CE08 - Matériaux métalliques et inorganiques et procédés associés

Wave Propagation in Resonant Matematerials – METARESO


Wave propagation in resonant metamaterials


In the interests of miniaturization, new metamaterials of subwavelength thickness (metasurfaces / metafilms) are currently being considered. The strong effect of these metastructures on acoustic and elastic waves is due to the presence of resonators. However, conventional homogenization methods are no longer effective, being by nature suitable for structures with thicknesses large in relation to the wavelength.

The METARESO project proposes to
-develop effective models for resonant metastructures based on a new homogenization technique: resonant interface homogenization,
- design a new generation of subwavelength thick metastructures combining different types of resonators in order to obtain «extraordinary« properties for the waves, properties which can be anticipated thanks to these effective models.

The expected results at the end of the METARESO project are 1) of a fundamental nature, the main ambition being the establishment of effective models for resonant metasurfaces / metafilms combining different resonators, 2) of a more applied nature with the design of new structures thick sub-wavelength whose design will be guided by these models.

The perspective will be to lay out the contours of a multi-disciplinary group including an experimental component for the production of prototypes, and in the medium term to propose industrial applications.

« Effective model for elastic waves in a substrate supporting an array of plates/beams with flexural and longitudinal resonances” publié en septembre dernier dans le Journal of Elasticity (doi : 10.1007/s10659-021-09854-4).

Metamaterials are artificial materials constructed from a periodically repeated sub-wavelength elementary cell, which gives the material extraordinary properties for wave propagation. For example, media with refractive index close to zero or negative, which have led to advances in terms of perfect transmission and subwavelength guidance. From a theoretical point of view, these materials have revived among physicists, mechanics and applied mathematicians, interest in homogenization techniques in more or less conventional forms. Among these techniques, two-scale asymptotic homogenization provides a rigorous mathematical framework for obtaining the actual behavior of the material. In its classical form, homogenization provides a model of effective propagation in the volume of the metamaterial but does not question the transmission conditions at the edges (except in practice, the metamaterial has finite dimensions, therefore borders with other materials).

For the sake of miniaturization, the metamaterial community has been moving for some years towards structures of small thickness, that is to say, typically small in front of the wavelength. These structures are called metafilms or metasurfaces. Most often, these structures have a significant effect on the waves that pass through them (perfect transmission / reflection / absorption, guided waves) because they involve local resonances in the elementary cell. These are typically the resonances of Mie in electromagnetism and elastodynamics, the resonances of Helmholtz and Minnaert in acoustics.
For these thin structures, it is now widely accepted that conventional homogenization techniques are unsuitable, for at least two reasons: (i) because local resonances must be captured in effective parameters dependent on the frequency, (ii) because edge effects become dominant over volume effects and should be taken into account;

The METARESO project proposes to develop effective models for these metastructures which will be obtained by relying on a new homogenization technique: the resonant homogenization of interface, and to design new metastructures whose properties can be anticipated thanks to these effective models. In the actual problem resulting from this homogenization, the metafilm is replaced by actual jump conditions, the metasurface is replaced by an effective boundary condition. These actual conditions are obtained at the end of the asymptotic analysis without any adjustable parameter and they involve effective parameters depending on the frequency. We have shown that these new effective models make it possible to reproduce the behavior of a microstructure with great precision.

Ultimately, the goal of the METARESO project is to use the three families of resonance (Mie, Helmholtz, Minnaert) as elementary bricks that will be possible to combine in order to build and optimize metasurfaces with specific properties toward the propagation of acoustic / elastic waves. This type of approach has been used successfully to produce negative index materials for massive metamaterials but it has never been proposed in the case of metafilm / metasurface. In addition, the project proposes to overcome the usual limitations of asymptotic homogenization, confined to perfectly periodic systems, in order to take into account a gradient of material properties or a disorder to develop its field of application by including multiphysical aspects (visco -elasticity) and non-linear responses. It will then be possible to consider the design of a new generation of films / surfaces whose behavior can be anticipated through these models.

Project coordinator

Monsieur Kim Pham (Institut des Sciences de la Mécanique et Applications Industrielles)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.


IMSIA Institut des Sciences de la Mécanique et Applications Industrielles

Help of the ANR 249,993 euros
Beginning and duration of the scientific project: December 2019 - 48 Months

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