【摘要】 基于异向介质中包一到三阶非线性色散的非归一化扩展非线性传输方程,利用德鲁德电磁模型和线性稳定性分析法,导出了调制不稳定的色散关系和增益谱.以实际单位形式计算和讨论了传输方程系数、正负折射区及自聚焦和自散焦情况下调制不稳定增益谱随归一化角频率的变化关系.结果表明:随归一化频率增加,负折射区在自聚焦时的增益谱谱宽和谱峰都先增加再减为零;负折射区在自散焦时调制不稳定只出现在禁带附近,且谱宽和谱峰都单调减小.正折射区调制不稳定只出现在自聚焦情形,且谱宽一直增加,而谱峰先减小后增加.总体而言,三阶非线性色散的存在不利于调制不稳定的产生.更多还原

【Abstract】 On the basis of the extended nonlinear propagation equation without normalization in metamaterials with the first-order to third-order nonlinear dispersion effects,the dispersion relation and gain spectra of modulation instability were deduced by adopting the linear stability analysis and the Drude electromagnetic model.Variations of the equation coefficients and gain spectra with the normalized angular frequencies were calculated and discussed in real units in both the positive and negative refractive-index regions in cases of self-focusing and self-defocusing.The results show that,the third-order nonlinear dispersion coefficients are all along positive in both the positive and negative refractive-index regions.In the negative refractive-index region,with increase of normalized angular frequencies,the spectral widths of the gain spectra increase before become zero and the peak gains increase before decrease and then become zero in the selffocusing case.While in the case of self-defocusing,modulation instability can only occur near the forbidden band and both the spectral widths and peak gains decrease monotonically.In the positive refractive-index region,modulation instability can only occur in the self-focusing case.And the spectral widths increase monotonically and the peak gains decrease before increase with the normalized angular frequencies.Generally,the third-order nonlinear dispersion is detrimental to modulation instability generation.更多还原