arXiv subjects

Stefan Enoch

Publications and source records attributed to Stefan Enoch.

34 records · Page 2Linked to original sources

arXiv2016

Seismic waves damping with arrays of inertial resonators

We investigate the elastic stop band properties of a theoretical cubic array of iron spheres connected to a bulk of concrete via iron or rubber ligaments. Each sphere can move freely within a surrounding air cavity, but ligaments couple it to the bulk and further facilitate bending and rotational motions. Associated low frequency local resonances are well predicted by an asymptotic formula. We find complete stop bands (for all wave-polarizations) in the frequency range $[16,21]$ Hertz (resp. $[6,11]$ Hertz) for $7.4$-meter (resp. $0.74$-meter) diameter iron spheres with a $10$-meter (resp. $1$-meter) center-to-center spacing, when they are connected to concrete via steel (resp. rubber) ligaments. The scattering problem shows that only bending modes are responsible for damping and that rotational modes are totally overwritten by bending modes. Regarding seismic applications, we further consider soil as a bulk medium, in which case the relative bandwidth of the low frequency stop band can be enlarged through ligaments of different sizes that allow for well separated bending and rotational modes. We finally achieve some damping of elastodynamic waves from $8$ to $49$ Hertz (relative stop band of $143$ percent) for iron spheres $0.74$-meter in diameter that are connected to soil with six rubber ligaments of optimized shapes. These results represent a preliminary step in the design of seismic shields placed around, or underneath, the foundations of large civil infrastructures.

physics.class-ph↗

arXiv2014

Invisible waveguides on metal plates for plasmonic analogues of electromagnetic wormholes

We introduce two types of toroidal metamaterials which are invisible to surface plasmon polaritons (SPPs) propagating on a metal surface. The former is a toroidal handlebody bridging remote holes on the metal surface: It works as a kind of plasmonic counterpart of electromagnetic wormholes. The latter is a toroidal ring lying on the metal surface: This bridges two disconnected metal surfaces i.e. It connects a thin metal cylinder to a flat metal surface with a hole. Full-wave numerical simulations demonstrate that an electromagnetic field propagating inside these metamaterials does not disturb the propagation of SPPs at the metal surface. A multilayered design of these devices is proposed, based on effective medium theory for a set of reduced parameters: The former plasmonic analogue of electromagnetic wormhole requires homogeneous isotropic magnetic layers, while the latter merely requires dielectric layers.

physics.optics↗

arXiv2013

Seismic metamaterial: how to shake friends and influence waves?

Materials engineered at the micro- and nano-meter scale have had a tremendous and lasting impact in photonics and phononics, with applications ranging from periodic structures disallowing light and sound propagation at stop band frequencies, to subwavelength focussing and cloaking with metamaterials. Here, we present the description of a seismic test held on a soil structured at the meter scale using vibrocompaction probes. The most simplistic way to interact with a seismic wave is to modify the global properties of the medium, acting on the soil density and then on the wave velocity. The main concept is then to reduce the amplification of seismic waves at the free surface, called site effects in earthquake engineering. However, an alternative way to counteract the seismic signal is by modifying the distribution of seismic energy thanks to a metamaterial made of a grid of vertical, cylindrical and empty inclusions bored in the initial soil, in agreement with numerical simulations using an approximate plate model.

physics.geo-ph↗

arXiv2011

Invisibility carpet in a channel with a structured fluid

We first note it is possible to construct two linear operators defined on two different domains, yet sharing the same spectrum using a geometric transform. However, one of these two operators will necessarily have spatially varying, matrix valued, coefficients. This mathematical property can be used in the design of metamaterials whereby two different domains behave in the same electromagnetic, acoustic, or hydrodynamic way (mimetism). To illustrate this property, we describe a feasible invisibility carpet for linear surface liquid waves in a channel. This structured metamaterial bends surface waves over a finite interval of Hertz frequencies.

physics.flu-dyn↗

arXiv2011

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.

math-ph↗

arXiv2011

Plasmonic interaction of light with negative index and gold nano-checkerboards

Negative refractive index materials (NRIM) make possible unique effects such as a convergent at lens due to the reversed Snell-Descartes laws of refraction. NRIM are also known to be able to support a host of surface plasmon states for both polarizations of light which are responsible for the sub-wavelength image resolution achieved by a slab of NRIM. A generalized lens theorem provides us with a class of spatially varying slab lenses satisfying the prerequisite symmetries to fold the optical space onto itself. This theorem can be derived using powerful tools of transformational optics. A paradigm of such complementary media are checkerboards consisting of alternating cells of positive and negative refractive index that represent a very singular situation in which the local density of modes at the corners are enormously enhanced. We have considered several theoretical and numerical aspects of such structured films including a finite slabs of multi-scale checkerboards of NRIM satisfying the generalized lens theorem which are host of strongly enhanced electromagnetic feld. Such checkerboards can be mapped using transformational optics onto three-dimensional corner lenses consisting of semi-infinite heterogeneous anisotropic regions of space satisfying the generalized lens theorem. It is also possible to design three-dimensional checkerboards of complementary media, the only restriction being that corresponding unfolded structures in the plane are constrained by the four color theorem. Some of these meta-surfaces in the plane display thin bridges of complementary media, and this further enhances their plasmonic response. Since plasmonic metals mimic the behaviour of NRIM at small length scales, opaque gold films structured at sub-micron scales in a checkerboard fashion were fabricated using focussed-ion-beam technologies and their scattering spectra measured.

physics.optics↗

arXiv2011

Curved trajectories on transformed metal surfaces: Luneburg lens, beam-splitter, invisibility carpet and black hole for surface plasmon polaritons

Transformational optics are shown to markedly enhance the control of the electromagnetic wave trajectories within metamaterials with unconventional functionalities such as a beam splitter, a toroidal carpet, a Luneburg lens and a black hole, all of which are specially designed for surface plasmon polaritons propagating on a metal plate

physics.optics↗

arXiv2010

Plasmonic space folding: focussing surface plasmons via negative refraction in complementary media

We extend designs of perfect lenses to the focussing of surface plasmon polaritons (SPPs) propagating at the interface between two anisotropic media of opposite permittivity sign. We identify the role played by the components of anisotropic and heterogeneous tensors of permittivity and permeability, deduced from a coordinate transformation, in the dispersion relation governing propagation of SPPs. We illustrate our theory with three-dimensional finite element computations for focussing of SPPs by perfect flat and cylindrical lenses.

physics.optics↗

arXiv2010

Controlling surface plasmon polaritons in transformed coordinates

Transformational optics allow for a markedly enhanced control of the electromagnetic wave trajectories within metamaterials with interesting applications ranging from perfect lenses to invisibility cloaks, carpets, concentrators and rotators. Here, we present a review of curved anisotropic heterogeneous meta-surfaces designed using the tool of transformational plasmonics, in order to achieve a similar control for surface plasmon polaritons in cylindrical and conical carpets, as well as cylindrical cloaks, concentrators and rotators of a non-convex cross-section. Finally, we provide an asymptotic form of the geometric potential for surface plasmon polaritons on such surfaces in the limit of small curvature.

physics.optics↗

arXiv2010

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.

physics.comp-ph↗

arXiv2010

Electromagnetic analysis of arbitrarily shaped pinched carpets

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and perme- ability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map a non convex region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components, and this may lead to some broadband cloaking.

physics.comp-ph↗

arXiv2010

Hidden progress: broadband plasmonic invisibility

The key challenge in current research into electromagnetic cloaking is to achieve invisibility over an extended bandwidth. There has been significant progress towards this using the idea of cloaking by sweeping under the carpet of Li and Pendry, with dielectric structures superposed on a mirror. Here, we show that we can harness surface plasmon polaritons at a metal surface structured with a dielectric material to obtain a unique control of their propagation. We exploit this to control plasmonic coupling and demonstrate both theoretically and experimentally cloaking over an unprecedented bandwidth (650-900 nm). Our non-resonant plasmonic metamaterial allows a curved reflector to mimic a flat mirror. Our theoretical predictions are validated by experiments mapping the surface light intensity at the wavelength 800 nm.

physics.optics↗

arXiv2009

Acoustic cloaking and mirages with flying carpets

Carpets under consideration here, in the context of pressure acoustic waves propagating in a compressible fluid, do not touch the ground: they levitate in mid-air (or float in mid-water), which leads to approximate cloaking for an object hidden underneath, or touching either sides of a square cylinder on, or over, the ground. The tentlike carpets attached to the sides of a square cylinder illustrate how the notion of a carpet on a wall naturally generalizes to sides of other small compact objects. We then extend the concept of flying carpets to circular cylinders. However, instead of reducing its scattering cross-section like in acoustic cloaks, we rather mimic that of another obstacle, say a square rigid cylinder. For instance, show that one can hide any type of defects under such circular carpets, and yet they still scatter waves just like a smaller cylinder on its own. Interestingly, all these carpets are described by non-singular acoustic parameters. To exemplify this important aspect, we propose a multi-layered carpet consisting of isotropic homogeneous fluids with constant bulk modulus and varying density which works over a finite range of wavelengths. We have discussed some applications, with the sonar boats or radars cases as typical examples. For instance, we would like to render a pipeline lying on the bottom of the sea or floating in mid-water undetectable for a boat with a sonar at rest just above it on the surface of the sea. Another possible application would be protecting parabolic antennas.

physics.optics↗

arXiv2009

Revolution analysis of three-dimensional arbitrary cloaks

We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its eigenvalues vanishes on the inner boundary of the cloaks, while the other two remain strictly positive and bounded. The validity of our approach is confirmed by finite edge-elements computations for a non-convex cloak of varying thickness.

physics.optics↗

arXiv2009

Directive Emission from Defect-Free Dodecagonal Photonic Quasicrystals: A Leaky-Wave Characterization

In this paper, we study the radiation from embedded sources in two-dimensional finite-size "photonic-quasicrystal" (PQC) slabs made of dielectric rods arranged according to a 12-fold symmetric aperiodic tiling. The results from our investigation, based on rigorous full-wave simulations, show the possibility of achieving broadside radiation at multiple frequencies, with high-directivity (e.g., 15 dB) and low-sidelobes (e.g., -12 dB). We also show that leaky waves are supported by a PQC slab, and that the beamwidth is directly proportional to the leaky-wave attenuation constant, which provides a physically-incisive interpretation of the observed radiation characteristics.

physics.optics↗

arXiv2008

Quasi-TEM modes in rectangular waveguides: a study based on the properties of PMC and hard surfaces

Hard surfaces or magnetic surfaces can be used to propagate quasi-TEM modes inside closed waveguides. The interesting feature of these modes is an almost uniform field distribution inside the waveguide. But the mechanisms governing how these surfaces act, how they can be characterized, and further how the modes propagate are not detailed in the literature. In this paper, we try to answer these questions. We give some basic rules that govern the propagation of the quasi-TEM modes, and show that many of their characteristics (i.e. their dispersion curves) can be deduced from the simple analysis of the reflection properties of the involved surfaces.

physics.class-ph↗