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

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 Nicorovicci in [21] and attracted a lot attention in the scientific community. Two key figures 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 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 in [24]. It was showed in [29] that complementary property of media is not enough to ensure a connection between the blow up of the power and the localized resonance. In this paper, we study CALR for a subclass of complementary media called the class of doubly complementary media. This class is rich enough to allow us to cloak an arbitrary source concentrating on an arbitrary smooth bounded manifold of codimension 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 the source is near the plasmonic structure; 3) The power remains bounded if the source is far away from the plasmonic structure. Property 2), the blow up of the power, is in fact established for reflecting complementary media…