SIAM Journal on Imaging Sciences, Volume 14, Issue 3, Page 946-975, January 2021.
We present the discovery of a novel and intriguing global geometric structure of the (interior) transmission eigenfunctions associated with the Helmholtz system. It is shown in generic scenarios that there always exists a sequence of transmission eigenfunctions with the corresponding eigenvalues going to infinity such that those eigenfunctions are localized around the boundary of the domain. We provide a comprehensive and rigorous justification in the case within the radial geometry, whereas for the nonradial case, we conduct extensive numerical experiments to quantitatively verify the localizing behaviors. The discovery provides a new perspective on wave localization. As significant applications, we develop a novel inverse scattering scheme that can produce super-resolution imaging effects and propose a method of generating the so-called pseudo surface plasmon resonant (PSPR) modes with a potential sensing application.

中文翻译：

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表面局部传输本征态、超分辨率成像和伪表面等离子体模式

SIAM 成像科学杂志，第 14 卷，第 3 期，第 946-975 页，2021 年 1 月。
我们发现了与亥姆霍兹系统相关的（内部）传输本征函数的一种新颖而有趣的全局几何结构。在通用场景中表明，总是存在一系列传输特征函数，相应的特征值趋于无穷大，使得这些特征函数定位在域的边界附近。我们在径向几何中的情况下提供了全面而严格的理由，而对于非径向情况，我们进行了广泛的数值实验以定量验证定位行为。这一发现为波定位提供了一个新的视角。作为重要的应用，