Elastodynamic cloaking and field enhancement for soft spheres

In this paper, we bring to the awareness of the scientific community and civil engineers, an important fact: the possible lack of wave protection of transformational elastic cloaks. To do so, we propose spherical cloaks described by a non-singular asymmetric elasticity tensor depending upon a small parameter $\eta,$ that defines the softness of a region one would like to conceal from elastodynamic waves. By varying $\eta$, we generate a class of soft spheres dressed by elastodynamic cloaks, which are shown to considerably reduce the soft spheres' scattering. Importantly, such cloaks also provide some wave protection except for a countable set of frequencies, for which some large elastic field enhancement (resonance peaks) can be observed within the cloaked soft spheres, hence entailing a possible lack of wave protection. We further present an investigation of trapped modes in elasticity via which we supply a good approximation of such Mie-type resonances by some transcendental equation. Next, after a detailed presentation of spherical elastodynamic PML of Cosserat type, we introduce a novel generation of cloaks, the mixed cloaks, as a solution to the lack of wave protection in elastodynamic cloaking. Indeed, mixed cloaks achieve both invisibility cloaking and protection throughout a large range of frequencies. We think, mixed cloaks will soon be generalized to other areas of physics and engineering and will in particular foster studies in experiments.Comment: V2: major changes. More details on the study of trapped modes in elasticity. Mixed cloaks introduced. Latex files, 27 pages, 14 figures. The last version will appear at Journal of Physics D: Applied Physics. Pacs:41.20.Jb,42.25.Bs,42.70.Qs,43.20.Bi,43.25.Gf. arXiv admin note: text overlap with arXiv:1403.184

Cloaking via change of variables in elastic impedance tomography

We discuss the concept of cloaking for elastic impedance tomography, in which, we seek information on the elasticity tensor of an elastic medium from the knowledge of measurements on its boundary. We derive some theoretical results illustrated by some numerical simulations.Comment: latex, 2 figures, 11 pages, submitte

Controlling solid elastic waves with spherical cloaks

We propose a cloak for coupled shear and pressure waves in solids. Its elastic properties are deduced from a geometric transform that retains the form of Navier equations. The spherical shell is made of an anisotropic and heterogeneous medium described by an elasticity tensor C' (without the minor symmetries) which has 21 non-zero spatially varying coefficients in spherical coordinates. Although some entries of C, e.g. some with a radial subscript, and the density (a scalar radial function) vanish on the inner boundary of the cloak, this metamaterial exhibits less singularities than its cylindrical counterpart studied in [M. Brun, S. Guenneau, A.B. Movchan, Appl. Phys. Lett. 94, 061903 (2009).] In the latter work, C' suffered some infinite entries, unlike in our case. Finite element computations confirm that elastic waves are smoothly detoured around a spherical void without reflection.Comment: Version 3: minor typos corrected. Figures captions improved. 5 figures. Key words: 3D elastic cloaking, seismic metamaterials. This paper is the cover of the 14 July 2014 issue of Applied Physics Letter

High-frequency homogenization of zero frequency stop band photonic and phononic crystals

We present an accurate methodology for representing the physics of waves, for periodic structures, through effective properties for a replacement bulk medium: This is valid even for media with zero frequency stop-bands and where high frequency phenomena dominate. Since the work of Lord Rayleigh in 1892, low frequency (or quasi-static) behaviour has been neatly encapsulated in effective anisotropic media. However such classical homogenization theories break down in the high-frequency or stop band regime. Higher frequency phenomena are of significant importance in photonics (transverse magnetic waves propagating in infinite conducting parallel fibers), phononics (anti-plane shear waves propagating in isotropic elastic materials with inclusions), and platonics (flexural waves propagating in thin-elastic plates with holes). Fortunately, the recently proposed high-frequency homogenization (HFH) theory is only constrained by the knowledge of standing waves in order to asymptotically reconstruct dispersion curves and associated Floquet-Bloch eigenfields: It is capable of accurately representing zero-frequency stop band structures. The homogenized equations are partial differential equations with a dispersive anisotropic homogenized tensor that characterizes the effective medium. We apply HFH to metamaterials, exploiting the subtle features of Bloch dispersion curves such as Dirac-like cones, as well as zero and negative group velocity near stop bands in order to achieve exciting physical phenomena such as cloaking, lensing and endoscope effects. These are simulated numerically using finite elements and compared to predictions from HFH. An extension of HFH to periodic supercells enabling complete reconstruction of dispersion curves through an unfolding technique is also introduced

Finite Element Analysis of Electromagnetic Waves in Two-Dimensional Transformed Bianisotropic Media

We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations (PDEs) for longitudinal electric and magnetic field components. Perfectly Matched Layers (PMLs) are discussed to model such unbounded media. We implement these PDEs and PMLs in a finite element software. We apply transformation optics in order to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. We propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magneto-electric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that well-known metamaterials can be transposed to bianisotropic media.Comment: 26 pages, 8 figure

Novel topological beam-splitting in photonic crystals

We create a passive wave splitter, created purely by geometry, to engineer three-way beam splitting in electromagnetism in transverse electric polarisation. We do so by considering arrangements of Indium Phosphide dielectric pillars in air, in particular we place several inclusions within a cell that is then extended periodically upon a square lattice. Hexagonal lattice structures more commonly used in topological valleytronics but, as we discuss, three-way splitting is only possible using a square, or rectangular, lattice. To achieve splitting and transport around a sharp bend we use accidental, and not symmetry-induced, Dirac cones. Within each cell pillars are either arranged around a triangle or square; we demonstrate the mechanism of splitting and why it does not occur for one of the cases. The theory is developed and full scattering simulations demonstrate the effectiveness of the proposed designs

Experiments on transformation thermodynamics: Molding the flow of heat

It has recently been shown theoretically that the time-dependent heat conduction equation is form-invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped onto (meta-)materials with spatially inhomogeneous and anisotropic heat-conductivity tensors in the laboratory space. On this basis, we design, fabricate, and characterize a micro-structured thermal cloak that molds the flow of heat around an object in a metal plate. This allows for transient protection of the object from heating, while maintaining the same downstream heat flow as without object and cloak.Comment: 10 pages, 4 figure