[Invisibilité par résonance localisée anormale. Une liaison entre la résonance localisée et l'exposion de la puissance pour les milieux doublement complémentaires]
Nous étudions l'invisibilité par résonance localisée anormale (CALR) en deux et trois dimensions en régime quasi-statique. Deux figures principales de CALR sont i) la résonance localisée et ii) la liaison entre la résonance localisée et l'exposion de la puissance quand la perte de la matériel tend vers 0. Une importante classe de matériels de l'indice négatif pour laquel la résonance localisée peut apparaître est la classe de milieux complémentaires introduite et analysée dans [8–10]. Il a été noté dans [12] que la propriété complémentaire ne suffit pas à assurer une telle liaison. Dans cette note, nous introduisons une sous-classe des milieux complémentaires s'appelée la classe des milieux doublement complémentaires. Cette classe est suffisament large pour accomplir l'invisibilité par résonance localisée anormale une source arbitraire concentrant sur une sous-variété arbitraire de codimension 1 placé dans un milieu arbitraire. Les trois propriétés suivantes sont établies : 1) CALR apparaît si et seulement si la puissance explose ; 2) la puissance explose si la source est « placée » près de la structure plasmonique ; 3) la puissance reste bornée si la source est loin de la structure plasmonique. Propriété P2), l'explosion de la puissance est en fait établie pour les milieux complémentaires.
This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in two and three dimensions in the quasistatic regime. Two key figures of CALR are (i) the localized resonance and (ii) the connection between the localized resonance and the blow up of the power of the fields as the loss goes to 0. An important class of negative index materials for which the localized resonance might appear is the class of (reflecting) complementary media introduced and analyzed in [8–10]. It was shown in [12] that the complementary property of media is not enough to ensure such a connection. In this paper, we introduce a subclass of complementary media called the class of doubly complementary media. This class is rich enough to allow us to do cloaking via anomalous localized resonance for an arbitrary source concentrating on an arbitrary smooth bounded manifold of codimension 1 located in an arbitrary medium. The following three properties are established: 1) CALR appears if and only if the power blows up; 2) the power blows up if the source is “located” near the plasmonic structure; 3) the power remains bounded if the source is far away from the plasmonic structure. Property P2), the blow up of the power, is in fact established for reflecting complementary media.
Accepté le :
Publié le :
@article{CRMATH_2015__353_1_41_0,
author = {Hoai-Minh Nguyen},
title = {Cloaking via anomalous localized resonance. {A} connection between the localized resonance and the blow up of the power for doubly complementary media},
journal = {Comptes Rendus. Math\'ematique},
pages = {41--46},
publisher = {Elsevier},
volume = {353},
number = {1},
year = {2015},
doi = {10.1016/j.crma.2014.10.014},
language = {en},
}
TY - JOUR AU - Hoai-Minh Nguyen TI - Cloaking via anomalous localized resonance. A connection between the localized resonance and the blow up of the power for doubly complementary media JO - Comptes Rendus. Mathématique PY - 2015 SP - 41 EP - 46 VL - 353 IS - 1 PB - Elsevier DO - 10.1016/j.crma.2014.10.014 LA - en ID - CRMATH_2015__353_1_41_0 ER -
%0 Journal Article %A Hoai-Minh Nguyen %T Cloaking via anomalous localized resonance. A connection between the localized resonance and the blow up of the power for doubly complementary media %J Comptes Rendus. Mathématique %D 2015 %P 41-46 %V 353 %N 1 %I Elsevier %R 10.1016/j.crma.2014.10.014 %G en %F CRMATH_2015__353_1_41_0
Hoai-Minh Nguyen. Cloaking via anomalous localized resonance. A connection between the localized resonance and the blow up of the power for doubly complementary media. Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 41-46. doi : 10.1016/j.crma.2014.10.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.10.014/
[1] Spectral theory of a Neumann–Poincaré-type operator and analysis of cloaking due to anomalous localized resonance, Arch. Ration. Mech. Anal., Volume 218 (2013), pp. 667-692
[2] Anomalous localized resonance using a folded geometry in three dimensions, Proc. R. Soc. Lond. Ser. A, Volume 469 (2013), p. 20130048
[3] Spectral theory of a Neumann–Poincaré-type operator and analysis of cloaking due to anomalous localized resonance II, Contemp. Math., Volume 615 (2014), pp. 1-14
[4] Cloaking of small objects by anomalous localized resonance, Q. J. Mech. Appl. Math., Volume 63 (2010), pp. 437-463
[5] A variational perspective on cloaking by anomalous localized resonance, Commun. Math. Phys., Volume 328 (2014), pp. 1-27
[6] A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance, Proc. R. Soc. Lond. Ser. A, Volume 461 (2005), pp. 3999-4034
[7] On the cloaking effects associated with anomalous localized resonance, Proc. R. Soc. Lond. Ser. A, Volume 462 (2006), pp. 3027-3059
[8] Asymptotic behavior of solutions to the Helmholtz equations with sign changing coefficients, Trans. Amer. Math. Soc. (2014) (in press) | arXiv
[9] Cloaking using complementary media in the quasistatic regime, 2013 | arXiv
[10] Superlensing using complementary media, Ann. Inst. Henri Poincaré, Anal. Non Linéaire (2014) (in press) | DOI
[11] Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime, 2014 | arXiv
[12] Complete resonance and localized resonance in plasmonic structures, ESAIM Math. Model. Numer. Anal. (2014) (to appear) | arXiv
[13] Optical and dielectric properties of partially resonant composites, Phys. Rev. B, Volume 49 (1994), pp. 8479-8482
[14] Negative refraction makes a perfect lens, Phys. Rev. Lett., Volume 85 (2000), pp. 3966-3969
[15] Focusing light using negative refraction, J. Phys. Condens. Matter, Volume 15 (2003), p. 6345
[16] Experimental verification of a negative index of refraction, Science, Volume 292 (2001), pp. 77-79
[17] The electrodynamics of substances with simultaneously negative values of ε and μ, Usp. Fiz. Nauk, Volume 92 (1964), pp. 517-526
Cité par Sources :
Commentaires - Politique
A review of anomalous resonance, its associated cloaking, and superlensing
Ross C. McPhedran; Graeme W. Milton
C. R. Phys (2020)
Cloaking by plasmonic resonance among systems of particles: cooperation or combat?
Ross C. McPhedran; Nicolae-Alexandru P. Nicorovici; Lindsay C. Botten; ...
C. R. Phys (2009)