Heterogeneous media, Homogenization

Initiated during the ProCoMedia project (ANR, International Program, 2011-2014), in collaboration with Institut LangevinPoems-ENSTA and the Physics Department of the University of Chile, research works are also conducted within the group on the modeling of wave propagation in complex heterogeneous media, with the aim of providing relevant and accurate tools for the characterization and design of metamaterials and artificial materials. Indeed, metamaterials are essentially heterogeneous materials and a fine description and control of the microstructure and of the effective properties of the medium is required to achieve desired functionalities: perfect transmission or absorption, controlled directivity, localization, … 

A general multimodal method method has been developed to solve the wave propagation in heterogeneous anisotropic media [pdf] or in a waveguide containing penetrable inclusions [pdf]. One of the advantages of the proposed method relies with the ability to derive approximate analytical solutions in specific cases as, e.g., weak perturbations. It is through this that we revisited the Wood's anomalies for arrays of penetrable scatterers [pdf].

At low frequencies, when the wavelength is large compared with the characteristics lengths of the medium (say, the period, for a periodic medium), an obvious tool to describe the resulting macrostructure is homogenization, which "integrates" the local behavior. This process provides for a metamaterial or a complex material the effective parameters of the equivalent homogeneous medium, generally anisotropic [pdf]. Beside its interest in numerical terms - it is not necessary to mesh or solve at the sub-wavelength scale of the microsctructure - homogenization allows the development of simple analytical models, able to account for effects of this microstructure [pdfpdf]. In a series of works, we have investigated homogenized models to describe the scattering, in reflection or transmission, of a wave by a layer finite thickness of a periodic medium. If the non-resonant, low frequency, classical homogenization, is not able to describe possible resonant effects in the unit cell constituting the material, however, it can be used to describe resonant effects in the layer related to its thickness and its effective anisotropy. These resonances of the metamaterial layer can notably be related to guided waves in the homogenized layer, which generalize the spoof plasmons highlighted on the structured surface of rigid or perfectly conducting materials [pdfpdfpdf].

Subwavelength resonant guided modes along a grating of pénétrable scatterers




simon.felix @ univ-lemans.fr

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