基于描述超材料中超短脉冲传输的高阶非线性薛定谔方程,采用行波法得到一种精确的飞秒准亮孤子解及其存在条件。研究发现,在群速度色散、三阶色散、三次-五次非线性、自陡峭和二阶非线性色散效应的精确平衡下,超材料中可存在该飞秒准孤子;当三阶色散和二阶非线性色散不存在时,该准孤子无法存在。基于Drude模型,详细讨论了不同非线性超材料中该飞秒准亮孤子存在的不同折射区域。结果表明,该飞秒准孤子可存在于自散焦非线性超材料的负折射区和自聚焦非线性超材料的正折射区,而且在不同区域具有不同的脉冲强度和宽度。这意味着,通过选择不同非线性超材料和输入电磁波的频率,使其位于相应的存在区域,可以实现对孤子特性的调控。

Based on the higher-order nonlinear Schr?dinger equation describing ultrashort pulse transmission in metamaterials, this study presents an exact femtosecond quasi-bright soliton solution and determines its existence conditions by using the traveling wave method. When the group speed dispersion, third-order dispersion, cubic-quintic nonlinearities, self-steepening, and second-order nonlinear dispersion effects are properly balanced, the femtosecond quasi-soliton can exist in nonlinear metamaterials. Without the third-order dispersion and second-order nonlinear dispersion, the soliton in metamaterials can not occur. Based on the Drude model, the existence index regions of the femtosecond quasi-bright soliton are discussed in different nonlinear metamaterials. The results show that femtosecond quasi-soliton can exist in the negative index region of self-defocusing nonlinear metamaterials, and in the positive index region of self-focusing nonlinear metamaterials. Moreover, the intensities and widths of the solitons differ in different regions of the metamaterials, implying that the properties of the formed solitons can be adjusted by choosing different nonlinear metamaterials and different frequencies of the incident wave,making them in the corresponding existence areas.