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?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? formula. The Fokker-Planck 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.