论文标题
构建的梯度元曲面的数学和数值框架，建立在定期重复的Helmholtz谐振器的阵列上
A mathematical and numerical framework for gradient meta-surfaces built upon periodically repeating arrays of Helmholtz resonators
论文作者
论文摘要
在本文中，给出了一个数学模型，用于从覆盖有微小的小赫尔姆霍尔兹谐振的表面散射入射波，这是带有小开口的腔。更准确地说，表面是建立在晶胞中有限数量的Helmholtz谐振器上的，并且该单元电池会定期重复。为了解决散射问题，数学框架在[Ammari等人，渐近级。肛门，2019年]。主要的结果是根据开口的长度而言，散射波的近似公式。我们的框架为散射波矢量，角度和相移提供了分析表达式。它证明了明显的吸收合理。此外，它表明，在开口的特定长度和特定频率下，由于Helmholtz谐振器的亚波长谐振，散射波的相突然移动。给出了数值快速的实现，以确定开口和频率的特定值的区域。
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a finite number of Helmholtz resonators in a unit cell and that unit cell is repeated periodically. To solve the scattering problem, the mathematical framework elaborated in [Ammari et al., Asympt. Anal., 2019] is used. The main result is an approximate formula for the scattered wave in terms of the lengths of the openings. Our framework provides analytic expressions for the scattering wave vector and angle and the phase-shift. It justifies the apparent absorption. Moreover, it shows that at specific lengths for the openings and a specific frequency there is an abrupt shift of the phase of the scattered wave due to the subwavelength resonances of the Helmholtz resonators. A numerically fast implementation is given to identify a region of those specific values of the openings and the frequencies.
