Surface-localized transmission eigenstates, super-resolution imaging and pseudo surface plasmon modes

TL;DR

This paper uncovers boundary-localized transmission eigenstates in Helmholtz systems, enabling super-resolution imaging and pseudo surface plasmon modes, with theoretical and numerical validation of wave localization phenomena.

Contribution

It introduces a new understanding of boundary-localized transmission eigenfunctions and develops innovative inverse scattering and sensing methods based on these findings.

Findings

Existence of boundary-localized eigenfunctions with eigenvalues tending to infinity.

Numerical verification of localizing behavior in non-radial geometries.

Development of 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 non-radial case, we conduct extensive numerical experiments to quantitatively verify the localizing behaviours. 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.