On Anomalous Localized Resonance for the Elastostatic System

On the cloaking effects associated with anomalous localized resonance

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 dipole acts back on the polarizable line or point dipole and effectively cancels the field acting on it from outside sources. Cloaking is proved in the quasistatic limit for finite collections of polariz...

A variational perspective on cloaking by anomalous localized resonance

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 plane, ∇ · (a(x)∇u(x)) = f(x). The complex-valued coefficient has a matrix-shell-core geometry, with real part equal to 1 in the matrix and the core, and -1 in the shell; one is interested in understan...

Cloaking of small objects by anomalous localized resonance

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 twoand 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 u...

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

Cloaking a source via anomalous localized resonance (ALR) was discovered by Milton and Nicorovici in [14]. A general setting in which cloaking a source via ALR takes place is the settting of doubly complementary media. This was introduced and studied in [19] for the quasistatic regime. In this paper, we study cloaking a source via ALR for doubly complementary media in the finite frequency regim...