Active exterior cloaking for the two-dimensional Helmholtz equation with complex wavenumbers and application to thermal cloaking
Active exterior cloaking for the two-dimensional Helmholtz equation with complex wavenumbers and application to thermal cloaking
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DOI：
10.1098/rsta.2022.0073
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发表时间：
2022-10
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影响因子：
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通讯作者：
M. Cassier;T. DeGiovanni;S. Guenneau;F. Guevara Vasquez
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作者：
M. Cassier;T. DeGiovanni;S. Guenneau;F. Guevara Vasquez
我们为二维亥姆霍兹方程设计了源，它可以通过抵消某个区域中的入射场来掩盖物体，而不会将源完全包围在物体周围。正如在以前的工作真实的正波数，来源也确定的绿色身份。新颖之处在于，我们证明了同样的方法适用于复杂的波数，这使得它适用于各种媒体，包括媒体的色散，损耗和增益。此外，通过推导边界上的格拉夫的加法公式与复杂的参数，我们得到新的估计，允许量化的质量的隐身效果。我们说明了我们的结果，应用它们来实现热方程的主动外部隐身。这篇文章是“多尺度复杂介质和结构超材料中的波的产生和传输（第2部分）”主题的一部分。
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same approach works for complex wavenumbers which makes it applicable to a variety of media, including media with dispersion, loss and gain. Furthermore, by deriving bounds on Graf’s addition formulas with complex arguments, we obtain new estimates that allow to quantify the quality of the cloaking effect. We illustrate our results by applying them to achieve active exterior cloaking for the heat equation. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.