On Geometrical Properties of Electromagnetic Transmission Eigenfunctions and Artificial Mirage

Youjun Deng; Hongyu Liu; Xianchao Wang; Wei Wu

doi:10.1137/21M1413547

On Geometrical Properties of Electromagnetic Transmission Eigenfunctions and Artificial Mirage

Youjun Deng
, Hongyu Liu
, Xianchao Wang
, Wei Wu

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

18 Citations (Scopus)

Abstract

Transmission eigenfunctions are certain interior resonant modes that are of central importance to the wave scattering theory. In this paper, we present the discovery of novel global rigidity properties of the transmission eigenfunctions associated with the Maxwell system. It is shown that the transmission eigenfunctions carry the geometrical information of the underlying domain. We present both analytical and numerical results of these intriguing rigidity properties. As an interesting application, we propose an illusion scheme of artificially generating a mirage image of any given optical object.

Original language	English
Pages (from-to)	1-24
Number of pages	24
Journal	SIAM Journal on Applied Mathematics
Volume	82
Issue number	1
DOIs	https://doi.org/10.1137/21M1413547
Publication status	Published - Feb 2022

User-Defined Keywords

artificial mirage
electromagnetic scattering
geometric structure
surface localization
transmission eigenfunctions

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10.1137/21M1413547

Cite this

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title = "On Geometrical Properties of Electromagnetic Transmission Eigenfunctions and Artificial Mirage",

abstract = "Transmission eigenfunctions are certain interior resonant modes that are of central importance to the wave scattering theory. In this paper, we present the discovery of novel global rigidity properties of the transmission eigenfunctions associated with the Maxwell system. It is shown that the transmission eigenfunctions carry the geometrical information of the underlying domain. We present both analytical and numerical results of these intriguing rigidity properties. As an interesting application, we propose an illusion scheme of artificially generating a mirage image of any given optical object.",

keywords = "artificial mirage, electromagnetic scattering, geometric structure, surface localization, transmission eigenfunctions",

author = "Youjun Deng and Hongyu Liu and Xianchao Wang and Wei Wu",

note = "The work of the first author was supported by the NSFC through grant 11971487 and by the NSFC of Hunan grant 2020JJ2038. The work of the second author was supported by the Hong Kong RGC General Research Funds through projects 12302919, 12301420, and 11300821. The work of the third author was supported by the Hong Kong Scholars Program grant under XJ2019005 and the NSF grant of China through grants 11971133 and 12001140. The work of the fourth author was supported by the tier-2 startup grant from Hong Kong Baptist University and Hong Kong RGC General Research Funds projects 12302219 and 12300520. Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics",

year = "2022",

month = feb,

doi = "10.1137/21M1413547",

language = "English",

volume = "82",

pages = "1--24",

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AU - Deng, Youjun

AU - Liu, Hongyu

AU - Wang, Xianchao

AU - Wu, Wei

N1 - The work of the first author was supported by the NSFC through grant 11971487 and by the NSFC of Hunan grant 2020JJ2038. The work of the second author was supported by the Hong Kong RGC General Research Funds through projects 12302919, 12301420, and 11300821. The work of the third author was supported by the Hong Kong Scholars Program grant under XJ2019005 and the NSF grant of China through grants 11971133 and 12001140. The work of the fourth author was supported by the tier-2 startup grant from Hong Kong Baptist University and Hong Kong RGC General Research Funds projects 12302219 and 12300520. Publisher Copyright: © 2022 Society for Industrial and Applied Mathematics

PY - 2022/2

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N2 - Transmission eigenfunctions are certain interior resonant modes that are of central importance to the wave scattering theory. In this paper, we present the discovery of novel global rigidity properties of the transmission eigenfunctions associated with the Maxwell system. It is shown that the transmission eigenfunctions carry the geometrical information of the underlying domain. We present both analytical and numerical results of these intriguing rigidity properties. As an interesting application, we propose an illusion scheme of artificially generating a mirage image of any given optical object.

AB - Transmission eigenfunctions are certain interior resonant modes that are of central importance to the wave scattering theory. In this paper, we present the discovery of novel global rigidity properties of the transmission eigenfunctions associated with the Maxwell system. It is shown that the transmission eigenfunctions carry the geometrical information of the underlying domain. We present both analytical and numerical results of these intriguing rigidity properties. As an interesting application, we propose an illusion scheme of artificially generating a mirage image of any given optical object.

KW - artificial mirage

KW - electromagnetic scattering

KW - geometric structure

KW - surface localization

KW - transmission eigenfunctions

UR - https://www.scopus.com/pages/publications/85116808091

U2 - 10.1137/21M1413547

DO - 10.1137/21M1413547

M3 - Journal article

AN - SCOPUS:85116808091

SN - 0036-1399

VL - 82

SP - 1

EP - 24

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 1

ER -

On Geometrical Properties of Electromagnetic Transmission Eigenfunctions and Artificial Mirage

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