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.

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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).

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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.

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 description of local magnetic dissipation, enables the numerical analysis of rotational hysteresis losses on a sound theoretical basis. Originality/value -It proposes a simple, general purpose macroscopic model of hysteresis that is intrinsically a vector one, and not the vectorization of a scalar model.

Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies.For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This rises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM-solvers for computing and normalizing the QNMs of micro-and nanoresonators made of highly-dispersive materials. We benchmark several methods for three geometries, a twodimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, in the perspective to elaborate standards for the computation of resonance modes.