ABSTRACT

In this work, we study some nonlinear left-handed metamaterial lattices subjected to a harmonic driving source. Using the semi-discrete rotating-wave approximation, a nonlinear Schrödinger equation is obtained from the physical model. Using this Schrödinger system, we obtain an analytical approximation to the nonlinear supratransmission threshold of the left-handed lattice. As a consequence of the analytical approximation, if supratransmission is to occur in the pass-band left-handed line then it will only take place within the upper forbidden band-gap. On the other hand, supratransmission will never occur in the homogeneous left-handed transmission line. The numerical simulations of the discrete equation describing the voltage across the line and the total energy of the lattice show that there is no nonlinear band-gap transmission in the forbidden band predicted by the threshold. Contrary to the supratransmision phenomenon in conventional lattices, there is no threshold in the bang-gap where the phenomenon appears. The present manuscript advances the fundamental understanding of the nonlinear supratransmission phenomenon and, at the same time, opens the way for its application to left-handed metamaterial lattices. In that sense, the results of this manuscript may serve to provide a deeper understanding to this nonlinear process.

摘要

在这项工作中，我们研究了一些受谐波驱动源影响的非线性左手超材料晶格。使用半离散旋转波近似，从物理模型中得到非线性薛定谔方程。使用这个薛定谔系统，我们获得了左手晶格非线性超透射阈值的解析近似。作为解析近似的结果，如果超透射发生在通带左手线中，那么它只会发生在上禁止带隙内。另一方面，同质左手传输线永远不会发生超传输。描述线两端电压和晶格总能量的离散方程的数值模拟表明，在阈值预测的禁带中不存在非线性带隙传输。与传统晶格中的超透射现象相反，该现象出现的 bang-gap 中没有阈值。本手稿推进了对非线性超透射现象的基本理解，同时为其在左手超材料晶格中的应用开辟了道路。从这个意义上说，这份手稿的结果可能有助于对这个非线性过程有更深入的理解。本手稿推进了对非线性超透射现象的基本理解，同时为其在左手超材料晶格中的应用开辟了道路。从这个意义上说，这份手稿的结果可能有助于对这个非线性过程有更深入的理解。本手稿推进了对非线性超透射现象的基本理解，同时为其在左手超材料晶格中的应用开辟了道路。从这个意义上说，这份手稿的结果可能有助于对这个非线性过程有更深入的理解。