声波在含负参数缺陷的零折射率超材料中的全透射和全反射

Total Transmission and Total Reflection of Acoustic Wave in Zero-Index Metamaterial with Defects Possessing Negative Parameters

这个工作研究了声波在含矩形缺陷的二维各向同性零折射率超材料波导中的传播性质。我们知道在零折射率超材料波导中嵌入合适的正参数缺陷能够实现声波的全透射和全反射,但我们发现当缺陷的质量密度和体积弹性模量同时为合适的负数时,同样能够实现声波的全透射和全反射,并通过有限元模拟得到了验证。此外,在全透射和全反射情形下,缺陷中的声压场呈现出了不同的模态分布。全透射发生时,缺陷中的声压场呈现出的是很多个模态叠加的结果,而全反射发生时会呈现出某个模态的分布。在讨论零折射率超材料波导中含有多个缺陷时,我们发现当波导中嵌有偶数个缺陷,并且每两个缺陷的参数互为相反数时,会实现反常的透射现象。我们利用两个单独嵌入零折射率超材料中时导致声波全反射的缺陷实现了声波的全透射,这一有趣的现象在声隐身上有着潜在的应用。

In this work, the transmission properties of acoustic wave through a two dimensional isotropic zero-index metamaterial waveguide embedded with rectangular defects have been investigated. It is well known that total transmission and total reflection of acoustic wave can be achieved by embedding a proper defect with positive parameters into zero-index metamaterial. We have also found that total transmission and total reflection of acoustic wave can also be achieved when mass density and bulk modulus of defects are proper negative values simultaneously. Our results have been verified by finite element simulations. In addition, the sound pressure field in the defect presents different mode distributions when total transmission or total reflection occurs. In discussing several defects embedded into zero-index metamaterial, abnormal transmission occurs if the parameters of each of the two defects are opposite to each other. Particularly, we make use of two defects to achieve total transmission, while total reflection occurs when these two defects are embedded into zero-index metamaterial individually. This interesting phenomenon can be potentially applied in acoustic cloaking.