Anomalous localized resonance phenomena in the nonmagnetic, finite-frequency regime

TL;DR

This paper investigates anomalous localized resonance (ALR) at the interface of materials with contrasting permittivities, identifying conditions under which ALR occurs or is absent in a finite-frequency regime.

Contribution

It explicitly characterizes the frequency-width product limit for ALR occurrence and constructs sources that prevent ALR in a nonmagnetic slab context.

Findings

Identifies the critical frequency-width product threshold for ALR.

Provides explicit conditions for the absence of ALR.

Analyzes the behavior of fields near the interface in the ALR regime.

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 ($\mu=1$) with permittivity $\epsilon_s=-1-\mathrm{i}\delta$ for some small loss $\delta \ll 1$ 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.