André Nicolet

Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect

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.

Foundations of photonic crystal fibres

Photonic Crystals Optical Waveguides Photonic Crystal Fibres (PCF) PCF Materials and Fabrication Finite Element Method Propagation Modes Problems in Dielectric Waveguides The Multipole Method Rayleigh Method Pole Hunting Properties of MOF Twisted Fibres.

Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section

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 Greens 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.

Coupling of local and global quantities in various finite element formulations and its application to electrostatics, magnetostatics and magnetodynamics

A method for defining global quantities related to fluxes and circulations is proposed in the frame of the finite element method. The definition is in perfect accordance with the discretized weak formulations of the problems. It therefore enables a natural coupling between local and global quantities in various formulations, while keeping a symmetrical matrix for the system, and then is open to the coupling of physical problems. Applications are given for electrostatics, magnetostatics and magnetodynamics.

Mixed finite elements associated with a collection of tetrahedra, hexahedra and prisms

A generalization of the Whitney complex is proposed, which is not now associated with simplices, i.e. tetrahedra in three dimensions, but with collections of three kinds of geometric elements: tetrahedra, hexahedra and prisms. Nodal, edge, facet and volume finite elements, i.e. mixed elements, associated with collections of those geometric elements, are defined. Base functions for approximation relative to these finite elements are defined and their properties are established. A geometric interpretation of these functions is given. >

Geometrical transformations and equivalent materials in computational electromagnetism

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.

On the use of PML for the computation of leaky modes An application to microstructured optical fibres

Purpose – The purpose of this paper is to present a complete analysis of leaky modes within a microstructured optical fibre (MOF). Some new numerical results illustrating the versatility and accuracy of our approach are to be given.Design/methodology/approach – A method involving both finite elements and perfectly matched layer (PML) is proposed.Findings – A rigorous definition of the leaky modes is proposed that leads to a proof of the validity of the PML approach together with a rule for the choice of the PML parameters.Originality/value – The choice of parameters associated with the PML are discussed in great detail. The accuracy of the constant of propagation (and especially the imaginary part) are highlighted.

A homogenization route towards square cylindrical acoustic cloaks

We analyse the acoustic properties of a square cylindrical heterogeneous orthotropic cloak deduced from a geometric transform. We propose to achieve some of the properties of this cloak with an elastic square coating divided into 256 cracks preserving its four-fold symmetry. The cloaking mechanism renders freely vibrating and clamped inclusions neutral to some extent and is inherently broadband: provided that the working wavelength is at least three times larger than the outermost sectors of the coating, its homogenized elastic parameters display some transverse anisotropy. Finally, we compare such a cloak to an absorbing coating consisting of elliptical inclusions.

An energy‐based vector hysteresis model for ferromagnetic materials

Purpose – Proposes a new quasi‐static vector hysteresis model based on an energy approach, where dissipation is represented by a friction‐like force.Design/methodology/approach – The start point is the local energy balance of the ferromagnetic material. Dissipation is represented by a friction‐like force, which derives from a non‐differentiable convex functional. Several elementary hysteresis cells can be combined, in order to increase the number of free parameters in the model, and therefore improve the accuracy.Findings – A friction‐like force is a good way to represent magnetic dissipation at the macroscopic level. The proposed method is easy to implement and non‐differentiability amounts in this case to a simple “if” statement.Research limitations/implications – The next steps are the extension to dynamic hysteresis and the in‐depth analysis of the identification process, which is only sketched in this paper.Practical implications – This vector model, which is based on a reasonable phenomenological de...

Modelling of electromechanical relays taking into account movement and electric circuits

This paper presents a numerical modelling of an electromechanical relay connected with an electric excitation circuit. This transient modelling not only takes into account the classical electromagnetic equations of the device but also the movement and circuit equations. The use of the finite element-boundary element coupling method facilitates the computation of the movement while the actual coupling with circuit equations is necessary for an accurate and reliable representation of transient phenomena. >