Metasurface Analysis Using Finite Difference Techniques

RÉSUMÉ Les métasurfaces sont des structures très minces par rapport à la longueur d’onde de fonc-tionnement et des dimensions des métamatériaux tridimensionnels. Ils sont réalisés par la juxtaposition de cellule-unitaire en dessous de la longueur d’onde. Tout en étant légers et offrant moins de pertes, ils offrent une gamme d’applications plus étendue que les métamatériaux 3D classiques. Étant capables de modifier l’amplitude, la polarisation, la phase et la fréquence des ondes, leurs applications vont des fréquences radio aux optiques dans la formation de faisceaux, radômes, capes, lentilles, structures non réciproques et hologrammes, pour n’en nommer que quelques-uns. En général, les métasurfaces sont des structures bianisotropes, qui, par le fait même, présentent des discontinuités spatiales et temporelles très complexes. Leur synthèse est basée sur les conditions généralisées de transition de feuille (GSTC) qui sont calculées à l’aide de la théorie de la distribution. Suivant cette théorie, ils sont modélisés comme une structure d’épaisseur nulle. Cependant, dans le calcul des particules diffusantes, l’utilisation des paramètres S ou des matrices d’impédance permet de les cartographier dans des inclusions de cellules unitaires appropriées avec une dimension inférieure à longueur d’onde. La bianisotropie et l’épaisseur nulle impliquent une discontinuité à la fois des champs électriques et magnétiques qui est connues sous le nom de problème général de discontinuité électromagnétique. Cela rend donc leur analyse très compliquée et impossible à faire avec les techniques numériques conventionnelles. Par conséquent, ce manuscrit traitera du manque significatif de méthode d’analyse précise et entièrement numérique. Dans cette thèse, nous effectuons un examen approfondi des conditions aux limites classiques et discutons de leurs limites et de leurs conditions d’applicabilité. Les GSTC sont dérivés, et leur utilité est discutée. Ensuite, nous développons des techniques de calcul dans le schéma des différences finies (FD) pour l’analyse de discontinuité électromagnétique générale. Nous prouvons que les techniques numériques développées pour discontinuité simple, discontinuité du champ électrique ou magnétique, constituent un cas particulier de notre développement. Les formulations sont effectuées dans les domaines temporel et fréquentiel et sont étendues au cas général des métasurfaces dispersives, bianisotropes, variant dans le temps et l’espace. Nous présentons l’interprétation physique des équations dérivées. À chaque chapitre, nous étendons la méthode du chapitre précédent et le prouvons par de nombreux exemples illustratifs, dans lesquels les résultats sont comparés aux solutions analytiques, aux champs spécifiés ou au résultat approximatif du logiciel de simulation.----------ABSTRACT Metasurfaces are very thin structures compared to the operating wavelength and dimensional reduction of three-dimensional metamaterials. They are realized by the juxtaposition of sub-wavelength scattering particles. While being lightweight and less lossy, they offer a broader range of applications than the conventional 3D metamaterials. Being capable of altering the wave amplitude, polarization, phase, and frequency, their application range from radio frequencies to optics in beam-forming, radomes, cloaks, lenses, non-reciprocal structures, and holograms, to name a few. In general, metasurfaces are bianisotropic structures, thus, representing very complex spatial and temporal discontinuity. Their synthesis is based on the generalized sheet transition conditions (GSTCs), which is calculated using distribution theory. As a result of this theory, they are modeled as a zero thickness structure. However, in the calculation of the scattering particles, using S-parameters or impedance matrices, they are mapped into proper unit-cell inclusions with sub-wavelength dimension. Bianisotropy and zero thickness imply discontinuity on both electric and magnetic fields, which is known as the general electromagnetic discontinuity problem. This consequence makes their analysis very complicated and undoable using conventional numerical techniques. Consequently, there has been a significant lack of an accurate and fully-numeric analysis method, which is covered by this manuscript. In this thesis, we perform an in-depth review of the classical boundary conditions and dis-cuss their limitations and conditions of applicability. GSTCs are derived and their usefulness is discussed. Then, we develop computational techniques in Finite Difference (FD) scheme for the analysis of the general electromagnetic discontinuity. We prove that the numerical techniques developed for the simple discontinuity, only electric field or magnetic field discontinuity, is a particular case of our development. The formulations are performed in both of the time and frequency domains and extended to the general case of dispersive, bianisotropic, space-time varying metasurfaces. We present the physical interpretation of the derived equations. At each chapter, we extend the method of the previous chapter and prove them by numerous illustrative examples, where the results are compared with the analytic solutions, specified fields or the approximate result of simulation software

Symmetry in Electromagnetism

Electromagnetism plays a crucial role in basic and applied physics research. The discovery of electromagnetism as the unifying theory for electricity and magnetism represents a cornerstone in modern physics. Symmetry was crucial to the concept of unification: electromagnetism was soon formulated as a gauge theory in which local phase symmetry explained its mathematical formulation. This early connection between symmetry and electromagnetism shows that a symmetry-based approach to many electromagnetic phenomena is recurrent, even today. Moreover, many recent technological advances are based on the control of electromagnetic radiation in nearly all its spectra and scales, the manipulation of matter–radiation interactions with unprecedented levels of sophistication, or new generations of electromagnetic materials. This is a fertile field for applications and for basic understanding in which symmetry, as in the past, bridges apparently unrelated phenomena―from condensed matter to high-energy physics. In this book, we present modern contributions in which symmetry proves its value as a key tool. From dual-symmetry electrodynamics to applications to sustainable smart buildings, or magnetocardiography, we can find a plentiful crop, full of exciting examples of modern approaches to electromagnetism. In all cases, symmetry sheds light on the theoretical and applied works presented in this book

Double-grid finite-difference frequency-domain (DG-FDFD) method for scattering from chiral objects

<![CDATA[This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-gri

Electromagnetic scattering from chiral objects using double-grid finite-difference frequency-domain (DG-FDFD) method

In this dissertation, a double-grid finite-difference frequency-domain (DG-FDFD) method is introduced to solve for scattering of electromagnetic waves from bianisotropic objects. The formulations are based on a double-grid scheme in which a traditional Yee grid and a transverse Yee grid are combined to achieve coupling of electric and magnetic fields that is imposed by the bianisotropy. Thus the underlying grid naturally supports the presented formulations. Introduction of a double-grid scheme doubles the number of electromagnetic field components to be solved, which in turn implies increased time and memory of the computational resources for solution of the resulting matrix equation. As a remedy to this problem, an efficient iterative solution technique is presented that effectively reduces the solution time and memory. While the presented formulations can solve problems including bianisotropic objects, the validity of the formulations is verified by calculating bistatic radar cross-sections of three-dimensional chiral objects and comparing the results to those obtained from analytical and other numerical solutions