介质光波导中非线性薛定谔方程的一种近似解法及其应用

An Approximate Solution of Non-Linear Schrodinger Equation in Optical Wave-Guide and It's Application

为了对长距离无中继光传输系统中距离和容量极限进行估计 ,提出了一种非线性薛定谔方程的近似分段解法 ,该方法可同时考虑自相位调制、群速度色散、SRS和SBS的影响。它将整个传输距离分为两段 ,在第一段只考虑自相位调制作用 ,而第二段只考虑色散的作用 ,频率啁啾是联系两段的纽带 ,从而得出距离带宽与入纤初啁啾的解析关系式 ,将图解法得出的最佳初啁啾带入就可得到距离带宽的简单关系式。对 2 .5Gbps系统采用此法得出最大无中继距离 ,采用分步傅里叶算法验证了这一结果的正确性。

In order to estimate the maximal repeater length in long-haul repeaterless light-wave system, a new approximate method, which is used to solve Non-linear Schrodinger Equation piecewisely, is given in this paper. By this method, self phase modulation (SPM) , group velocity dispersion (GVD) as well as attenuation are considered. The whole transmission distance is treated as two segments, SPM is considered only in the former segment, while GVD is considered in the latter. Frequency chirp is the link between two segments. By which, the relation formula between distance, bandwidth and initial frequency chirp is given. Adding the optimal initial frequency chirp given by graphic method, we get the simple relationship between distance and bandwidth. The maximal repeater length of 2.5Gbps system is obtained by this method. Its validity is also proved by slip-step Fourier algorithm.