基于描述超短脉冲在超常介质中传输的非线性薛定谔方程,本文数值研究了高阶效应影响下高阶亮、暗孤子在超常介质中的传输情况。数值模拟表明,三阶色散和自陡峭效应都会引起高阶孤子的分裂和辐射,破坏高阶亮孤子周期性演化特性,导致高阶暗孤子分裂出的灰孤子不对称;孤子的阶数越高,三阶色散和自陡峭的影响越大。利用超常介质可控的色散和非线性特性,通过调节三阶色散和自陡峭效应的系数,发现超常介质中可以基本支持二阶亮孤子、二阶暗孤子和三阶暗孤子的稳定演化。本文的研究结果为将来进一步研究超常介质中高阶亮、暗孤子的存在及传输特性提供了一定的参考价值。

Based on the higher-order nonlinear Schrdinger equation describing the propagation of ultrashort pulses in metamaterials (MMs), the transmission of higher-order bright and dark solitons in MMs under the influence of higher-order effects are studied numerically. Numerical simulations show that the third-order dispersion and self-steepening effects lead to the split and radiation of higher-order solitons damaging the periodical evolutions of higher-order bright solitons, and result in asymmetry split of higher-order dark solitons. The higher the order of the solitons is, the stronger the influence of third-order dispersion and self-steepening effects is. Due to the controllable dispersion and nonlinearity of MMs, it is easy to obtain the stable transmission of bright 2-soliton, dark 2-soliton and dark 3-soliton in MMs by adjusting the coefficients of third-order dispersion and self-steepening effects. The obtained results may provide some references for further studies of the existence and transmission of higher-order bright solitons and dark solitons in MMs.