高阶效应下与扰动频率相关的调制不稳定性

Perturbation frequency related modulation instability in case of high-order effects

为了探讨光纤中高阶效应下与扰动频率相关的交叉相位调制不稳定性条件和增益谱特点,从包含5阶非线性和4阶色散的耦合非线性薛定谔方程出发,采用线性稳定性分析,计算分析了两光波扰动频率不等时的不稳定性条件和增益谱。结果表明,当2阶、4阶色散同号时,增益谱有两种可能的形式,其中一种的谱范围包含了另一种的。被包含谱的不稳定条件与通常情况不同,且谱特性受色散和5阶非线性的影响小。随着某一扰动频率增大,增益谱的谱区数及变化规律将随两光波所处的光纤色散区的不同而不同。而正(负)5阶非线性可使谱峰增加(减小)、谱宽变宽(窄)。该研究对高重复率脉冲串产生具有一定意义。

In order to study the condition and gain spectra of perturbation frequency related modulation instability induced by cross-phase modulation in optical fibers with high order effects, starting from the coupled nonlinear Schrodinger equations including quintic nonlinearity and fourth-order dispersion effect and utilizing the linear-stability analysis, the condition and gain spectra are analyzed and calculated when the perturbation frequencies of the two optical waves are not equal. The results show that,when the second-order and the fourth-order dispersions are of the same sign,there are two possible kinds of gain spectra for modulation instability, and one spectrum includes the other. Moreover, the spectrum which is included by the other one has different condition of modulation instability from the ordinary case, and is scarcely affected by the sign of dispersion and parameter of quintic nonlinearity. With increase of one of the perturbation frequencies, the number of the spectral regions and its variation will be different for different dispersion regimes. The positive （negative） quintic nonlinearity can make the peak value of gain spectrum increase（decrease） and the spectral width wider（narrower）. This study is significant for generation of ultra-short optical pulse chain at high repetition rate.