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Section: New Results

Wave propagation in non classical media

Plasmonic black-hole waves at corners of metals

Participants : Anne-Sophie Bonnet-Ben Dhia, Camille Carvalho, Patrick Ciarlet.

This work, which is a part of the PhD of Camille Carvalho, is done in collaboration with Lucas Chesnel from CMAP at Ecole Polytechnique. We study the scattering of time-harmonic electromagnetic waves by a metallic obstacle in a 2D setting, at frequencies such that the dielectric permittivity of the metal has a negative real part and a small imaginary part. When the obstacle has corners, due to the sign-changing real part of the permittivity, unusual strong singularities for the electromagnetic field can appear. If the material dissipation is neglected, it can be necessary to consider a new functional framework, containing these singularities, to derive a well-posed problem. In this new framework, everything happens like if plasmonic waves were propagating to the corners, and a part of the energy is trapped by the corner, even if the material has been supposed non-dissipative. We have implemented an original numerical method consisting in using Perfectly Matched Layers at the corners to capture these black-hole waves. We have also proposed a new rule to mesh the corner in order to achieve convergence of classical finite elements in the simpler case where the problem is still well-posed in the classical framework. Finally, in collaboration with André Nicolet and Frédéric Zolla from Institut Fresnel in Marseille, we are now considering realistic dissipative metals. We show that there is still a significant effect of the black-hole phenomenon, which results in an unsual energy leakage in some frequency range.

Limiting amplitude principle for a two-layered dielectric/metamaterial medium

Participants : Maxence Cassier, Christophe Hazard, Patrick Joly.

This work has been a part of the PhD of Maxence Cassier and has allowed to initiate a collaboration with Boris Gralak from Institut Fresnel. For wave propagation phenomena, the limiting amplitude principle holds if the time-harmonic regime represents the large time asymptotic behavior of the solution of the evolution problem with a time-harmonic excitation. Considering a two-layered medium composed of a dielectric material and a Drude metamaterial separated by a plane interface, we prove that the limiting amplitude principle holds except for a critical situation related to a surface resonance phenomenon. Then the solution can either converge to the superposition of two time-periodic fields, or blow up linearly in time.

Perfectly Matched Layers in plasmas and metamaterials

Participants : Eliane Bécache, Patrick Joly, Maryna Kachanovska, Valentin Vinoles.

This work is a part of the PhD of Valentin Vinoles and is the subject of the post-doc of Maryna Kachanovska. It deals with the stability of Perfectly Matched Layers (PMLs) in dispersive media and is motivated by the fact that classical PMLs are unstable in negative index metamaterials and in some anisotropic plasmas. This led us to derive a new necessary criterion of stability which is valid for a large class of dispersive models and for more general PMLs than the classical ones. This criterion has been used to design new stable PMLs for negative index metamaterials and uniaxial anisotropic plasmas.

Retrieval method for anisotropic metamaterials

Participants : Aurore Castanié, Jean-François Mercier.

This work has been done during the post-doc of Aurore Castanié, in collaboration with Agnès Maurel from Institut Langevin at ESPCI and Simon Felix from the LAUM (Laboratoire d'Acoustique de l'Université du Maine). Electromagnetic or acoustic metamaterials can be described in terms of equivalent effective, in general anisotropic, media and several techniques exist to determine the effective permeability and permittivity (or effective mass density and bulk modulus in the context of acoustics). Among these techniques, retrieval methods use the measured scattering coefficients for waves incident on a metamaterial slab containing few unit cells. Until now, anisotropic effective slabs have been considered in the literature but they are limited to the case where one of the axes of anisotropy is aligned with the slab interface. We propose an extension to arbitrary orientations of the principal axes of anisotropy and oblique incidence. The retrieval method is illustrated in the electromagnetic case for layered media, and in the acoustic case for array of tilted elliptical particles.