Abstract
The phenomenon of anomalous localized resonance (ALR) is observed at the interface between materials with positive and negative material parameters and is characterized by the fact that when a given source is placed near the interface, the electric and magnetic fields start to have very fast and large oscillations around the interface as the absorption in the materials becomes very small while they remain smooth and regular away from the interface. In this paper, we discuss the phenomenon of anomalous localized resonance (ALR) in the context of an infinite slab of homogeneous, nonmagnetic material (μ=1) with permittivityϵs=-1-iδfor some small lossδ≪1surrounded by positive, nonmagnetic, homogeneous media. We explicitly characterize the limit value of the product between frequency and the width of slab beyond which the ALR phenomenon does not occur and analyze the situation when the phenomenon is observed. In addition, we also construct sources for which the ALR phenomenon never appears.
Highlights
In the following, we discuss the anomalous localized resonance phenomenon (ALR) appearing at the interface between materials with positive and negative material parameters in the finite frequency regime
We assume that all materials are homogeneous and nonmagnetic; the electrical permittivity is given by 1 for x < 0
In [13], Milton, Nicorovici, McPhedran, and Podolskiy showed that if f is a dipole and εc = εm = 1, ALR occurs if a < d0 < 2a, where d0 is the location of the dipole
Summary
We discuss the anomalous localized resonance phenomenon (ALR) appearing at the interface between materials with positive and negative material parameters in the finite frequency regime. In [13], Milton, Nicorovici, McPhedran, and Podolskiy showed that if f is a dipole and εc = εm = 1, ALR occurs if a < d0 < 2a, where d0 is the location of the dipole In this case there are two locally resonant strips — one centered on each face of the slab. Applications of ALR to cloaking in the quasistatic regime were first analyzed Milton and Nicorovici [11]; they showed that if εc = εm = 1 and a fixed field is applied to the system (e.g., a uniform field at infinity), a polarizable dipole located in the region a < d0 < 3a/2 causes anomalous localized resonance and is cloaked in the limit δ → 0+. The Appendix contains the technical proofs and derivations which where not included in the main text
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