三、五阶非线性光纤中的交叉相位调制非稳研究

从五阶感应电极化强度出发，导出了有损耗单模光纤中同偏振、不同波长的两光波交叉相位调制情况下的五阶非线性折射率；在同时考虑三、五阶非线性的情况下，推导了两光波的慢变振幅满足的耦合非线性薛定谔方程组，并进一步得出了线性化后微扰满足的方程组。分析了三、五阶非线性共存时的交叉相位调制不稳定条件和增益谱。结果表明，与只有三阶非线性的情形相比，在三、五阶非线性共存时，正五阶非线性加强调制不稳定性，使增益谱变宽，峰值变大，负五阶非线性则减弱调制不稳定性；和只有三阶非线性的情况类似，损耗也会使不稳定增益谱的谱宽变窄，谱峰减小；两光波扰动频率的大小关系会影响不稳定增益谱的谱宽、峰值和形状。

Modulation Instability Induced by Cross-Phase Modulation in Fibers with Cubic-Quintic Nonlinearity

tarting from the five-order electric polarization, the five-order nonlinear refractive index induced by cross-phase modulation of two optical waves of different frequencies with the same polarizations in loss single-mode optical fibers is derived. In the case of co-existence of cubic and quintic nonlinearity, the coulped nonlinear SchrAoGdinger equations of the slowly varying envelopes for two optical waves and the linearized nonlinear SchrAoGdinger equations for the perturbations are also derived. The condition and power gain spectra of modulation instability induced by the cross-phase modulation in the case of cubic-quintic nonlinearity are analyzed. The results show that, comparing with that of single cubic nonlinearity, in the case of co-existence of cubic and quintic nonlinearity, the positive quintic nonlinear refractive index intensifies the modulation instability, making the width of the power gain spectra of modulation instability become wider and the peak gain higher, otherwise, suppresses the modulation instability. Similar to the case of cubic nonlinear refractive index, the loss will make the width of the power gain spectra of modulation instability become narrower and the peak gain smaller. The shape, width and peak of the power gain spectra of modulation instability will be influenced by the size relationship of the perturbation frequencies of the two waves.