Time-domain investigation of a cylindrical acoustic external cloak

TL;DR

This paper explores a novel cylindrical acoustic external cloak with negative parameters, demonstrating its ability to reduce scattering at specific frequencies while initially acting as a superscatterer.

Contribution

It introduces a new external cloak design with negative density and bulk modulus, and develops a time-domain simulation method for such resonant acoustic materials.

Findings

Significant scattering reduction at the designed frequency.

Initial superscattering behavior at short times.

Effective cloaking demonstrated in numerical simulations.

Abstract

Space folding techniques based on non-monotonic transforms lead to a new class of cylindrical isotropic acoustic cloaks with a constant negative density and a spatially varying negative bulk modulus. We consider an external cloak consisting of a core with a positive definite density matrix and a positive compressibility, and a shell with simultaneously negative density and compressibility. Such a core-shell resonant system creates a virtual folded region outside the shell. To handle such negative physical parameters in the time-domain, a two-step strategy is used: (i) assuming resonant (Drude-type) effective parameters in the frequency-domain; (ii) returning to the time-domain by applying the formalism of the auxiliary fields. We numerically show that, at the designed central frequency, scattering of a cylindrical pressure wave incident upon a finite set of small rigid obstacles is drastically reduced after a lapse of time, when they are placed in the close neighborhood of the external cloak. However, at short times, the external cloak behaves rather like a superscatterer: the cloak itself scatters more than the set of scatterers.