Acoustic passive cloaking using thin outer resonators

TL;DR

This paper introduces a method for acoustic cloaking in a 2D waveguide by strategically placing thin outer resonators to cancel the obstacle's scattering effects, using asymptotic analysis around resonance lengths.

Contribution

It presents a novel asymptotic analysis approach for designing thin resonators that achieve near-perfect acoustic cloaking in waveguides.

Findings

Resonator placement can nearly eliminate obstacle scattering.

Design of phase shifters using thin resonators.

Numerical experiments confirm theoretical predictions.

Abstract

We consider the propagation of acoustic waves in a 2D waveguide unbounded in one direction and containing a compact obstacle. The wavenumber is fixed so that only one mode can propagate. The goal of this work is to propose a method to cloak the obstacle. More precisely, we add to the geometry thin outer resonators of width $\varepsilon$ and we explain how to choose their positions as well as their lengths to get a transmission coefficient approximately equal to one as if there were no obstacle. In the process we also investigate several related problems. In particular, we explain how to get zero transmission and how to design phase shifters. The approach is based on asymptotic analysis in presence of thin resonators. An essential point is that we work around resonance lengths of the resonators. This allows us to obtain effects of order one with geometrical perturbations of width $\varepsilon$. Various numerical experiments illustrate the theory.