用变分法研究高阶色散和五阶非线性对高斯脉冲在光纤中传输特性的影响

从修正的非线性薛定谔方程出发,采用变分法,导出了在高阶色散和五阶非线性共同作用情况下高斯型脉冲参量随传输距离的演化方程组;求出了振幅与脉宽、频率与啁啾、脉宽与啁啾之间的三个重要约束关系;并进一步得出了脉宽随传输距离演化的解析解和脉冲中心位置随传输距离的演化规律;描绘了高阶色散和五阶非线性下,脉宽随传输距离演化的图形.结果表明:光纤中的高阶色散和五阶非线性都会影响高斯型脉冲各个参量的演化,但脉宽和振幅间的绝热关系并未改变.高阶色散使高斯型脉冲的脉宽展宽,五阶非线性使高斯型脉冲的脉宽压缩,它们对脉宽或初始啁啾的影响可以在一定程度上抵消,从而有可能使脉冲近似实现保形传输.

Variational Study on Influence of High-Order Dispersion and Fifth-Order Nonlinearity on Propagation Properties of Gaussian Pulse in Optical Fibers

The evolution equations for the parameters of Gaussian pulse with propagation distance in optical fibers is derived, considering high-order dispersion and the fifth-order nonlinearity by means of variational method from the modified nonlinear Schrdinger (MNLS) equation. Then, the relations between amplitude and width, frequency and chirp, width and chirp are obtained. The analytical solution about the pulse width and pulse center evolution on the propagation distance is obtained. The graph of the pulse width evolution with transmission distance is described. The results show that the high-order dispersion and fifth-order nonlinearity in fiber will affect Gaussian pulse parameters of evolution, but the adiabatic relation between the pulse width and amplitude has not been changed. High-order dispersion causes the compression of Gaussian pulse width spread, and the fifth-order nonlinearity causes Gaussian pulse width, which may offset the pulse width or the influence of the initial chirp in a certain degree, and thus realize the conformal pulse transmission.