高阶色散下饱和非线性负折射介质中的调制不稳定性

直接从负折射介质中包含高阶色散及饱和非线性效应的扩展非线性传输方程出发，采用线性稳定性分析法和德鲁德电磁模式，导出了调制不稳定性的色散关系和增益谱公式。考虑到今后的实验验证，以实际单位的形式计算了方程系数随归一化角频率的变化规律。再以实际单位的形式计算并讨论了增益谱随归一化角频率和归一化入射光强的变化关系。结果表明，当归一化角频率固定时，截止频率及峰值增益都随归一化入射光强的增加先增加后减少，归一化角频率不同，截止频率及峰值增益也不同，在靠近禁带处，增益谱远离零点。当归一化入射光强固定时，截止频率及峰值增益随归一化角频率的增加而增加，当归一化角频率增大到靠近禁带时，增益谱由紧挨零点变成远离零点。

Modulation Instability in Saturable Nonlinear Negatve-Index Materials with Higher-Order Dispersion

The dispersion relation and gain spectra of modulation instability (MI) are analytically deduced in negative-index materials by directly starting from the extended nonlinear propagation equation including saturable nonlinearity and higher-order dispersion and by adopting the linear stability analysis and Drode electromagnetic model. And the variations of the equation coefficients with the normalized angular frequencies are calculated in real units for future experimental demonstrations. Then the variations of the gain spectra with the normalized angular frequencies and normalized optical intensities are also calculated and discussed in real units. The results show that, when the normalized angular frequencies are fixed, with the increasing normalized optical intensities, the cut-off frequencies and peak gains of MI will increase before decrease. And the cut-off frequencies and peak gains are different for different normalized angular frequencies. Moreover, the gain spectra will depart far away from the zero point when the normalized angular frequencies are close to the forbidden band region. When the normalized optical intensities are fixed, the cut-off frequencies and peak gains increase with the normalized angular frequencies. And when the normalized angular frequency increases to be close to the forbidden band region, the gain spectrum will shift far away from the zero point.