无色散光纤信道的非线性演化
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摘要
在单模光纤中由于非线性效应和拉曼增益效应的共同作用,导致光子在各向同性介质中传输时满足非线性薛定谔方程。利用随机微分方程研究了长距离光纤通信中噪声对光纤信道的影响,给出了光纤信道的动力学机理模型。首先在非线性薛定谔方程的基础上引入噪声项,然后利用It觝公式将其整理成极坐标系下标准的随机微分方程组,最后利用福克尔-普朗克(Fokker-Planck)方程得到了光脉冲在光纤信道中的概率密度函数,精细地研究了光纤信道的非线性演化规律。即在加入噪声项的情况下,分析了光纤通信的传输性能指标,得到了概率密度函数。
It is considered that optical fiber channels modeled by the stochastic nonlinear Schrodinger equation and operating at zero dispersion. The statistic characteristic of optical fiber channel with noise was analyzed. In order to find the capacity of the dispersionless optical fiber channel, one first needs to statistically model the communication channel. The Schrodinger equation added noise was modeled. The stochastic differential equations(SDEs) in polar coordinates were built by using It觝 formula. The FokkerPlanck equation of SDEs were presented and the probability density function(PDF) was given. As a result of the Kerr nonlinearity and its interaction with amplified spontaneous emission noise, the amplitude and phase channels correlate with each other and the statistics of the received signal are non-Gaussian.
It is considered that optical fiber channels modeled by the stochastic nonlinear Schrodinger equation and operating at zero dispersion. The statistic characteristic of optical fiber channel with noise was analyzed. In order to find the capacity of the dispersionless optical fiber channel, one first needs to statistically model the communication channel. The Schrodinger equation added noise was modeled. The stochastic differential equations(SDEs) in polar coordinates were built by using It觝 formula. The FokkerPlanck equation of SDEs were presented and the probability density function(PDF) was given. As a result of the Kerr nonlinearity and its interaction with amplified spontaneous emission noise, the amplitude and phase channels correlate with each other and the statistics of the received signal are non-Gaussian.
引文
[1]Qiao Hailong,Jia Weiguo,Liu Baolin,et al.Effect of Ramam gain on the characteristic of soliton propagation[J].Acta Phys,2013,62(10):104212.(in Chinese)乔海龙,贾维国,刘宝林,等.拉曼增益对孤子传输特性的影响[J].物理学报,2013,62(10):104212.
[2]Nga N T H,Sangirov J,Joo G C,et al.10 Gbps/ch fullduplex optical link using a single-fiber channel for signal transimission[J].IEEE Photonics Technology Letters,2014,26(6):609-612.
[3]Hager C,Beygi L,Agrell E,et al.A low-complexity detector for memoryless polarization-multiplexed fiber optical channels[J].IEEE Communications Letters,2014,18(2):368-371.
[4]Beygi L,Agrell E,Johannisson P,et al.A discrete-time model for uncompensated sigle-channel fiber optical links[J].IEEE Transactions on Communications,2012,60(11):3440-3450.
[5]Silva N A,Almeida A J,Pinto A N.Interference in a quantum channel due to classical four-wave mixing in optical fibers[J].IEEE Journal of Quantum Electronics,2012,48(4):472-479.
[6]Zhao Jiasheng.Influences of finite gain bandwidth on evolution of self-Similar pulse propagation in fiber amplifiers[J].Chinese J Lasers,2012,39(8):0802006.(in Chinese)赵佳生.光纤放大器中有限增益带宽对自相似脉冲放大演化的数值研究[J].中国激光,2012,39(8):0802006.
[7]Xiang Lian,Li Hu,Zhang Xiaoping.Modified perturbation method for multi-span nonlinear fiber[J].Chinese J Lasers,2010,37(4):1033-1036.(in Chinese)向练,李虎,张晓萍.多跨距非线性光纤链路中基于微扰理论的优化方法[J].中国激光,2010,37(4):1033-1036.
[8]Li Chao,Zhao Lei,Huang Zhihua et al.Theory study on self-similar pulse in mode-locked fiber laser[J].Chinese J Lasers,2013,40(6):0602017-1-0602017-6.(in Chinese)李超,赵磊,黄志华,等.自相似脉冲在锁模光纤激光器中产生的理论研究[J].中国激光,2013,40(6):0602017.
[9]Ren Liping.Selfsimilar propagation of linearly chirped pulses in fibers with longitudinal gain profile[J].Acta Photonica Sinica,2012,41(8):1004-1008.(in Chinese)任丽平.线性光脉冲在具有纵向增益光纤中的自相似传播研究[J].光子学报,2012,41(8):1004-1008.
[2]Nga N T H,Sangirov J,Joo G C,et al.10 Gbps/ch fullduplex optical link using a single-fiber channel for signal transimission[J].IEEE Photonics Technology Letters,2014,26(6):609-612.
[3]Hager C,Beygi L,Agrell E,et al.A low-complexity detector for memoryless polarization-multiplexed fiber optical channels[J].IEEE Communications Letters,2014,18(2):368-371.
[4]Beygi L,Agrell E,Johannisson P,et al.A discrete-time model for uncompensated sigle-channel fiber optical links[J].IEEE Transactions on Communications,2012,60(11):3440-3450.
[5]Silva N A,Almeida A J,Pinto A N.Interference in a quantum channel due to classical four-wave mixing in optical fibers[J].IEEE Journal of Quantum Electronics,2012,48(4):472-479.
[6]Zhao Jiasheng.Influences of finite gain bandwidth on evolution of self-Similar pulse propagation in fiber amplifiers[J].Chinese J Lasers,2012,39(8):0802006.(in Chinese)赵佳生.光纤放大器中有限增益带宽对自相似脉冲放大演化的数值研究[J].中国激光,2012,39(8):0802006.
[7]Xiang Lian,Li Hu,Zhang Xiaoping.Modified perturbation method for multi-span nonlinear fiber[J].Chinese J Lasers,2010,37(4):1033-1036.(in Chinese)向练,李虎,张晓萍.多跨距非线性光纤链路中基于微扰理论的优化方法[J].中国激光,2010,37(4):1033-1036.
[8]Li Chao,Zhao Lei,Huang Zhihua et al.Theory study on self-similar pulse in mode-locked fiber laser[J].Chinese J Lasers,2013,40(6):0602017-1-0602017-6.(in Chinese)李超,赵磊,黄志华,等.自相似脉冲在锁模光纤激光器中产生的理论研究[J].中国激光,2013,40(6):0602017.
[9]Ren Liping.Selfsimilar propagation of linearly chirped pulses in fibers with longitudinal gain profile[J].Acta Photonica Sinica,2012,41(8):1004-1008.(in Chinese)任丽平.线性光脉冲在具有纵向增益光纤中的自相似传播研究[J].光子学报,2012,41(8):1004-1008.