We present a finite-element analysis of a diffraction problem involving a coated cylinder enabling the electromagnetic cloaking of a lossy object with sharp wedges located within its core. The coating consists of a heterogeneous anisotropic material deduced from a geometrical transformation as first proposed by Pendry [Science 312, 1780 (2006)]. We analyze the electromagnetic response of the cloak in the presence of an electric line source in p polarization and a loop of magnetic current in s polarization. We find that the electromagnetic field radiated by such a source located a fraction of a wavelength from the cloak is perturbed by less than 1%. When the source lies in the coating, it seems to radiate from a shifted location.

/pdf/electromagnetic-analysis-of-cylindrical-invisibility-cloaks-1dkft879rm.pdf

Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect

We extend the design of radially symmetric invisibility cloaks through transformation optics as proposed by Pendry et al. [Science 312, 1780 (2006)] to coated cylinders of an arbitrary cross section. The validity of our Fourier-based approach is confirmed by both analytical and numerical results for a cloak displaying a non-convex cross section of varying thickness. In the former case, we evaluate the Green's function of a line source in the transformed coordinates. In the latter case, we implement a full-wave finite-element model for a cylindrical antenna radiating a p-polarized electric field in the presence of a F-shaped lossy object surrounded by the cloak.

https://www.fresnel.fr/perso/nicolet/Publi/opl2008.pdf

Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section.

Purpose – This paper aims to review various techniques used in computational electromagnetism such as the treatment of open problems, helicoidal geometries and the design of arbitrarily shaped invisibility cloaks. This seemingly heterogeneous list is unified by the concept of geometrical transformation that leads to equivalent materials. The practical set‐up is conveniently effected via the finite element method.Design/methodology/approach – The change of coordinates is completely encapsulated in the material properties.Findings – The most significant examples are the simple 2D treatment of helicoidal geometries and the design of arbitrarily shaped invisibility cloaks.Originality/value – The paper provides a unifying point of view, bridging several techniques in electromagnetism.

/pdf/geometrical-transformations-and-equivalent-materials-in-4quivat4qq.pdf

Geometrical transformations and equivalent materials in computational electromagnetism

Transformation of space coordinates can be used as a convenient tool for producing a controlled electromagnetic field pattern. In this paper, using a conformal transformation, the design procedure of a lens antenna with high gain and low sidelobes is presented which can be realized by isotropic graded refractive index (GRIN) materials. Applying proper simplifying techniques, the designed lens can be made by non-resonant metamaterials or non-magnetic dielectrics having wide frequency band and low loss. A graded photonic crystal (GPC) operating in metamaterial regime is used for this purpose. By placing the lens in a horn antenna, a highly directive beam is achieved. It is also shown that by lateral displacement of the lens medium, the beam direction can be controlled to some extent. A multibeam antenna in which each beam can be controlled independently is also presented. Simulation results are used to justify the design approach.

Design of High-Gain Lens Antenna by Gradient-Index Metamaterials Using Transformation Optics

We present a survey of results from various research groups under the unifying viewpoint of transformational physics, which has been recently introduced for the design of metamaterials in optics and acoustics. We illustrate the versatility of underlying geometric transforms in order to bridge wave phenomena (the different 'colours' of waves) ranging from transverse electric waves, to linear surface water waves at an air–fluid interface, to pressure waves in fluids and out-of-plane shear waves in elastic media: these waves are all governed by a second order scalar partial differential equation (PDE) invariant under geometric transform. Moreover, flexural waves propagating in thin plates represent a very peculiar situation whereby the displacement field satisfies a fourth order scalar PDE which also retains its form under geometric transform (unlike for the Navier equation in elastodynamics). Control of flexural wave trajectories is illustrated with a multilayered cloak and a carpet. Interestingly, the colours of waves can be revealed through an analysis of the band spectra of invisibility cloaks. In the context of acoustics, this suggests one can hear the shape of a drum. Alternative avenues towards cloaking based upon anomalous resonances of a negatively refracting coating (which can be seen as the result of folding the space back onto itself), and even plasmonic shells reducing the scattering cross-section of nano-objects are also addressed.

https://iopscience.iop.org/article/10.1088/2040-8978/13/2/024014/pdf

The colours of cloaks

The representation of electromagnetic quantities by differential forms allows the use of nonorthogonal coordinate systems. A judicious choice of coordinate system facilitates the finite element modeling of infinite or very thin domains.

B. Meys

Papers

Transformation methods in computational electromagnetism