Biharmonic Split Ring Resonator Metamaterial: Artificially dispersive effective density in thin periodically perforated plates

We present in this paper a theoretical and numerical analysis of bending waves localized on the boundary of a platonic crystal whose building blocks are split ring resonators (SRR). We first derive the homogenized parameters of the structured plate using a three-scale asymptotic expansion in the linearized biharmonic equation. In the limit when the wavelength of the bending wave is much larger than the typical heterogeneity size of the platonic crystal, we show that it behaves as an artificial plate with an anisotropic effective Young modulus and a dispersive effective mass density. We then analyze dispersion diagrams associated with bending waves propagating within an infinite array of SRR, for which eigen-solutions are sought in the form of Floquet-Bloch waves. We finally demonstrate that this structure displays the hallmarks of All-Angle-Negative-Refraction(AANR) and it leads to superlensing and ultrarefraction effects, interpreted thanks to our homogenization model as a consequence of negative and vanishing effective density, respectively.Comment: 17 pages, 6 figure

Subwavelength sound screening by coupling space-coiled Fabry-Perot resonators

We explore broadband and omnidirectional low frequency sound screening based on locally resonant acoustic metamaterials. We show that the coupling of different resonant modes supported by Fabry-Perot cavities can efficiently generate asymmetric lineshapes in the transmission spectrum, leading to a broadband sound opacity. The Fabry-Perot cavities are space-coiled in order to shift the resonant modes under the diffraction edge, which guaranty the opacity band for all incident angles. Indeed, the deep subwavelength feature of the cavities leads to avoid diffraction that have been proved to be the main limitation of omnidirectional capabilities of locally resonant perforated plates. We experimentally reach an attenuation of few tens of dB at low frequency, with a metamaterial thickness fifteen times smaller than the wavelength (lambda / 15). The proposed design can be considered as a new building block for acoustic metasurfaces having a high level of manipulation of acoustic waves.Comment: 7 pages, 8 figure

Finite elements modelling of scattering problems for flexural waves in thin plates: Application to elliptic invisibility cloaks, rotators and the mirage effect

We propose a finite elements algorithm to solve a fourth order partial differential equation governing the propagation of time-harmonic bending waves in thin elastic plates. Specially designed perfectly matched layers are implemented to deal with the infinite extent of the plates. These are deduced from a geometric transform in the biharmonic equation. To numerically illustrate the power of elastodynamic transformations, we analyse the elastic response of an elliptic invisibility cloak surrounding a clamped obstacle in the presence of a cylindrical excitation i.e. a concentrated point force. Elliptic cloaking for flexural waves involves a density and an orthotropic Young's modulus which depend on the radial and azimuthal positions, as deduced from a coordinates transformation for circular cloaks in the spirit of Pendry et al. [Science {\bf 312}, 1780 (2006)], but with a further stretch of a coordinate axis. We find that a wave radiated by a concentrated point force located a couple of wavelengths away from the cloak is almost unperturbed in magnitude and in phase. However, when the point force lies within the coating, it seems to radiate from a shifted location. Finally, we emphasize the versatility of transformation elastodynamics with the design of an elliptic cloak which rotates the polarization of a flexural wave within its core.Comment: 14 pages, 5 figure

Cavitation Induction by Projectile Impacting on a Water Jet

The present paper focuses on the simulation of the high-velocity impact of a projectile impacting on a water-jet, causing the onset, development and collapse of cavitation. The simulation of the fluid motion is carried out using an explicit, compressible, density-based solver developed by the authors using the OpenFOAM library. It employs a barotropic two-phase flow model that simulates the phase-change due to cavitation and considers the co-existence of non-condensable and immiscible air. The projectile is considered to be rigid while its motion through the computational domain is modelled through a direct-forcing Immersed Boundary Method. Model validation is performed against the experiments of Field et al. [Field, J., Camus, J. J., Tinguely, M., Obreschkow, D., Farhat, M., 2012. Cavitation in impacted drops and jets and the effect on erosion damage thresholds. Wear 290–291, 154–160. doi:10.1016/j.wear.2012.03.006. URL http://www.sciencedirect.com/science/article/pii/S0043164812000968 ], who visualised cavity formation and shock propagation in liquid impacts at high velocities. Simulations unveil the shock structures and capture the high-speed jetting forming at the impact location, in addition to the subsequent cavitation induction and vapour formation due to refraction waves. Moreover, model predictions provide quantitative information and a better insight on the flow physics that has not been identified from the reported experimental data, such as shock-wave propagation, vapour formation quantity and induced pressures. Furthermore, evidence of the Richtmyer-Meshkov instability developing on the liquid-air interface are predicted when sufficient dense grid resolution is utilised

Cloaking and anamorphism for light and mass diffusion

We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we consider the equation for diffusive photon density in transformed coordinates, which is valid for diffusive light in scattering media. More precisely, generalizing transformations for star domains introduced in [Diatta and Guenneau, J. Opt. 13, 024012, 2011] for matter waves, we numerically demonstrate that infinite conducting objects of different shapes scatter diffusive light in exactly the same way. We also propose a design of external light-diffusion cloak with spatially varying sign-shifting parameters that hides a finite size scatterer outside the cloak. We next analyse non-physical parameter in the transformed Fick's equation derived in [Guenneau and Puvirajesinghe, R. Soc. Interface 10, 20130106, 2013], and propose to use a non-linear transform that overcomes this problem. We finally investigate other form invariant transformed diffusion-like equations in the time domain, and touch upon conformal mappings and non-Euclidean cloaking applied to diffusion processes.Comment: 42 pages, Latex, 14 figures. V2: Major changes : some formulas corrected, some extra cases added, overall length extended from 21 pages (V1) to 42 pages (present version V2). The last version will appear at Journal of Optic

Tunable Graphene Antennas for Selective Enhancement of THz-Emission

In this paper, we will introduce THz graphene antennas that strongly enhance the emission rate of quantum systems at specific frequencies. The tunability of these antennas can be used to selectively enhance individual spectral features. We will show as an example that any weak transition in the spectrum of coronene can become the dominant contribution. This selective and tunable enhancement establishes a new class of graphene-based THz devices, which will find applications in sensors, novel light sources, spectroscopy, and quantum communication devices

Techniques for Generating Centimetric Drops in Microgravity and Application to Cavitation Studies

This paper describes the techniques and physical parameters used to produce stable centimetric water drops in microgravity, and to study single cavitation bubbles inside such drops (Parabolic Flight Campaigns, European Space Agency ESA). While the main scientific results have been presented in a previous paper, we shall herein provide the necessary technical background, with potential applications to other experiments. First, we present an original method to produce and capture large stable drops in microgravity. This technique succeeded in generating quasi-spherical water drops with volumes up to 8 ml, despite the residual g-jitter. We find that the equilibrium of the drops is essentially dictated by the ratio between the drop volume and the contact surface used to capture the drop, and formulate a simple stability criterion. In a second part, we present a setup for creating and studying single cavitation bubbles inside those drops. In addition, we analyze the influence of the bubble size and position on the drop behaviour after collapse, i.e. jets and surface perturbations

Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets

We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordinates. A spherical acoustic cloak consisting of an alternation of homogeneous isotropic concentric layers is further proposed based on the effective medium theory. This cloak is characterised by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with a inhomogeneous and anisotropic distribution of material parameters. The latter suffers from singular material parameters on its inner surface. This singularity depends upon the sharpness of corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak becomes more and more singular when the number of vertices increases if it is star shaped. We thus analyse the acoustic response of a non-singular spherical cloak designed by blowing up a small ball instead of a point, as proposed in [Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The multilayered approximation of this cloak requires less extreme densities (especially for the lowest bound). Finally, we investigate another type of non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev. Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion. OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices; (160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility; (230.3205) Invisibility cloak

Analytical Approximations for the Collapse of an Empty Spherical Bubble

The Rayleigh equation 3/2 R'+RR"+p/rho=0 with initial conditions R(0)=Rmax, R'(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density rho. The solution for r=R/Rmax as a function of time t=T/Tcollapse, where R(Tcollapse)=0, is independent of Rmax, p, and rho. While no closed-form expression for r(t) is known we find that s(t)=(1-t^2)^(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t^2 further yields the 0.001%-approximation r*(t)=s(t)[1-a Li(2.21,t^2)], where a=-0.01832099 is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity.Comment: 5 pages, 2 figure