title: Use of complex frequency plane to design broadband and sub-wavelength absorbers.
abstract: The reflection of sound of frequency below 1 kHz, by a rigid-backed structure that contains sub-wavelength resonators is studied in this work. In particular, only single mode reflected waves are considered, an approximation which is accurate in this low frequency regime. A method of analysis of absorption that uses the structure of the reflection coefficient in the complex frequency plane is proposed. In the absence of losses, the reflection coefficient supports pairs of poles and zeros that are complex conjugate and which have imaginary parts linked to the energy leakage by radiation. When losses are introduced and balanced to the leakage, the critical coupling condition is satisfied and total absorption is obtained. Examples of a slot resonator and of multiple Helmholtz resonators are analyzed to obtain both narrow and broadband total absorption.
authors.affiliation: LUNAM Université, Université du Maine, Laboratoire d'Acoustique de l'Université du Maine UMR CNRS 6613 (LAUM), Av. O. Messiaen, 72085 Le Mans, France.
authors.forename: V
authors.initials: V
authors.lastname: Romero-García
authors.affiliation: LUNAM Université, Université du Maine, Laboratoire d'Acoustique de l'Université du Maine UMR CNRS 6613 (LAUM), Av. O. Messiaen, 72085 Le Mans, France.
authors.forename: G
authors.initials: G
authors.lastname: Theocharis
authors.affiliation: LUNAM Université, Université du Maine, Laboratoire d'Acoustique de l'Université du Maine UMR CNRS 6613 (LAUM), Av. O. Messiaen, 72085 Le Mans, France.
authors.forename: O
authors.initials: O
authors.lastname: Richoux
authors.affiliation: LUNAM Université, Université du Maine, Laboratoire d'Acoustique de l'Université du Maine UMR CNRS 6613 (LAUM), Av. O. Messiaen, 72085 Le Mans, France.
authors.forename: V
authors.initials: V
authors.lastname: Pagneux