# Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime

@article{Nguyen2014CloakingVA, title={Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime}, author={Hoai-Minh Nguyen}, journal={Journal of the European Mathematical Society}, year={2014}, volume={17}, pages={1327-1365} }

This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two- and three-dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovici [21] for constant plasmonic structures in the two- dimensional quasistatic regime. Two key features of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized…

## 33 Citations

### Cloaking via anomalous localized resonance for doubly complementary media in the finite frequency regime

- MathematicsJournal d'Analyse Mathématique
- 2019

Cloaking a source via anomalous localized resonance (ALR) was discovered by Milton and Nicorovici in \cite{MiltonNicorovici}. A general setting in which cloaking a source via ALR takes place is the…

### Cloaking using complementary media for the Helmholtz equation and a three spheres inequality for second order elliptic equations

- Mathematics
- 2015

Cloaking using complementary media was suggested by Lai et al. in [11]. This was proved in [21] in the quasistatic regime. One of the difficulties in the study of this problem is the appearance of…

### Anomalous localized resonance phenomena in the nonmagnetic, finite-frequency regime

- Physics
- 2016

The phenomenon of anomalous localized resonance (ALR) is observed at the interface between materials with positive and negative material parameters and is characterized by the fact that, when a given…

### Cloaking Property of a Plasmonic Structure in Doubly Complementary Media and Three-Sphere Inequalities with Partial Data

- MathematicsSIAM J. Math. Anal.
- 2022

We investigate cloaking property of negative-index metamaterials in the time-harmonic electromagnetic setting for the so-called doubly complementary media. These are media consisting of…

### Cloaking an Arbitrary Object via Anomalous Localized Resonance: The Cloak is Independent of the Object

- PhysicsSIAM J. Math. Anal.
- 2017

This paper confirms the possibility that a lens can act like a cloak and conversely and shows that in the two dimensional quasi-static regime an annular plasmonic structure of coefficient $-1$ cloaks small but finite size objects nearby.

### LOCALIZED AND COMPLETE RESONANCE IN PLASMONIC STRUCTURES

- Physics
- 2013

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…

### Mathematical analysis of plasmonic resonance for 2-D photonic crystal

- PhysicsJournal of Differential Equations
- 2019

### Localization and geometrization in plasmon resonances and geometric structures of Neumann-Poincaré eigenfunctions

- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2020

This paper reports some interesting discoveries about the localization and geometrization phenomenon in plasmon resonances and the intrinsic geometric structures of Neumann-Poincaré eigenfunctions.…

### Bounds on Herglotz functions and fundamental limits of broadband passive quasistatic cloaking

- Mathematics
- 2016

Using a sum rule, we derive new bounds on Herglotz functions that generalize those given in Bernland et al. [J. Phys. A: Math. Theor. 44(14), 145205 (2011)] and Gustafsson and Sjoberg [New J. Phys.…

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### Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime

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This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the twoand three-dimensional quasistatic regimes. CALR associated with negative index materials was…

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This paper considers cloaking by anomalous localized resonance (CALR) on structures where the core and the shell are confocal ellipses and compute the critical elliptic radii such that, for any source inside it, CALR takes place and, forAny source outside it,calR does not take place.

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Cloaking using complementary media was suggested by Lai et al. in [11]. This was proved in [21] in the quasistatic regime. One of the difficulties in the study of this problem is the appearance of…

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Regions of anomalous localized resonance, such as occurring near superlenses, are shown to lead to cloaking effects. This occurs when the resonant field generated by a polarizable line or point…

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The aim of this paper is to give a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a…

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We analyze cloaking due to anomalous localized resonance in the quasistatic regime in the case when a general charge density distribution is brought near a slab superlens. If the charge density…

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A body of literature has developed concerning “cloaking by anomalous localized resonance.” The mathematical heart of the matter involves the behavior of a divergence-form elliptic equation in the…

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Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent…