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

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.