非线性管理光纤光栅中的调制不稳定性研究

Modulation Instability in Fiber Grating with Nonlinearity Management

基于非线性耦合模方程,研究了非线性管理光纤光栅中的调制不稳定性,得到了调制不稳定性的色散关系。与常规的非线性光纤光栅相比,在非线性管理光纤光栅中,克尔非线性的变化改变了调制不稳定性增益谱的谱宽和幅度,并导致新的不稳定性区域的出现:在反常色散区,原来关于零波数对称的两个旁瓣随着克尔非线性变化的增加其增益幅度递减至零,在经历了一段无增益区域之后,又逐渐形成了在零波数附近区域的一个新的单峰;而在正常色散区,除了原来的两个增益区域之外,零波数附近出现了新的增益区,增益的幅度随克尔非线性变化的增加而递增。可见,非线性管理光纤光栅给调制不稳定性的产生提供了更多的空间。

Modulation instability in fiber grating with nonlinearity management is studied based on the nonlinear coupled-mode equations. The dispersion relation for modulation instability is obtained. Compared with normal nonlinear fiber grating, in the fiber grating with nonlinearity management the variance of Kerr nonlinearity alters the spectral width and amplitude of the gain spectrum for modulation instability, and leads to the occurrence of new ranges of instability. In the anomalous dispersion regime, the gain amplitude of two distinct sidelobes originally on either side of the zero wave number region diminishes to zero as the variance of Kerr nonlinearity increases, and a new single peak around zero wave number appears gradually after a region of zero gain; while in the normal dispersion regime, besides the original two gain regions, a new gain region occurs around the zero wave number region, and its gain amplitude increases as the nonlinearity management coefficient augments. As a result, the fiber gratine with nonlinear manaeement provides a larger space for the generation of modulation nonlinearitv.