Acoustic passive cloaking using thin outer resonators

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 $\epsilon$ 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 $\epsilon$. Various numerical experiments illustrate the theory.

References in corpus (15)

• Acoustic cloaking theory
• Generic transmission zeros and in-phase resonances in time-reversal symmetric single channel transport
• Active Exterior Cloaking
• Bounds on Herglotz functions and fundamental limits of broadband passive quasi-static cloaking
• Source amplitudes for active exterior cloaking
• Acoustic integrated extinction
• Perfect transmission invisibility for waveguides with sound hard walls
• Spoof surface plasmons guided by narrow grooves
• Integral identities for reflection, transmission and scattering coefficients
• Active Thermal Cloaking and Mimicking
• Boundary-layer effects on electromagnetic and acoustic extraordinary transmission through narrow slits
• From zero transmission to trapped modes in waveguides
• Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides
• Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater tomography
• Design of an acoustic energy distributor using thin resonant slits

Cited by in corpus (1)

• Acoustic waveguide with a dissipative inclusion