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Métamatériaux cristallins : du motif sub-longueur d'onde au comportement macroscopique.

Abstract : Many material properties arise from the interaction between their constituents and a wave. This is mainly conditioned by two characteristics: the composition and the structural arrangement. This interdependence is precisely described by condensed matter physics. This motivated the discovery of composite materials whose characteristics also stem from these two criteria. They divide in two categories. The first is the photonic/phononic crystals, whose properties are linked to their periodic arrangement. The second category is the one of metamaterials, whose properties come from the interaction of their constituents with the waves. The structural effects are generally neglected in the description of these media and they are considered to be homogeneous media with effective parameters. These two types of systems seem very different from the point of view of the interaction with the waves. In this thesis, we focus on locally resonant metamaterials, whose unit cell is a sub-wavelength resonator. Instead of seeing them as effective homogeneous media, the idea is to start from the characteristics of the unit cell of the medium as well as from its spatial arrangement in order to obtain its macroscopic properties. This microscopic approach makes it possible to jointly apprehend the effects of structure and composition. This is described in Chapter I, where we introduce the concept of polariton whose dispersion relation has a band linked to subwavelength modes, and a hybridization bandgap. In Chapter II, we use the latter to induce a localized coupling between resonant defects that is similar to the hopping term found in tight-binding solid-state physics Hamiltonians. We reproduce the band structures of graphene and of the dice lattice, which allows us to measure Dirac cones within the system. In Chapter III, we introduce the concept of crystalline metamaterials, which amounts to seeing these media as photonic/phononic crystals, but on a very small scale compare to the operating wavelength. This allows us to induce a negative band in the system but also a relatively flat band, and Dirac cones. In Chapter IV we break these cones by creating an analogue of the quantum Hall effect of Valley, which amounts to jointly modifying the structure and composition of the unit cell. In Chapter V we again break these cones in order to induce topological properties in the medium and to create a macroscopic analogue of a topological isolator.
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Simon Yves. Métamatériaux cristallins : du motif sub-longueur d'onde au comportement macroscopique.. Acoustique [physics.class-ph]. Université Sorbonne Paris Cité, 2018. Français. ⟨NNT : 2018USPCC226⟩. ⟨tel-02468822⟩

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