Propagation of few-cycle optical pulses in nonlinear optical Kerr (cubic) and non-Kerr (quintic) type metamaterials, exhibiting frequency-dependent dielectric susceptibility and magnetic permeability, is considered. Considering the theory of electromagnetic waves from Maxwell’s equations, a new nonlinear evolution equation describing the combined influences of higher-order nonlinearities and higher-order linear and nonlinear dispersions, appropriate for electromagnetic ultrashort pulse propagation in negative index materials, is derived beyond the slowly varying envelope approximation. A fully numerical simulation of the newly derived model equation, based on the lossy Drude model, shows the propagation of soliton-like stable few-cycle optical pulses under some parameter values. The change in types of self-steepening parameters induces structural changes of the initial input pulse, characterized by a soliton molecule made of either asymmetric or symmetric optical pulses. Also, the mutual balancing between Kerr and non-Kerr nonlinearities and higher-order dispersions is found to support the formation of soliton-molecules in both the normal and anomalous group velocity dispersion regimes.

中文翻译：

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具有色散介电常数和磁导率的负折射率材料中的几个周期光脉冲

考虑了非线性光学克尔（立方）和非克尔（五次）型超材料中几周期光脉冲的传播，这些材料表现出随频率变化的介电常数和磁导率。考虑麦克斯韦方程组的电磁波理论，得出了一个新的非线性演化方程，描述了高阶非线性和高阶线性与非线性色散的组合影响，适用于负折射率材料中电磁超短脉冲的传播，它超出了缓慢变化的范围。包络近似。对新推导的模型方程的全数值模拟，基于有损Drude模型，显示了在某些参数值下类孤子状稳定的几个周期光脉冲的传播。自增强参数类型的变化会引起初始输入脉冲的结构变化，其特征是由不对称或对称光脉冲组成的孤子分子。而且，发现在正常和异常群速度色散状态下，克尔和非克尔非线性与高阶色散之间的相互平衡可支持孤子分子的形成。