Frédéric Zolla

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.

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.

Quasimodal expansion of electromagnetic fields in open two-dimensional structures

A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional (2-D) open structures. In contrast with the bounded case which have only discrete spectrum (real in the lossless media case), open resonators show a continuous spectrum composed of radiation modes and may also be characterized by resonances associated to complex eigenvalues (quasimodes). The use of a complex change of coordinates to build Perfectly Matched Layers (PMLs) allows the numerical computation of those quasimodes and of approximate radiation modes. Unfortunately, the transformed operator at stake is no longer self-adjoint, and classical modal expansion fails. To cope with this issue, we consider an adjoint eigenvalue problem which eigenvectors are bi-orthogonal to the eigenvectors of the initial problem. The scattered field is expanded on this complete set of modes leading to a reduced order model of the initial problem. The different contributions of the eigenmodes to the scattered field unambiguously appears through the modal coefficients, allowing us to analyze how a given mode is excited when changing incidence parameters. This gives new physical insights to the spectral properties of different open structures such as nanoparticles and diffraction gratings. Moreover, the QMEM proves to be extremely efficient for the computation of Local Density Of States (LDOS).

Finite-Element Analysis of Cylindrical Invisibility Cloaks of Elliptical Cross Section

We present a finite-element analysis of a diffraction problem involving a coated cylinder enabling the electromagnetic cloaking of a finite conducting object with sharp wedges located within its core. The coating consists of a hollow cylinder with a circular cross section made of heterogeneous anisotropic material deduced from a geometric transformation as first proposed by Pendry The shape of the cloak is then generalized to elliptic cross sections.

The finite element method as applied to the diffraction by an anisotropic grating.

The main goal of the method proposed in this paper is the numerical study of various kinds of anisotropic gratings deposited on isotropic substrates, without any constraint upon the diffractive pattern geometry or electromagnetic properties. To that end we propose a new FEM (Finite Element Method) formulation which rigorously deals with each infinite issue inherent to grating problems. As an example, 2D numerical experiments are presented in the cases of the diffraction of a plane wave by an anisotropic aragonite grating on silica substrate (for the two polarization cases and at normal or oblique incidence). We emphasize the interesting property that the diffracted field is non symmetric in a geometrically symmetric configuration.

Numerical and Theoretical Study of Photonic Crystal Fibers

In this work, we study a novel type of optical waveguide, whose properties derive from a periodic arrangement of fibers (not necessarily circular), and from a central structural defect along which the light is guided. We first look for propagating modes in photonic crystal fibers of high indexcore region which can be single mode at any wavelength (1-4). Unlike the first type of photonic crystal fibers, whose properties derive from a high effective index, there exists some fundamentally different type of novel optical waveguides which consist in localizing the guided modes in air regions (4-5). These propagating modes are localized in a low-indexstructural defect thanks to a photonic bandgap guidance for the resonant frequencies (coming from the photonic crystal cladding). We achieve numerical computations with the help of a new finite element formulation for spectral problems arising in the determination of propagating modes in dielectric waveguides and particularly in optical fibers (7). The originality of the paper lies in the fact that we take into account both the boundness of the crystal (no Bloch wave expansion or periodicity boundary conditions) and the unboundness of the problem (no artificial boundary conditions at finite distance). We are thus led to an unbounded operator (open guide operator) and we must pay a special attention to its theoretical study before its numerical treatment. For this, we choose the magnetic field as the variable. It involves both a transverse field in the section of the guide and a longitudinal field along its axis. The section of the guide is meshed with triangles and Whitney finite elements are used, i.e., edge elements for the transverse field and node elements for the longitudinal field. To deal with the open problem, a judicious choice of coordinate transformation allows the finite element modeling of the infinite exterior domain. It is to be noticed that the discretization of the open guide operator leads to a generalized eigenvalue problem, solved thanks to the Lanczos algorithm. The code is validated by a numerical study of the classical