| Issue |
ESAIM: M2AN
Volume 49, Number 3, May-June 2015
|
|
|---|---|---|
| Page(s) | 741 - 754 | |
| DOI | https://doi.org/10.1051/m2an/2014051 | |
| Published online | 08 April 2015 | |
Localized and complete resonance in plasmonic structures∗
1 EPFL SB MATHAA CAMA, Station
8, 1015
Lausanne,
Switzerland.
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2 School of Mathematics, University of
Minnesota, MN, 55455
Minnesota,
USA.
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Received:
15
October
2013
Revised:
8
September
2014
Abstract
This paper studies a possible connection between the way the time averaged electromagnetic power dissipated into heat blows up and the anomalous localized resonance in plasmonic structures. We show that there is a setting in which the localized resonance takes place whenever the resonance does and moreover, the power is always bounded and might go to 0. We also provide another setting in which the resonance is complete and the power goes to infinity whenever resonance occurs; as a consequence of this fact there is no localized resonance. This work is motivated from recent works on cloaking via anomalous localized resonance.
Mathematics Subject Classification: 78A25 / 78M35 / 78.35 / 35A20 / 35B25 / 35B40
Key words: Localized resonance / complete resonance / plasmonic structures / negative index materials / complementary media
The research is supported by NSF grant DMS-1201370 and by the Alfred P. Sloan Foundation.
© EDP Sciences, SMAI 2015
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