Enhancement of near-cloaking. Part II: the Helmholtz equation

TL;DR

This paper develops advanced near-cloaking structures for the Helmholtz equation, significantly improving cloaking effectiveness by designing layered structures with vanishing first scattering coefficients, applicable over a frequency band.

Contribution

It introduces a novel layered structure design that enhances near-cloaking for the Helmholtz equation, extending previous conductivity cloaking methods to scattering problems.

Findings

First scattering coefficients are effectively nullified.

Cloaking performance is significantly improved over a frequency band.

The method is analytically validated for the Helmholtz equation.

Abstract

The aim of this paper is to extend the method of improving cloaking structures in the conductivity to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new structures are, before using the transformation optics, layered structures and are designed so that their first scattering coefficients vanish. Inside the cloaking region, any target has near-zero scattering cross section for a band of frequencies. We analytically show that our new construction significantly enhances the cloaking effect for the Helmholtz equation.