Steering in-plane shear waves with inertial resonators in platonic crystals

Numerical simulations shed light on control of shear elastic wave propagation in plates structured with inertial resonators. The structural element is composed of a heavy core connected to the main freestanding plate through tiny ligaments. It is shown that such a configuration exhibits a complete band gap in the low frequency regime. As a byproduct, we further describe the asymmetric twisting vibration of a single scatterer via modal analysis, dispersion and transmission loss. This might pave the way to new functionalities such as focusing and self-collimation in elastic plates

Homogenization of 3D finite chiral photonic crystals

International audienceWe homogenize Maxwell's equations for Drude-Born-Fedorov chiral crystals, using the multi-scale technique. We find that the homogenized material is described by dispersive anisotropic effective matrices, derived from frequency-dependent coupled auxiliary problems. For low frequencies, these matrices may not be positive definite

Bloch-wave homogenization for spectral asymptotic analysis of the periodic Maxwell operator

International audienceThis paper is devoted to the asymptotic behavior of the spectrum of the three-dimensional Maxwell operator in a bounded periodic heterogeneous dielectric medium T = [-T,T]3, T > 0, as the structure period , such that -1 T is a positive integer, tends to 0. The domain T is extended periodically to the whole of 3, so that the original operator is understood as acting in a space of T-periodic functions. We use the so-called Bloch-wave homogenization technique which, unlike the classical homogenization method, is capable of characterizing a renormalized limit of the spectrum (called the Bloch spectrum) [6]. The related procedure is concerned with sequences of eigenvalues of the resolvent of the order of the square of the medium period, which correspond to the oscillations of high-frequencies of order -1. The Bloch-wave description is obtained via the notion of two-scale convergence for bounded self-adjoint operators, and a proof of the 'completeness' of the limiting spectrum is provided. The results obtained theoretically are illustrated by finite element computations

Morphing for faster computations in transformation optics

International audienceWe propose to use morphing algorithms to deduce some approximate wave pictures of scattering by cylindrical invisibility cloaks of various shapes deduced from the exact computation (e.g. using a finite element method) of scattering by cloaks of two given shapes, say circular and elliptic ones, thereafter called the source and destination images. The error in L 2 norm between the exact and approximate solutions deduced via morphing from the source and destination images is typically less than 1 percent if control points are judiciously chosen. Our approach works equally well for rotators and concentrators, and also unveils some device which we call rotacon since it both rotates and concentrates electromagnetic fields. However, it breaks down for superscatterers (deduced from non-monotonic transforms): The error in L 2 norm is about 25 percent. We stress that our approach might greatly accelerate numerical studies of 2D and 3D cloaks

Spectral efficiency of engineered thermal cloaks in the frequency regime

We analyse basic thermal cloaks designed via different geometric transforms applied to thermal cloaking. We evaluate quantitatively the efficiency of these heterogeneous anisotropic thermal cloaks through the calculation of the standard deviation of the isotherms. The study addresses the frequency regime and we point out the cloak's spectral efficiencies. We find that all these cloaks have comparable efficiency irrespective of whether or not they have singular conductivity at their inner boundary. However, approximate cloaking with multi-layered cloak critically depends upon the homogenization algorithm and a large number of thin layers (at least fifty) is required to reduce substantially the standard deviation of the isotherms.Comment: 13 pages, 7 figures. The results from this article will be presented on a poster at the Metamaterials 2014 Copenhague conferenc