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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 4156072, 28 pages
Research Article

Anomalous Localized Resonance Phenomena in the Nonmagnetic, Finite-Frequency Regime

1Department of Mathematics, University of Houston, Houston, TX 77204, USA
2Institute for Mathematics and Its Applications, University of Minnesota, College of Science and Engineering, Minneapolis, MN 55455, USA

Received 23 May 2016; Accepted 7 August 2016

Academic Editor: Jacopo Bellazzini

Copyright © 2016 Daniel Onofrei and Andrew E. Thaler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 () with permittivity for some small loss surrounded 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.