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本文以非线性增益超材料中描述电磁波传输的非线性薛定谔方程为模型,采用拟解法给出了线性增益和非线性损耗平衡下精确的具有非线性啁啾的自孤子解,详细研究了该自孤子在不同非线性电极化或/和磁极化超材料中的存在条件及其传输特性。结果发现,当非线性损耗与线性增益平衡时,超材料中可以存在两种形式的自孤子;而且在不同非线性极化的超材料中两种自孤子的振幅、波宽及空间频率啁啾随着归一化频率、增益系数的变化也不同,这意味着可以通过改变入射波的频率、选择具有不同非线性极化和不同增益的超材料来调节自孤子的传输特性。
In this paper, the nonlinear Schrödinger equation describing the transmission of electromagnetic waves in nonlinear gain metamaterials is used as a model, and the exact soliton solutions with nonlinear chirp at linear gain and nonlinear loss balances are given by using the solution method. Solitons in Different Nonlinear Electroplated or / and Polarized Metamaterials: Existence Conditions and Transport Properties. The results show that there are two kinds of self-solitons in the metamaterials when the nonlinear losses are balanced with the linear gain. Moreover, the chirp of amplitude, width and spatial frequency of two self-solitons in different nonlinearly polarized metamaterials With the normalized frequency, the variation of the gain coefficient is also different, which means that the transmission properties of the self-soliton can be adjusted by changing the frequency of the incident wave and choosing metamaterials with different nonlinear polarizations and different gains.