光纤中扰动的小信号增益

从非线性薛定谔方程出发，在小信号近似下，推导并求解了光纤中扰动相位和幅度的演化方程，利用得到的扰动相位及功率增益的表达式，研究了初相位和频率对传输过程中扰动增益的影响。研究表明：扰动的初相位对扰动增益的初值和初始阶段的演化规律有重要影响；取决于扰动初相位，任何一个频率的扰动增益都有可能达到一个共同的最大值；在被认为无调制不稳定的正色散区和扰动频率大于截止频率的负色散区，扰动增益随距离是振荡的；在被认为有调制不稳定的扰动频率小于截止频率的负色散区，频率相同而初相位不同的扰动增益将经历不同形式的演化后趋于同一正值。

Small Signal Gains of Perturbation Propagating in Optical Fibers

Starting from the nonlinear Schr??dinger equation, the evolution equations of the perturbation phase and magnitude in optical fibers have been deduced under small signal approximation. Using the obtained solutions of the perturbation phase and power gain, the influence of gain of perturbation propagation is investigated for different initial phases and frequencies. The results show that at the initial stage, the gain is greatly affected by the perturbation initial phase. Depending on the initial phase, all the unstable perturbations have the chance to claim a common maximum gain that is frequency independent. In the normal dispersion region, as well as in the abnormal region where the perturbation frequency is larger than the cut-off frequency and modulation instability is thought not to occur, the perturbation gains oscillate with the propagation distance. In the abnormal dispersion region when the perturbation frequency is smaller than the cut-off frequency, where modulation instability is thought to occur, the gains of perturbations with different initial phases while with the same frequency will evolve to the same positive value through different ways.