Sensitivity of anomalous localized resonance phenomena with respect to dissipation

TL;DR

This paper investigates how the phenomenon of cloaking via anomalous localized resonance in a superlens is affected by dissipation, revealing a critical distance dependent on dissipation rates that determines when cloaking occurs.

Contribution

It provides a detailed analysis of the critical distance for cloaking due to anomalous localized resonance considering dissipation effects in a quasistatic regime.

Findings

Cloaking occurs when charge density is within a critical distance of the slab.

Power dissipation blows up as dissipation parameters approach zero within this distance.

Critical distance depends on the dissipation rate outside the slab.

Abstract

We analyze cloaking due to anomalous localized resonance in the quasistatic regime in the case when a general charge density distribution is brought near a slab superlens. If the charge density distribution is within a critical distance of the slab, then the power dissipation within the slab blows up as certain electrical dissipation parameters go to zero. The potential remains bounded far away from the slab in this limit, which leads to cloaking due to anomalous localized resonance. On the other hand, if the charge density distribution is further than this critical distance from the slab, then the power dissipation within the slab remains bounded and cloaking due to anomalous localized resonance does not occur. The critical distance is shown to strongly depend on the the rate at which the dissipation outside of the slab goes to zero.