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This paper is devoted to the study of cloaking via anomalous localizedresonance (CALR) in the two and three dimensional quasistatic regimes. CALRassociated with negative index materials was discovered by Milton andNicorovicci in [21] and attracted a lot attention in the scientific community.Two key figures of this phenomenon are the localized resonance, i.e., thefields blow up in some regions and remain bounded in some others, and theconnection between the localized resonance and the blow up of the power of thefields as the loss goes to 0. An important class of negative index materialsfor which the localized resonance might appear is the class of reflectingcomplementary media introduced in [24]. It was showed in [29] thatcomplementary property of media is not enough to ensure a connection betweenthe blow up of the power and the localized resonance. In this paper, we studyCALR for a subclass of complementary media called the class of doublycomplementary media. This class is rich enough to allow us to cloak anarbitrary source concentrating on an arbitrary smooth bounded manifold ofcodimension 1 placed in an arbitrary medium via anomalous localized resonance.The following three properties are established for doubly complementary media:1) CALR appears if and only if the power blows up; 2) The power blows up if thesource is near the plasmonic structure; 3) The power remains bounded if thesource is far away from the plasmonic structure. Property 2), the blow up ofthe power, is in fact established for reflecting complementary media...

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