# 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…

## 36 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 [15]. A general setting in which cloaking a source via ALR takes place is the setting of doubly…

### 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.…

### Cloaking using complementary media for electromagnetic waves

- MathematicsESAIM: Control, Optimisation and Calculus of Variations
- 2019

Negative index materials are artificial structures whose refractive index has negative value over some frequency range. The study of these materials has attracted a lot of attention in the scientific…

### Reflecting complementary media and superlensing using complementary media for electromagnetic waves

- Mathematics
- 2015

Negative index materials were first investigated theoretically by Veselago in \cite{Veselago} and were confirmed experimentally by Shelby, Smith, and Schultz in \cite{ShelbySmithSchultz}.…

## References

SHOWING 1-10 OF 42 REFERENCES

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

- Mathematics
- 2015

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…

### Cloaking Due to Anomalous Localized Resonance in Plasmonic Structures of Confocal Ellipses

- MathematicsSIAM J. Appl. Math.
- 2014

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.

### A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2005

Enlarging upon work of Nicorovici, McPhedran & Milton (Nicorovici et al. 1994 Phys. Rev. B 49(12), 8479–8482), a rigorous proof is given that in the quasistatic regime a cylindrical superlens can…

### On the cloaking effects associated with anomalous localized resonance

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2006

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…

### Spectral Theory of a Neumann–Poincaré-Type Operator and Analysis of Cloaking Due to Anomalous Localized Resonance

- Mathematics
- 2011

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…

### Sensitivity of anomalous localized resonance phenomena with respect to dissipation

- Physics
- 2014

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…

### A Variational Perspective on Cloaking by Anomalous Localized Resonance

- Mathematics
- 2012

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…

### Solutions in folded geometries, and associated cloaking due to anomalous resonance

- Physics
- 2008

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…

### Cloaking of Small Objects by Anomalous Localized Resonance

- Mathematics
- 2010

We investigate solutions of ∇ · (a∇u) = 0 with various boundary conditions. The coefficient a is assumed to have a real part with changing sign and a small, non-negative imaginary part of order η. We…