Surface-Localized Transmission Eigenstates, Super-resolution Imaging, and Pseudo Surface Plasmon Modes
Abstract
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.
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© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 28 December 2020
Accepted: 5 April 2021
Published online: 13 July 2021
Keywords
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Funding Information
Hong Kong Research Grants Council : 12301218, 12302919, 12301420
Funding Information
City University of Hong Kong https://doi.org/10.13039/100007567
Funding Information
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 : 11971133, 11971487, 12001140
Funding Information
Natural Science Foundation of Hunan Province https://doi.org/10.13039/501100004735 : 2020JJ2038
Funding Information
Society of Hong Kong Scholars https://doi.org/10.13039/501100005953 : XJ2019005
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