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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。
Based on the modified nonlinear Schrödinger equation, the variational method is used to derive the evolution equations of the Gaussian pulse parameters with the transmission distance under the condition of the high-order dispersion and the fifth-order nonlinearity. The amplitude and pulse width, frequency And the relationship between chirp, pulse width and chirp. Furthermore, the evolution of pulse width with the transmission distance and the evolution of pulse center with the transmission distance are further derived. The high-order dispersion and five Order nonlinearity, pulse width with the transmission distance evolution of the graph. The results show that both the high-order dispersion and the fifth-order nonlinearity in fiber affect the evolution of Gaussian pulse parameters. However, the adiabatic relationship between pulse width and amplitude does not change. Higher-order dispersion broadens the pulse width of the Gaussian pulse. Fifth-order nonlinearity compresses the pulse width of the Gaussian pulse. Their effects on pulse width or initial chirp can be offset to some extent, making it possible to approximate the pulse Transmission.