Guillaume Dupont

Hidden progress: broadband plasmonic invisibility

One of the key challenges in current research into electromagnetic cloaking is to achieve invisibility at optical frequencies and 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. 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 control to demonstrate both theoretically and experimentally cloaking over an unprecedented bandwidth (650-900 nm). Our non-resonant plasmonic metamaterial is designed using transformational optics extended to plasmonics and allows a curved reflector to mimic a flat mirror. Our theoretical predictions are validated by experiments mapping the surface light intensity at a wavelength of 800 nm.

Enhanced control of light and sound trajectories with three-dimensional gradient index lenses

We numerically study the focusing and bending effects of light and sound waves through heterogeneous isotropic cylindrical and spherical devices. We first point out that transformation optics and acoustics show that the control of light requires spatially varying anisotropic permittivity and permeability, while the control of sound is achieved via spatially anisotropic density and isotropic compressibility. Moreover, homogenization theory applied to electromagnetic and acoustic periodic structures leads to such artificial (although not spatially varying) anisotropic permittivity, permeability and density. We stress that homogenization is thus a natural mathematical tool for the design of structured metamaterials. To illustrate the two-step geometric transform-homogenization approach, we consider the design of cylindrical and spherical electromagnetic and acoustic lenses displaying some artificial anisotropy along their optical axis (direction of periodicity of the structural elements). Applications are sought in the design of Eaton and Luneburg lenses bending light at angles ranging from 90° to 360°, or mimicking a Schwartzchild metric, i.e. a black hole. All of these spherical metamaterials are characterized by a refractive index varying inversely with the radius which is approximated by concentric layers of homogeneous material. We finally propose some structured cylindrical metamaterials consisting of infinitely conducting or rigid toroidal channels in a homogeneous bulk material focusing light or sound waves. The functionality of these metamaterials is demonstrated via full-wave three-dimensional computations using nodal elements in the context of acoustics, and finite edge-elements in electromagnetics.

Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets

Abstract We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way toward 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 characterized by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with an 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 analyze 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.

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.

Controlling surface plasmon polaritons in transformed coordinates

Transformational optics allows 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 (for the latter we provide some analytical insight), 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 a small curvature.

Broadband cloaking and mirages with flying carpets

This paper extends the proposal of Li and Pendry [Phys. Rev. Lett. 101, 203901-4 (2008)] to invisibility carpets for infinite conducting planes and cylinders (or rigid planes and cylinders in the context of acoustic waves propagating in a compressible fluid). Carpets under consideration here 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 touch 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 and 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 parameters. To exemplify this important aspect, we propose a multi-layered carpet consisting of isotropic homogeneous dielectrics rings (or fluids with constant bulk modulus and varying density) which works over a finite range of wavelengths.

Type of dike using C-shaped vertical cylinders

The present study investigates a way to design dikes which can filter the wavelengths of ocean surface waves. This offers the possibility to achieve a structure that can attenuate waves associated with storm swell, without affecting coastline in other conditions. Our approach is based on low-frequency resonances in metamaterials combined with Bragg frequencies for which waves cannot propagate in periodic lattices.

From transformational optics to plasmonics

In this paper, we adapt tools of transformational optics to the control of surface plasmon polaritons propagating on curved metallic surfaces. The theoretical analysis leads to a dispersion relation for surface plasmon polaritons propagating at an interface between a metal and an anisotropic heterogeneous medium. The theoretical concept is illustrated by full wave finite element computations for a three‐dimensional carpet.