解析求解光纤中非稳定扰动的实部和虚部

对线性化后的非线性薛定谔方程进行了求解，导出了光纤中传输的扰动场复振幅的实部和虚部的解析解。这些普适的表达式表明：在传输距离不太长的初期阶段，扰动的虚部和实部以及幅角的演化都对输入条件十分敏感；在传输距离趋于无穷大时扰动电场增益系数趋于渐近值；波数在初始阶段随传输距离变化，只有当传输距离足够大时才趋于一个常数。

Analytical solutions of real and imaginary parts of unstable perturbations propagating in optical fibers

Analytical solutions representing the real and imaginary parts of a perturbation field traveling in optical fibers have been derived for the linearized version of the nolinear Ｓhr-dinger equation. These generalized expressions show that the initial variations of the real and imaginary parts of the perturbation are very sensitive to the input conditions.The analytical results show that when z →∞,the gain coefficient of the perturbation approximates to g ,at the initial period the wave number k varies as-z changes, only when-z is sufficient long does the -k approximate to a constant.