During recent decades, metamaterials have revolutionized the way waves are controlled in the broad field of wave physics due to the extraordinary physical properties they present. Their locally resonant structure, introducing deep subwavelength band gaps, regions of frequencies where propagation is forbidden, among other properties, have motivated a plethora of applications not available up to now and creating an inflection point in the material science conception. In particular, acoustic metamaterials have shown extraordinary functionalities giving rise to breakthroughs. In many cases, they are able to replace traditional treatments in practical situations due to the better performances in targeted and tunable frequency ranges with strongly reduced dimensions. Acoustic and mechanical metamaterials themselves represent a scientific breakthrough with respect to the conventional treatments for noise, vibrations and radiofrequency problems.

Precursors of such metamaterials are the periodic media. Wave propagation in periodic media has been exploited in the field of wave physics revolutionizing the way of controlling waves in several branches of physics and technology. The secret of these materials lies in their structuring, the origin of peculiar effects like negative refraction or the spatial filtering, explaining, for example, the structural color in nature such as butterfly wings have. Today, these materials count as part of the class of photonic crystals for light or phononic crystals for elastic and acoustic waves with particular dispersion relation. It has been shown that periodic distributions of scatterers embedded in a host medium can be used in the design of effective media in the low frequency regime. When the wavelength, λ, is big compared to the separation between the scatterers, a, (long wavelength regime), homogenization theories can be applied and as a result, this periodic medium behaves as an effective homogeneous medium. If the scatterers are resonators, the effective properties can present extraordinary properties around the resonance frequency, and in this case, the material becomes a metamaterial. However, in the diffraction regime, the periodic structures present bandgaps at wavelengths of the order of the periodicity of the structure. Among other potential applications, in acoustics these systems have motivated tunable frequency filters, beam forming devices, waveguides, wave traps and slow wave systems. In this regime, these materials are strongly anisotropic, presenting an angular dependence of its scattering properties.

During the summer school Metagenierie 2017, organized by the GdR (Groupement de recherche) Meta, the principles of acoustic metamaterials and their possible engineer/industrial applications were discussed with main goal of creating a training course with different steps of the learning procedure: global state of the art, principles and fundamentals and applications. This book is devoted to gathering all the discussions and provides a training book with a large overview on the field of acoustic metamaterials through its nine chapters. The book is divided into three parts:

• – Part 1: Overview of the Current Research in Acoustic Metamaterials
• – Part 2: Principles and Fundamentals of Acoustic Metamaterials
• – Part 3: Applications of Acoustic Metamaterials

Part 1, Chapters 1–3, highlights the properties of the locally resonant structures with deep subwavelength bandgaps, and how the viscothermal losses can affect the physical properties. Chapter 1 shows the recent advances in the study of the presence of losses in double-negative metamaterial; Chapter 2 focuses on the use of deep subwavelength bandgaps to attenuate seismic waves; and finally, Chapter 3 shows how we can make use of both viscothermal losses and slow sound phenomena to create perfect absorbers as well as metadiffusers with deep subwavelength structures.

Part 2, Chapters 4–6, provides the principles and fundamentals of the basic theoretical frameworks to deal with metamaterials and periodic structures. Chapter 4 discusses the homogenization theory for 3D structures in the time domain; Chapter 5 shows the fundamentals of the plane wave expansion method to calculate the dispersion relation of periodic media; and finally, Chapter 6 shows a complete introduction to the multiple scattering theory in order to deal with the finite size effects of periodic structures.

Part 3, Chapters 7–9, shows a broad overview of the industrial applications of metamaterials and periodic media. Chapter 7 shows a review of the acoustic metamaterials for the industrial applications of audible sound; Chapter 8 shows also an extensive review of the possible radiofrequency applications of acoustic metamaterials for radiofrequency applications; and finally, Chapter 9 shows the possibilities of acoustic metamaterials for underwater applications.

The editors of this book would like to acknowledge all the speakers and participants of Metagenierie 2017, who have highly enriched scientific discussions. In particular, the editors would like to kindly thank all the participants of this book. They made a great effort and we hope the readers can note this by reading the chapters. We hope that this book will be useful for the community of acoustic metamaterials and motivate future development in this field.

Vicente ROMERO-GARCÍA

Anne-Christine HLADKY-HENNION

May 2019