Abstract

In this paper, we propose and numerically study a nonlinear, asymmetric, passive metamaterial that achieves giant non-reciprocity with (i) broadband frequency operation and (ii) robust signal integrity. Previous studies have shown that nonlinearity and geometric asymmetry are necessary to break reciprocity passively. Herein, we employ strongly nonlinear coupling, triangle-shaped asymmetric cell topology, and spatial periodicity to break reciprocity with minimal frequency distortion. To investigate the nonlinear band structure of this system, we propose a new representation, namely a wavenumber–frequency–amplitude band structure, where amplitude-dependent dispersion is quantitatively computed and analyzed. Additionally, we observe and document the new nonlinear phenomenon of time-delayed wave transmission, whereby wave propagation in one direction is initially impeded and resumes only after a duration delay. Based on numerical evidence, we construct a nonlinear reduced-order model (ROM) to further study this phenomenon and show that it is caused by energy accumulation, instability, and a transition between distinct branches of certain nonlinear normal modes of the ROM. The implications and possible practical applications of our findings are discussed.

中文翻译：

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三角形非线性一维超材料中具有可靠信号完整性的宽带互易性

摘要

在本文中，我们提出并数值研究了非线性，不对称，无源超材料，该材料通过（i）宽带频率操作和（ii）鲁棒的信号完整性实现了巨大的不可逆性。先前的研究表明，非线性和几何不对称是被动破坏互惠性所必需的。在这里，我们采用强非线性耦合，三角形非对称单元拓扑和空间周期性来以最小的频率失真破坏互易性。为了研究该系统的非线性频带结构，我们提出了一种新的表示形式，即波数-频率-振幅频带结构，在其中定量地计算和分析了振幅相关的色散。此外，我们观察并记录了延时波传输的新非线性现象，因此，最初会阻止一个方向的波传播，并且仅在持续时间延迟后才恢复。基于数值证据，我们构建了非线性降阶模型（ROM）来进一步研究该现象，并表明它是由能量积累，不稳定性以及ROM的某些非线性法线模式的不同分支之间的过渡引起的。我们的发现的含义和可能的实际应用进行了讨论。