Surface-Localized Transmission Eigenstates, Super-resolution Imaging, and Pseudo Surface Plasmon Modes
Surface-Localized Transmission Eigenstates, Super-resolution Imaging, and Pseudo Surface Plasmon Modes
复制标题
表面局域传输本征态、超分辨率成像、超分辨率成像和伪表面等离子体模式
DOI：
10.1137/20m1388498
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发表时间：
2021-01-01
影响因子：
2.1
通讯作者：
Wang, Xianchao
中科院分区：
文献类型：
--
作者：
Chow, Yat Tin;Deng, Youjun;Wang, Xianchao
我们提出了一个新的和有趣的全球几何结构的（内部）传输本征函数与亥姆霍兹系统的发现。它示出在一般的情况下，总是存在一个序列的传输本征函数与相应的本征值去无穷大，使这些本征函数是本地化的域的边界周围。我们提供了一个全面和严格的理由在径向几何的情况下，而对于非径向的情况下，我们进行了广泛的数值实验，定量验证本地化行为。这一发现为波的定位提供了新的视角。作为重要的应用，我们开发了一种新的逆散射方案，可以产生超分辨率成像效果，并提出了一种方法，产生所谓的伪表面等离子体共振（PSPR）模式与潜在的传感应用。
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.