Design of acoustic metamaterials made of Helmholtz resonators for perfect absorption by using the complex frequency plane

V Romero-García,A Merkel,O Richoux,V Pagneux,V Achilleos,V Tournat,J.-P Groby,G Theocharis,N Jiménez

doi:10.5802/crphys.32

Abstract

In this review, we present the results on sub-wavelength perfect acoustic absorption using acoustic metamaterials made of Helmholtz resonators with different setups. Low frequency perfect absorption requires to increase the number of states at low frequencies and finding the good conditions for impedance matching with the background medium. If, in addition, one wishes to reduce the geometric dimensions of the proposed structures for practical issues, one can use properly designed local resonators and achieve sub-wavelength perfect absorption. Helmholtz resonators have been shown good candidates due to their easy tunability of the geometry, so of the resonance frequency, the energy leakage and the intrinsic losses. When plugged to a waveguide or a surrounding medium they behave as open, lossy and resonant systems characterized by their energy leakage and intrinsic losses. The balance between these two represents the critical coupling condition and gives rise to maximum energy absorption. The critical coupling mechanism is represented here in the complex frequency plane in order to interpret the impedance matching condition. In this review we discuss in detail the possibility to obtain perfect absorption by these critical coupling conditions in different systems such as reflection (one-port), transmission (two-ports) or three-ports systems.

Highlights

The ability to perfectly absorb an incoming wave field in a sub-wavelength material is advantageous for several applications in wave physics as energy conversion [1], time reversal technology [2], coherent perfect absorbers [3] or soundproofing [4] among others
In this review we discuss the technique based on the analysis of the zeros and poles of the eigenvalues of the scattering matrix. In general these zeros and poles correspond to complex frequencies, we introduce a representation in the complex frequency plane, i.e., real versus imaginary part of the complex frequency, applied to the case of acoustic metamaterials made of Helmholtz resonators (HRs) for deep sub-wavelength perfect absorption (PA)
To further illustrate the fact that the incident wave amplitude can be employed as a tuning parameter to obtain coherent perfect absorption (CPA), we show, in Figure 10(b), the absorption for the resonance frequency f0 as a function of incident amplitude wave |a|

Summary

Introduction

The ability to perfectly absorb an incoming wave field in a sub-wavelength material is advantageous for several applications in wave physics as energy conversion [1], time reversal technology [2], coherent perfect absorbers [3] or soundproofing [4] among others. The solution of this challenge requires to solve a complex problem: reducing the geometric dimensions of the structure while increasing the number of states at low frequencies and finding the good conditions to match the impedance to the background medium.

Methods

Results

Conclusion