On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials

This work deals with Perfectly Matched Layers (PMLs) in the context of dispersive media, and in particular for Negative Index Metamaterials (NIMs). We first present some properties of dispersive isotropic Maxwell equations that include NIMs. We then demonstrate numerically the inherent instabilities of the classical PMLs applied to NIMs. We propose and analyse the stability of very general PMLs for a large class of dispersive systems using a new change of variable. We give necessary criteria for the stability of such models. For dispersive isotropic Maxwell equations, this analysis is completed by giving necessary and sufficient conditions of stability. Finally, we propose new PMLs that satisfy these criteria and demonstrate numerically their efficiency

Finite Element Analysis of Electromagnetic Waves in Two-Dimensional Transformed Bianisotropic Media

We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations (PDEs) for longitudinal electric and magnetic field components. Perfectly Matched Layers (PMLs) are discussed to model such unbounded media. We implement these PDEs and PMLs in a finite element software. We apply transformation optics in order to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. We propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magneto-electric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that well-known metamaterials can be transposed to bianisotropic media.Comment: 26 pages, 8 figure

Mathematical models for dispersive electromagnetic waves: an overview

In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is devoted to the notion of non-dissipativity and passivity. We consider successively the case of so-called local media and general passive media. The models are studied through energy techniques, spectral theory and dispersion analysis of plane waves. For making the article self-contained, we provide in appendix some useful mathematical background.Comment: 46 pages, 16 figure

Electromagnetic wave propagation in media consisting of dispersive metamaterials

We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwell's equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials obeying Drude's and Lorentz' models. The causality and the passivity are the two main assumptions and play a crucial role in the analysis. It is worth noting that by contrast the well-posedness in the frequency domain is not ensured in general. We also provide some numerical experiments using the Drude's model to illustrate its dispersive behaviour

Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: Necessary and sufficient conditions of stability

Extended VersionInternational audienceIn this work we consider a problem of modelling of 2D anisotropic dispersive wave propagation in unbounded domains with the help of perfectly matched layers (PML). We study the Maxwell equations in passive media with a frequency-dependent diagonal tensor of dielectric permittivity and magnetic permeability. An application of the traditional PMLs to this kind of problems often results in instabilities. We provide a recipe for the construction of new, stable PMLs. For a particular case of non-dissipative materials, we show that a known necessary stability condition of the perfectly matched layers is also sufficient. We illustrate our statements with theoretical and numerical arguments

High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics

We propose a method for engineering thermally excited far field electromagnetic radiation using epsilon-near-zero metamaterials and introduce a new class of artificial media: epsilon-near-pole metamaterials. We also introduce the concept of high temperature plasmonics as conventional metamaterial building blocks have relatively poor thermal stability. Using our approach, the angular nature, spectral position, and width of the thermal emission and optical absorption can be finely tuned for a variety of applications. In particular, we show that these metamaterial emitters near 1500 K can be used as part of thermophotovoltaic devices to surpass the full concentration Shockley-Queisser limit of 41%. Our work paves the way for high temperature thermal engineering applications of metamaterials.Comment: 15 pages, 8 figure

A Positive Future for Double-Negative Metamaterials

Metamaterials (MTMs), which are formed by embedding inclusions and material components in host media to achieve composite media that may be engineered to have qualitatively new physically realizable response functions that do not occur or may not be easily available in nature, have raised a great deal of interest in recent years. In this paper, we highlight a large variety of the physical effects associated with double- and single-negative MTMs and some of their very interesting potential applications. The potential ability to engineer materials with desired electric and magnetic properties to achieve unusual physical effects offers a great deal of excitement and promise to the scientific and engineering community. While some of the applications we will discuss have already come to fruition, there are many more yet to be explored

FDTD modelling of electromagnetic transformation based devices

PhDDuring this PhD study, several finite-difference time-domain (FDTD) methods were developed to numerically investigate coordinate transformation based metamaterial devices. A novel radially-dependent dispersive FDTD algorithm was proposed and applied to simulate electromagnetic cloaking structures. The proposed method can ac- curately model both lossless and lossy cloaks with ideal or reduced parameters. It was demonstrated that perfect “invisibility” from electromagnetic cloaks is only available for lossless metamaterials and within an extremely narrow frequency band. With a few modifications the method is able to simulate general media, such as concentrators and rotation coatings, which are produced by means of coordinate transformations techniques. The limitations of all these devices were thoroughly studied and explo- red. Finally, more useful cloaking structures were proposed, which can operate over a broad frequency spectrum. Several ways to control and manipulate the loss in the electromagnetic cloak ba- sed on transformation electromagnetics were examined. It was found that, by utili- sing inherent electric and magnetic losses of metamaterials, as well as additional lossy materials, perfect wave absorption can be achieved. These new devices demonstrate super-absorptivity over a moderate wideband range, suitable both for microwave and optical applications. Furthermore, a parallel three-dimensional dispersive FDTD method was introdu- ced to model a plasmonic nanolens. The device has its potential in subwavelength imaging at optical frequencies. The finiteness of such a nano-device and its impact on the system dynamic behaviour was numerically exploited. Lastly, a parallel FDTD method was also used to model another interesting coordinate transformation based device, an optical black hole, which can be characterised as an omnidirectional broad- band absorber

Accurate simulation of THz generation with Finite-Element Time Domain methods

We investigate the accurate full broadband simulation of complex nonlinear optical processes. A mathematical model and numerical simulation techniques in the time domain are developed to simulate complex nonlinear optical processes without the usual used slowly varying envelope approximation. We illustrate the accuracy by numerical simulations. Furthermore, they are used to elucidate THz generation in periodically poled Lithium Niobate (PPLN) including optical harmonic generation.Comment: Submitted to Optics Expres