On the problem of comparing graded metamaterials
On the problem of comparing graded metamaterials
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DOI：
10.1098/rspa.2023.0537
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发表时间：
2023-09-06
影响因子：
3.5
通讯作者：
Putley，Henry J.
中科院分区：
文献类型：
--
作者：
Davies，Bryn;Fehertoi-Nagy，Lili;Putley，Henry J.
我们使用一个简单有效的模型，通过应用高频均匀化，来解决梯度函数的选择如何影响分级超材料的性能的基本问题。这种方法提供了一个统一的框架，有效地比较梯度函数，并在某种程度上，使我们能够得出适用于一系列不同的波制度的结论。我们考虑的具体问题的单频本地化，适当的有效模型是一个一维薛定谔方程。我们的分析结果既证实了现有的研究（使用昂贵的全场波模拟或黑箱数值优化算法），并将其扩展到其他超材料制度。基于我们的分析，我们能够提出一个优化单调梯度超材料的设计策略，并提供一个解释缺乏一个通用的最佳梯度函数。
We use a simple effective model, obtained through the application of high-frequency homogenization, to tackle the fundamental question of how the choice of gradient function affects the performance of a graded metamaterial. This approach provides a unified framework for comparing gradient functions efficiently and in a way that allows us to draw conclusions that apply to a range of different wave regimes. We consider the specific problem of single-frequency localization, for which the appropriate effective model is a one-dimensional Schrödinger equation. Our analytic results both corroborate those of existing studies (which use either expensive full-field wave simulations or black-box numerical optimization algorithms) and extend them to other metamaterial regimes. Based on our analysis, we are able to propose a design strategy for optimizing monotonically graded metamaterials and offer an explanation for the lack of a universal optimal gradient function.