,2004,6(1):71-76
[24]王飞.单模光纤中二阶孤子间相互作用研究[D].西安:陕西师范大学光学专业,2004.
[25]张妍,李康,孔凡敏.脉冲内拉曼散射效应影响下高阶孤子之间的相互作用及其控制[J].量子电子学报,2005,22(5):784-788
[26]方云团,姜春明,杨伟群.三阶孤子传输和相互作用的数值研究[J].激光与红外,2004,34(4):302-304
[27]田慧平,李仲豪,王钢,周国生.飞秒光脉冲间相互作用的数值研究[J].光学学报,2001,21(5):513-517
[28]DESEM C and CHU P L.Soliton interaction in the presence of loss and periodic amplification in optical fibers[J].Opt.Lett.,1987,12(5):349-351
[29]NAKAZAWA M,SAZUKI KMURA Y.Trans-form-limited pulse generation in the gigahertz region from a gain-switched distributed-feedback laser diode using spectral windowing[J].Opt.Lett,1990,15(12):715-717
[30]PIERRE L F and THIERRY G.Reduction of averaged soliton interaction forces by amplitude modulation[J].Opt.Lett.,1993,18(8):583-585
[31]UZUNOV I M,MUSCHALL R,GOLLES M etc.Effect of nonlinear gain and filtering on soliton interaction[J].Opt.Commun.,1995,118(5-6):577-580
[32]DUNG J C,CHI S,and WEN S.Reduction of soliton interactions by zigzag-sliding-frequency guiding filters[J].Opt.Lett.,1995,20(18):1862-1864
[33]WEN S and CHI S.Reduction of the soliton interaction and the Gordon-Haus effect by optical phase conjugation[J].Opt.Lett.,1995,20(9):976-978
[34]曲林杰,曲昕.利用相位共轭与色散配置实现具有大占空比和大放大器间隔的长距离光孤子传输[J].光学学报,1997,17(5):565-571
[35]GOLOVCHENKO T Y E A,PILIPETSKII A N and MENYUK C R.Dispersion-managed soliton interactions in optical fibers[J].Opt.Lett.,1997,22(11):793-795
[36]王晶,苗洪利,杨爱玲,任志君.偏振复用通信系统中偏振模耦合产生的啁啾[J].光学学报,2003,32(1):31-34
[37]CHERNIKOV S V,MAMYSHEV P V.Femto second soliton propagation in fiber with slowly decreasing dispersion[J].J.Opt.Soc.Am.(B),1991,8(8):1633-1641.
[38]OZYAZICI M S.Interaction of higher order solitons[J].Journal of Optoelectromics and Advanced Materials,2004,6(1):71-76.
[39]黄洪涛,聂再清.线双折射光纤与正交极化孤子碰撞的研究[J].中国激光,1999,A26(2):163-170.
[40]MATSUMOTO M,IKEDA M,UDA T,et al.Stable soliton transmission in the system with nonlinear gain[J].J.Lightwave Technol.,1995,13(4):658-665.
[41]GOEDDE C G,KATH W L,KUMAT P.Periodic amplification and conjugation of optical soliton[J].Opt.Lett.,1995,20(12):1365-1367.
[42]曹文华,刘颂豪.孤子效应脉冲压缩中的三阶色散抑制[J].中国激光,1999,26(1):70-74.
[43]YARIV A,FEKETE D,PEPPER D M.Compensation for channel dispersion by nonlinear optical phase conjugation[J].Opt.Lett.,1979,4(2):52-54.
[44]FISHER R A,SUYDAM B R,YEVICK D.optical phase conjugation for time-domain undoing of dispersive self-phase-modulation effects[J].Opt.Lett.,1983,8:611-613.
[45]步扬,王向朝,钱锋.利用相位共轭技术补偿光纤传输信号的失真[J].光电子激光,2002,13(5):538-541.
[46]钱锋,王向朝,王学锋.脉冲相位共轭光研究的进展[J].光电子激光,2001,12(5):536-539.
[47]WEINER A M,LEAIRD D E,REITZE D H,PAEK E G..Femtosecond spectral holography[J].IEEE J.Quantum Electron.,1992,28(10):2251-2261.
[48]CHANG C,SARDESAI H P,WEINER A M.Dispersion-free fiber transmission for femosecond pulses by use of a dispersion-compensating fiber and a programmable pulse shaper[J],opt.Lett.,1998,23(4):283-285.
[49]曹文华,刘颂豪.孤子效应脉冲压缩中的三阶色散抑制[J].中国激光,1999,26(1):70-74.
[50]孙洪波,赵永安.相位共轭法解决光纤传输中的信号失真[J].光电子技术与信息,2003,16(6):41-43.
[2] LEE J, RYU U C, AHN S J, et al. Enhancement of power conversion efficiency for a L-band EDFA with a secondary pumpong effect in the unpumped EDF section[J]. IEEE Photon. Techonol. Lett., 1999,11(1): 42-44
[3] HASEGAWA A, TAPPERT F. Transmission of stationary nonlinear optical pulse in dispersive fiber[J]. Appl. Phys. Lett., 1973, 23(4): 142-144
[4] MOLLENAUER L F, STOLEN R H, GORDEN J P. Experiment observation of picosecond pulse narrowing solution in optical fiber[J]. Phys. Rev. Lett. , 1982, 3(13):890-894
[5] HASEGAWA A, KODAMA Y. Amplification and reshaping of optical solitons in a glass fiber[J]. Opt. Lett., 1982, 7(6): 285-287
[6] 吴紫标．光纤中的光孤子[J]．大学物理,2000,19(3)：37-42
[7] MOLLENAUER L F, LICHTMAN E, HARVEY G T, NEUBELT M J and NYMAN B M. Demonstration of error-free soliton transmission over more than 1500km at 5Gbit/s, single-channel, and over more than 11000km at 10Gbit/s in two-channel WDM[J]. Elec. Lett., 1992, 28(8): 792-794
[8] MOLLENAUER L F, LICHTMAN E, NEUBELT M J, and HARVE G T. Demonstration, using sliding-frequency guiding filtering, of error-free soliton transmission over more than 20Mm at 10 Gbit/s, single channel, and over more than 13Mm at 20 Gbit/s in a two-channel WDM[J]. Elec. Lett., 1993,29(10): 910-911
[9] NAKAZAWA M, SUZUKI K, YAMADA E, KUBOTA H, KIMURA Y and TAKAYA M. Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains[J]. Elec. Lett. , 1993, 9(9): 729-730
[10] MECOZZI A and HAUS H A. Effect of filters on soliton interactions in wavelength-division-multiplexing systems[J]. Opt. Lett., 1992,17(14): 988-990
[11] ANGELIS C D, WABNITZ S and HAELTERMAN M. Bandwidth limits due to polarization multiplexed soliton interactions[J]. Elec. Lett., 1993,29(17): 1568-1570
[12] EVANGELIDES S G, MOLLENAUER L F, GORDON J P and BERGANO N S. Polarization multiplexing with solitons[J]. Lightwave Technol., 1992,10(1): 28-35
[13] NAKAZAWA M and.KUBOTA H. Physical interpretation of reduction of soliton interaction forces by bandwidth limited amplification[J]. Electron. Lett., 1992,28(10):958-960
[14] AFANASJEV V V. Interpretation of the effect of reduction of soliton interaction by bandwidth-limited amplification[J]. Opt. Lett., 1993,18(10):790-792
[15] UZUNOV I M, MUSCHALL R,GOLLES M etc. Effect of nonlinear gain and filtering on soliton interaction[J].Opt.Commun.,1995,118(5-6):577-580
[16]张介秋,陈砚圃,冯大毅,梁昌洪.用正弦变频滤波器抑制孤子间的相互作用[J].光学学报,2002,22(2):148-152.
[17]DUNG J C,CHI S,and WEN S.Reduction of soliton interactions by zigzag-sliding-frequency guiding filters[J].Opt.Lett.,1995,20(18):1862-1864
[18]MAEDA S,KASHIWA T and FUKAI I.Experimental observation of interaction forces between solitons in optical fibers[J].Opt.Lett.,1986,11(3):174-176
[19]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].天津:天津大学出版社
[20]HASEGAWA A.Eigenvalue Communication[J].J.Lightwave Technol.,1993,11(3):395-399
[21]蔡炬,杨祥林.光孤子通信技术的现状与未来[J].半导体光电,2003,24(1):67-70
[22]殷德京.三阶色散效应下的二阶光孤子裂变分析与控制[J].光电子 激光,2001,12(12):1305-1309
[23]OZYAZICI M S.Interaction of high order solitons[J].Journal of Optoelectronics And Advanced Materials,2004,6(1):71-76
[24]王飞.单模光纤中二阶孤子间相互作用研究[D].西安:陕西师范大学光学专业,2004.
[25]张妍,李康,孔凡敏.脉冲内拉曼散射效应影响下高阶孤子之间的相互作用及其控制[J].量子电子学报,2005,22(5):784-788
[26]方云团,姜春明,杨伟群.三阶孤子传输和相互作用的数值研究[J].激光与红外,2004,34(4):302-304
[27]田慧平,李仲豪,王钢,周国生.飞秒光脉冲间相互作用的数值研究[J].光学学报,2001,21(5):513-517
[28]DESEM C and CHU P L.Soliton interaction in the presence of loss and periodic amplification in optical fibers[J].Opt.Lett.,1987,12(5):349-351
[29]NAKAZAWA M,SAZUKI KMURA Y.Trans-form-limited pulse generation in the gigahertz region from a gain-switched distributed-feedback laser diode using spectral windowing[J].Opt.Lett,1990,15(12):715-717
[30]PIERRE L F and THIERRY G.Reduction of averaged soliton interaction forces by amplitude modulation[J].Opt.Lett.,1993,18(8):583-585
[31]UZUNOV I M,MUSCHALL R,GOLLES M etc.Effect of nonlinear gain and filtering on soliton interaction[J].Opt.Commun.,1995,118(5-6):577-580
[32]DUNG J C,CHI S,and WEN S.Reduction of soliton interactions by zigzag-sliding-frequency guiding filters[J].Opt.Lett.,1995,20(18):1862-1864
[33]WEN S and CHI S.Reduction of the soliton interaction and the Gordon-Haus effect by optical phase conjugation[J].Opt.Lett.,1995,20(9):976-978
[34]曲林杰,曲昕.利用相位共轭与色散配置实现具有大占空比和大放大器间隔的长距离光孤子传输[J].光学学报,1997,17(5):565-571
[35]GOLOVCHENKO T Y E A,PILIPETSKII A N and MENYUK C R.Dispersion-managed soliton interactions in optical fibers[J].Opt.Lett.,1997,22(11):793-795
[36]王晶,苗洪利,杨爱玲,任志君.偏振复用通信系统中偏振模耦合产生的啁啾[J].光学学报,2003,32(1):31-34
[37]CHERNIKOV S V,MAMYSHEV P V.Femto second soliton propagation in fiber with slowly decreasing dispersion[J].J.Opt.Soc.Am.(B),1991,8(8):1633-1641.
[38]OZYAZICI M S.Interaction of higher order solitons[J].Journal of Optoelectromics and Advanced Materials,2004,6(1):71-76.
[39]黄洪涛,聂再清.线双折射光纤与正交极化孤子碰撞的研究[J].中国激光,1999,A26(2):163-170.
[40]MATSUMOTO M,IKEDA M,UDA T,et al.Stable soliton transmission in the system with nonlinear gain[J].J.Lightwave Technol.,1995,13(4):658-665.
[41]GOEDDE C G,KATH W L,KUMAT P.Periodic amplification and conjugation of optical soliton[J].Opt.Lett.,1995,20(12):1365-1367.
[42]曹文华,刘颂豪.孤子效应脉冲压缩中的三阶色散抑制[J].中国激光,1999,26(1):70-74.
[43]YARIV A,FEKETE D,PEPPER D M.Compensation for channel dispersion by nonlinear optical phase conjugation[J].Opt.Lett.,1979,4(2):52-54.
[44]FISHER R A,SUYDAM B R,YEVICK D.optical phase conjugation for time-domain undoing of dispersive self-phase-modulation effects[J].Opt.Lett.,1983,8:611-613.
[45]步扬,王向朝,钱锋.利用相位共轭技术补偿光纤传输信号的失真[J].光电子激光,2002,13(5):538-541.
[46]钱锋,王向朝,王学锋.脉冲相位共轭光研究的进展[J].光电子激光,2001,12(5):536-539.
[47]WEINER A M,LEAIRD D E,REITZE D H,PAEK E G..Femtosecond spectral holography[J].IEEE J.Quantum Electron.,1992,28(10):2251-2261.
[48]CHANG C,SARDESAI H P,WEINER A M.Dispersion-free fiber transmission for femosecond pulses by use of a dispersion-compensating fiber and a programmable pulse shaper[J],opt.Lett.,1998,23(4):283-285.
[49]曹文华,刘颂豪.孤子效应脉冲压缩中的三阶色散抑制[J].中国激光,1999,26(1):70-74.
[50]孙洪波,赵永安.相位共轭法解决光纤传输中的信号失真[J].光电子技术与信息,2003,16(6):41-43.