  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...
