In this work, we provide experimental evidence of nonlinear wave propagation in a triangular lattice of repulsive magnets supported by an elastic foundation of thin pillars, and we interpret all the individual features of the nonlinear wave field through the lens of a phonon band calculation that precisely accounts for the interparticle repulsive forces. We confirm the coexistence of two spectrally distinct components (homogeneous and forced) in the wave response that is induced via second harmonic generation (SHG) as a result of the quadratic nonlinearity embedded in the magnetic interaction. The detection of the forced component, specifically, allows us to attribute unequivocally the generation of harmonics to the nonlinear mechanisms germane to the lattice. We show that the spatial characteristics of the second harmonic components are markedly different from those exhibited by the fundamental harmonic. This endows the lattice with a functionality enrichment capability, whereby additional modal characteristics and directivity patterns can be triggered and tuned by merely increasing the amplitude of excitation.

中文翻译：

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排斥磁体的二维晶格中的非线性谐波产生

在这项工作中，我们提供了在薄柱的弹性基础支撑下的排斥磁体的三角形晶格中非线性波传播的实验证据，并且我们通过声子带计算的透镜来解释非线性波场的所有单个特征，从而精确地解释了粒子间的排斥力。我们确认了由于二次谐波生成（SHG）所引起的电磁响应中嵌入的二次非线性效应，波响应中两个频谱不同的分量（均质和强迫）共存。特别地，对强制分量的检测使我们能够明确地将谐波的产生归因于与晶格密切相关的非线性机制。我们表明，二次谐波分量的空间特性与基波谐波表现出的空间特性明显不同。这使晶格具有功能丰富的能力，从而仅通过增加激励幅度就可以触发和调整其他模态特性和方向性图案。