论文标题
蜂窝状浮部质材料中的拓扑现象
Topological phenomena in honeycomb Floquet metamaterials
论文作者
论文摘要
我们将本文专门用于浮雕超材料中亚波长度溶液的拓扑分析。这项工作应被视为进一步研究散装材料的拓扑特性是否与边缘模式的发生有关的基础。亚波长度解决方案通过定期参数化的时间周期性线性线性普通微分方程$ \ left \ weft \ {\ frac {d} {dt} {dt} x =a_α（t）x \ right \ right \} _ {α\ in \ mathb {方程式并引入一种方法，以（拓扑）对相关基本解决方案的floquet formal formal $ f，〜p $进行分类$ \ left \ left \ weft \ {x_α（t）= p（α，t）\ exp（tf_α）\ right \ right \} _ {α\ in \ in \ in \ in \ mathbb {t}^d} $。这是通过分析单片矩阵$x_α（t）$和lyapunov变换$ p（α，t）$的特征值和特征向量的拓扑特性来实现的。然后，可以将相应的拓扑不变性应用于浮子变质物的设置。在本文中，在蜂窝浮子变质材料的情况下考虑了这些一般结果。我们提供了两个有趣的例子，这些例子是拓扑非平凡的时间调节蜂窝结构。
We dedicate this paper to the topological analysis of subwavelength solutions in Floquet metamaterials. This work should be considered as a basis for further investigation on whether topological properties of the bulk materials are linked to the occurrence of edge modes. The subwavelength solutions being described by a periodically parameterized time-periodic linear ordinary differential equation $\left\{\frac{d}{dt}X = A_α(t)X\right\}_{α\in \mathbb{T}^d}$, we put ourselves in the general setting of periodically parameterized time-periodic linear ordinary differential equations and introduce a way to (topologically) classify a Floquet normal form $F,~P$ of the associated fundamental solution $\left\{X_α(t) = P(α,t)\exp(tF_α)\right\}_{α\in \mathbb{T}^d}$. This is achieved by analysing the topological properties of the eigenvalues and eigenvectors of the monodromy matrix $X_α(T)$ and the Lyapunov transformation $P(α,t)$. The corresponding topological invariants can then be applied to the setting of Floquet metamaterials. In this paper these general results are considered in the case of honeycomb Floquet metamaterials. We provide two interesting examples of topologically non-trivial time-modulated honeycomb structures.
