非线性色散光纤中信号相位的微扰算法
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摘要
波分复用(WDM)技术和掺铒光纤放大器(EDFA)的引入大大提高了光纤通信系统的传输容量,如今单波长系统的传输速率已高达40Gb／s,单根光纤容量已超过10Tb／s。速率和容量的不断提高使得传统的强度调制-直接检测(IMDD)传输方式越来越不能满足系统的要求。因此,能够充分利用传输带宽、提高传输容量的相位调制方式逐渐成为现代光纤通信领域研究的重点。为了研究相位调制系统中光脉冲在光纤中的演变过程,尤其是载波相位的演变情况,本文针对传输特性方程-非线性薛定谔方程的求解问题进行了深入的研究,将微扰算法应用于相位调制系统中,对脉冲传输过程中相位的演变进行了求解,并设法实现信号幅度和相位的分离,得到了脉冲及相位的半解析解,根据相位的解析式考察了脉冲传输过程中相位的演变情况。包括单脉冲传输的相位演变和多脉冲传输的相位分布。并根据相位分布图分析了各种因素对相位的影响。研究结果可以为高功率大容量光纤传输系统的解析化模拟及相位调制系统的优化设计提供参考。
The application of the technology of Wavelength division multiplexing (WDM) and erbium-doped fiber amplifier (EDFA) has greatly enhanced the transmission capacity of optical fiber communication systems.The bit-rate of single-wavelength-system has now reached as high as 40Gb/s, and the capacity of single-fiber is more than 10Tb/s. Along with the increase of the capacity and speed,the traditional modulation:intensity modulation-direct detection (IMDD) transmission can not meet system requirements.So,the phase modulation which can make full use of transmission bandwidth and increase transmission capacity has become a Research focus in optical communication. In order to study the evolution of the pulse in fiber in phase modulation systems,particularly the evolution of carrier's phase,we make an in-depth study on the solution of the transfer equations-nonlinear Schrodinger equation.Perturbation algorithm will be applied to the phase modulation system. Then we try to achieve the separation of signal amplitude and phase.The semi-analytical solution of the phase is presented, by which the phase transfer process is studied,including evolution of single pulse and distribution of phases of multipulses.And based on the phase distribution we make an analysis about the impact of various factors on the phase.The results can supply references to the analytical simulation of the high_power and large_capacity optical fiber transmission systems and optimization design of the phase modulation systems
The application of the technology of Wavelength division multiplexing (WDM) and erbium-doped fiber amplifier (EDFA) has greatly enhanced the transmission capacity of optical fiber communication systems.The bit-rate of single-wavelength-system has now reached as high as 40Gb/s, and the capacity of single-fiber is more than 10Tb/s. Along with the increase of the capacity and speed,the traditional modulation:intensity modulation-direct detection (IMDD) transmission can not meet system requirements.So,the phase modulation which can make full use of transmission bandwidth and increase transmission capacity has become a Research focus in optical communication. In order to study the evolution of the pulse in fiber in phase modulation systems,particularly the evolution of carrier's phase,we make an in-depth study on the solution of the transfer equations-nonlinear Schrodinger equation.Perturbation algorithm will be applied to the phase modulation system. Then we try to achieve the separation of signal amplitude and phase.The semi-analytical solution of the phase is presented, by which the phase transfer process is studied,including evolution of single pulse and distribution of phases of multipulses.And based on the phase distribution we make an analysis about the impact of various factors on the phase.The results can supply references to the analytical simulation of the high_power and large_capacity optical fiber transmission systems and optimization design of the phase modulation systems
引文
[1]Masahiro Daikoku,Tetsuya Miyazaki Itsuro Morita, et al.8×160 Gb/s WDM field tranmission experiment with single-polarization RZ-DPSK signals and PMD compensator[J]. IEEE Photonics Technology Letters,2006,18 (2):391-393.
[2]Chen Yong, CAO Jihong, Tan Zhongwei, et al.8×10 Gb/s transmission system over 2015 km with dispersion compensation by FBG[J]. Journal of Optoelectronics Lasers (光电 子·激光),2005,16 (8):942-946. (in Chinese)
[3]Pavel Honzatko, Miroslav Karasek 10 and 20 Gb/s all-optical RZ to NRZ modulation format and wavelength converter based on nonlinear optical loop mirror[J].Optics Communications,2010,283:2061-2065
[4]Alberto Bononi, Paolo Serena, Nicola Rossi.Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats [J]. Optical Fiber Technology 2010,16:73-85
[5]Yogesh Chabaa, and R.S. Kaler.Comparison of various dispersion compensation techniques at high bit rates using CSRZ format [J]Optik-International Journal for Light and Electron Optics 2010,121(9):813-817
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[7]Van den Borne D,Fludger C R S,Duthel T,et al.Carrier phase estimation for coherent equalization of 43-Gb/s POLMUXNRZ-DQPSK transmission with 10.7-Gb/s NRZ neighbours.Proc.European Conf.on Opt.Commun.(ECOC)2007,Paper We7.2.3,2007.
[8]FANG Jianping, ZHENG Chunlong, ZHU Jiamin. New variable separation excitation, rectangle like solitons and fractal solitons in the Boiti-Leon-Pempinelli system[J]. Chin Phys Soc,2005,54(07):2990—2995.
[9]J.M.Dye and A.Parker.On bidirectional fifth-order nonlinear evolution equations,Lax pairs,and directionally dependent solitary waves[J].Journal of Mathematical Physics. 2001,(6).
[10]朱加民.高阶非线性薛定谔方程的精确解研究[J]激光与红外。2006(5)：389-391
[11]] Li Shuguang,Xing Guanglong,ZhouGuiyaoetal.Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres[J],Chinese Phys,2006,15(2):437-443
[12]Zhang Guanmao,Zhang XiaoPing. Rapid numerical difference recurrent formula of nonlinear Schr6dinger equation and its application[J].Optics Communications,2007 270:379-383
[13]张冠茂 张晓萍.光脉冲传输模拟的快速数值差分递推算法及其应用研究[J],物理学报,2007,56(5)：2678—2683
[14]Kumar.V Peddanarappagari, MaiteBrandt-Pearce.Volterra series transfer function of single-mode fibers[J].J.Lightwave Technol,1997,15(12):2232-2241.
[15]Kumar.V Peddanarappagari, MaiteBrandt-Pearce.Volterra series approach for optimizing fiber-optic communications system designs [J]. Lightwave Technol. 1998,16(11):2046-2055.
[16]Boxu,Maite Brandt-Pearce.ComParison of FWM-and XPM-induced crosstalk using the Volterra series transfer function method[J],Lightwave Technol,2003,21(1):40-53.
[17]Rick Lind,Richard J.Prazenica,Martin J.Brenner.Estimation nonlinearity using Volterra kernels in feedback with linear models[J].Nonlinear Dynamics,2005,39:3-23
[18]Lou Senyue.A direct perturbation method:Nonlinear Schrodinger Equation with loss[J].Chinese Physics Letter.1999,16(9)659-661
[19]Jong-Hyung Lee. Analysis and Characterization of Fiber Nonlinearities with Deterministic and Stochastic Signal Sources. Electrical Engineering.February 10,2000,pp:30-32
[20]Huiyou Yu,Jiaren Yan.Direct approach of perturbation theory for kink solitons [J].Physics letters A.2006,351:97-100
[21]陈启佳,余仲秋,魏保军,郭靓.非线性色散光纤中光脉冲传输模型的数值计算研究,信息工程大学学报,2006,7(2),pp：197
[22]D.Marcuse,Light Transmission optics [M].Van Nostrand Reinhold, New York, 1982,Chaps.8 and 12
[23]原荣.光纤通信(第二版)[M].北京：电子工业出版社,2006,77-78
[24]GJ. Foschini and C. D. Poole, Statistical theory of polarization dispersion in single-mode fibers[J]. Lightwave Technol.1991 9:1439-1456
[25]G.P.Agrawal,Nonlinear Fiber Optical[M],third ed., San Diego,Academic Press, 2001:42-43
[26]孙山林、张文.偏振模色散对波分复用系统的影响及补偿方案研究[J].光通信技术.2006.4：62-63
[27]刘式适,刘式达.物理学中的非线性方程[M].北京：北京大学出版社,2001.
[28]龚伦训.非线性薛定谔方程的Jacobi椭圆函数解[J].物理学报.2006.55(9)：4414-4419
[29]Yin Yan.Attractors and dimensions for discretizations of a weakly damped Schrodinger equation and a Sine-Gorden equation[J].Nonlinear Anal.1993,20:1417-1452
[30]Fa-yong Zhang,Shu-juan Lu.Long-time behavior of finite difference solutions of a nonlinear Schrodinger equation with weakly damped[J].J.Comput.Math.2001,19,393-406
[31]Xiaoqiong Qi,Xiaoping Zhang.Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations[J]. J.Opt.Soc.Am.B. 2006,23(10):1-8
[32]Hoon Kim,Alan H Gnauck. Experimental inve stigation of the performance limitation of DPSK systems due to nonlinear phase noise [J]. IEEE Photonics Technology Letters,2003,15 (2):320-322.
[33]漆晓琼,张晓萍.高速大容量光纤传输中的微扰理论优化算法[A].中国光学学会2006年学术大会论文摘要集[C],2006
[34]Xing Wei, Xiang Liu. Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion[J]. Optics Letters,2003,28 (23): 2300-2302.
[35]秦曦,陈勇,曹继红,简水生.RZ-DPSK传输系统相位噪声的比较分析[J].光电子激光,2006,17(12)：1482-1486
[36]Keang-Po Ho,Phase-Modulated Optical Communication Systems[M].New York:Springer Science Businness Media,Inc.,2005
[2]Chen Yong, CAO Jihong, Tan Zhongwei, et al.8×10 Gb/s transmission system over 2015 km with dispersion compensation by FBG[J]. Journal of Optoelectronics Lasers (光电 子·激光),2005,16 (8):942-946. (in Chinese)
[3]Pavel Honzatko, Miroslav Karasek 10 and 20 Gb/s all-optical RZ to NRZ modulation format and wavelength converter based on nonlinear optical loop mirror[J].Optics Communications,2010,283:2061-2065
[4]Alberto Bononi, Paolo Serena, Nicola Rossi.Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats [J]. Optical Fiber Technology 2010,16:73-85
[5]Yogesh Chabaa, and R.S. Kaler.Comparison of various dispersion compensation techniques at high bit rates using CSRZ format [J]Optik-International Journal for Light and Electron Optics 2010,121(9):813-817
[6]Charlet QMaaref N,Renaudier J,et al.Transmission of 40Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation. Proc.European Conf.on Opt.Commun.(ECOC)2006,Paper Th4.3.4,2006.
[7]Van den Borne D,Fludger C R S,Duthel T,et al.Carrier phase estimation for coherent equalization of 43-Gb/s POLMUXNRZ-DQPSK transmission with 10.7-Gb/s NRZ neighbours.Proc.European Conf.on Opt.Commun.(ECOC)2007,Paper We7.2.3,2007.
[8]FANG Jianping, ZHENG Chunlong, ZHU Jiamin. New variable separation excitation, rectangle like solitons and fractal solitons in the Boiti-Leon-Pempinelli system[J]. Chin Phys Soc,2005,54(07):2990—2995.
[9]J.M.Dye and A.Parker.On bidirectional fifth-order nonlinear evolution equations,Lax pairs,and directionally dependent solitary waves[J].Journal of Mathematical Physics. 2001,(6).
[10]朱加民.高阶非线性薛定谔方程的精确解研究[J]激光与红外。2006(5)：389-391
[11]] Li Shuguang,Xing Guanglong,ZhouGuiyaoetal.Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres[J],Chinese Phys,2006,15(2):437-443
[12]Zhang Guanmao,Zhang XiaoPing. Rapid numerical difference recurrent formula of nonlinear Schr6dinger equation and its application[J].Optics Communications,2007 270:379-383
[13]张冠茂 张晓萍.光脉冲传输模拟的快速数值差分递推算法及其应用研究[J],物理学报,2007,56(5)：2678—2683
[14]Kumar.V Peddanarappagari, MaiteBrandt-Pearce.Volterra series transfer function of single-mode fibers[J].J.Lightwave Technol,1997,15(12):2232-2241.
[15]Kumar.V Peddanarappagari, MaiteBrandt-Pearce.Volterra series approach for optimizing fiber-optic communications system designs [J]. Lightwave Technol. 1998,16(11):2046-2055.
[16]Boxu,Maite Brandt-Pearce.ComParison of FWM-and XPM-induced crosstalk using the Volterra series transfer function method[J],Lightwave Technol,2003,21(1):40-53.
[17]Rick Lind,Richard J.Prazenica,Martin J.Brenner.Estimation nonlinearity using Volterra kernels in feedback with linear models[J].Nonlinear Dynamics,2005,39:3-23
[18]Lou Senyue.A direct perturbation method:Nonlinear Schrodinger Equation with loss[J].Chinese Physics Letter.1999,16(9)659-661
[19]Jong-Hyung Lee. Analysis and Characterization of Fiber Nonlinearities with Deterministic and Stochastic Signal Sources. Electrical Engineering.February 10,2000,pp:30-32
[20]Huiyou Yu,Jiaren Yan.Direct approach of perturbation theory for kink solitons [J].Physics letters A.2006,351:97-100
[21]陈启佳,余仲秋,魏保军,郭靓.非线性色散光纤中光脉冲传输模型的数值计算研究,信息工程大学学报,2006,7(2),pp：197
[22]D.Marcuse,Light Transmission optics [M].Van Nostrand Reinhold, New York, 1982,Chaps.8 and 12
[23]原荣.光纤通信(第二版)[M].北京：电子工业出版社,2006,77-78
[24]GJ. Foschini and C. D. Poole, Statistical theory of polarization dispersion in single-mode fibers[J]. Lightwave Technol.1991 9:1439-1456
[25]G.P.Agrawal,Nonlinear Fiber Optical[M],third ed., San Diego,Academic Press, 2001:42-43
[26]孙山林、张文.偏振模色散对波分复用系统的影响及补偿方案研究[J].光通信技术.2006.4：62-63
[27]刘式适,刘式达.物理学中的非线性方程[M].北京：北京大学出版社,2001.
[28]龚伦训.非线性薛定谔方程的Jacobi椭圆函数解[J].物理学报.2006.55(9)：4414-4419
[29]Yin Yan.Attractors and dimensions for discretizations of a weakly damped Schrodinger equation and a Sine-Gorden equation[J].Nonlinear Anal.1993,20:1417-1452
[30]Fa-yong Zhang,Shu-juan Lu.Long-time behavior of finite difference solutions of a nonlinear Schrodinger equation with weakly damped[J].J.Comput.Math.2001,19,393-406
[31]Xiaoqiong Qi,Xiaoping Zhang.Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations[J]. J.Opt.Soc.Am.B. 2006,23(10):1-8
[32]Hoon Kim,Alan H Gnauck. Experimental inve stigation of the performance limitation of DPSK systems due to nonlinear phase noise [J]. IEEE Photonics Technology Letters,2003,15 (2):320-322.
[33]漆晓琼,张晓萍.高速大容量光纤传输中的微扰理论优化算法[A].中国光学学会2006年学术大会论文摘要集[C],2006
[34]Xing Wei, Xiang Liu. Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion[J]. Optics Letters,2003,28 (23): 2300-2302.
[35]秦曦,陈勇,曹继红,简水生.RZ-DPSK传输系统相位噪声的比较分析[J].光电子激光,2006,17(12)：1482-1486
[36]Keang-Po Ho,Phase-Modulated Optical Communication Systems[M].New York:Springer Science Businness Media,Inc.,2005