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International audience; The linear and non linear responses of nanostructures are investigated with the B-spline modal method. The study is depicted for both plane waves and focused beam illumination. The simulation of a focused beam can be used to simulate the real conditions of experiments. I will show how computations can be accelerated, using either specific implementations of the modal equations, sparse matrices or learning.

We analyse stacked rotated 1D gratings. Although the whole structure is bi-periodic, introducing non orthogonal coordinates allows to formulate the problem in each layer grating in terms of a sole 1D spectral problem. The numerical solution is then obtained by using the Galerkin method with B-splines basis.

International audience; In previous works [1], reduced models have been used for solving inverse problems, characterized by a complex geometry requiring a large number of nodes and / or an objective of online identification. The treated application was a brake disc in two-dimensional representation, in rotation at variable speed. The dissipated heat flux at the pad-disk interface had been identified by Beck's method. We present here a similar application using the adjoint method. The modal reduction is done by using special bases (called branch bases) that offer the advantage of dealing with nonlinear problems and / or unsteady parameters. Adjoint method provides particularly accurate results in this configuration.

The thesis is in the framework of developments made at CEA LIST of a module of the CIVA platform to simulate nondestructive testing (NDT) by ultrasonic guided waves; it is dedicated to the development and the validation of models simulating the examination of pipelines and is focussed on the case of pipeline comprising one or several elbows. To predict effects due to the curvature on guided waves, an extension in curvilinear coordinates of the semi-analytic finite element method is worked out to compute modes propagating in an elbow, by solving an eigen system restricted to the guide section. This development allows us to better understand effects due to the curvature such as displacement field distortions or cut-off frequencies splits. The scattering of waves at the junction between a straight tube and an elbow is then computed by means of the mode-matching method, leading to the modal scattering matrix of the junction; matrix elements are obtained by numerical evaluation of integrals over the junction surface. Local scattering matrices are finally combined to propagation matrices to account for the presence of several scatterers in the pipeline, to form a global scattering matrix. Its minimal computation cost allows us to study the influence of the parameters of the testing configuration and to optimize them. Models are validated by comparing their predictions to numerical and experimental results of the literature and to measurements made at CETIM on industrial mock-ups. Integrated in the platform CIVA, the developed models extend the capabilities of the guided wave NDT module.; La thèse s’inscrit dans les travaux du CEA LIST pour développer dans la plate-forme CIVA un module simulant le contrôle non-destructif (CND) par ondes ultrasonores guidées ; elle est dédiée au développement et à la validation de modèles simulant l’inspection de canalisations et se focalise sur le cas de canalisations comportant un ou plusieurs coudes. Pour prédire l’effet de la courbure sur les ondes guidées, une extension en coordonnées curvilignes de la méthode des éléments finis semi-analytiques est réalisée pour calculer les modes se propageant dans un coude, par résolution d’un système d’équations aux valeurs propres restreint à la section du guide. Ce développement a aidé à comprendre les effets de distorsion des champs ultrasonores et de décalage des fréquences de coupures dus à la courbure. La diffraction des ondes à la jonction entre un tube droit et un coude est ensuite calculée par raccordement modal donnant la matrice de diffraction de la jonction ; les éléments de la matrice s’obtiennent par évaluation numérique d’intégrales à la surface de la jonction. Les matrices de diffractions locales sont enfin combinées à des matrices de propagation pour rendre compte de la présence de plusieurs diffracteurs sur la canalisation, sous forme d’une matrice globale de diffraction. Le coût minimal de son calcul permet d’étudier l’influence des paramètres de contrôle et de les optimiser. Les modèles sont validés en comparant leurs prédictions avec des résultats numériques et expérimentaux de la littérature et des mesures faites au CETIM sur maquettes industrielles. Intégrés à la plate-forme CIVA, ils étendent les possibilités du module de simulation du CND par ondes guidées.

The thesis is in the framework of developments made at CEA LIST of a module of the CIVA platform to simulate nondestructive testing (NDT) by ultrasonic guided waves; it is dedicated to the development and the validation of models simulating the examination of pipelines and is focussed on the case of pipeline comprising one or several elbows. To predict effects due to the curvature on guided waves, an extension in curvilinear coordinates of the semi-analytic finite element method is worked out to compute modes propagating in an elbow, by solving an eigen system restricted to the guide section. This development allows us to better understand effects due to the curvature such as displacement field distortions or cut-off frequencies splits. The scattering of waves at the junction between a straight tube and an elbow is then computed by means of the mode-matching method, leading to the modal scattering matrix of the junction; matrix elements are obtained by numerical evaluation of integrals over the junction surface. Local scattering matrices are finally combined to propagation matrices to account for the presence of several scatterers in the pipeline, to form a global scattering matrix. Its minimal computation cost allows us to study the influence of the parameters of the testing configuration and to optimize them. Models are validated by comparing their predictions to numerical and experimental results of the literature and to measurements made at CETIM on industrial mock-ups. Integrated in the platform CIVA, the developed models extend the capabilities of the guided wave NDT module.; La thèse s’inscrit dans les travaux du CEA LIST pour développer dans la plate-forme CIVA un module simulant le contrôle non-destructif (CND) par ondes ultrasonores guidées ; elle est dédiée au développement et à la validation de modèles simulant l’inspection de canalisations et se focalise sur le cas de canalisations comportant un ou plusieurs coudes. Pour prédire l’effet de la courbure sur les ondes guidées, une extension en coordonnées curvilignes de la méthode des éléments finis semi-analytiques est réalisée pour calculer les modes se propageant dans un coude, par résolution d’un système d’équations aux valeurs propres restreint à la section du guide. Ce développement a aidé à comprendre les effets de distorsion des champs ultrasonores et de décalage des fréquences de coupures dus à la courbure. La diffraction des ondes à la jonction entre un tube droit et un coude est ensuite calculée par raccordement modal donnant la matrice de diffraction de la jonction ; les éléments de la matrice s’obtiennent par évaluation numérique d’intégrales à la surface de la jonction. Les matrices de diffractions locales sont enfin combinées à des matrices de propagation pour rendre compte de la présence de plusieurs diffracteurs sur la canalisation, sous forme d’une matrice globale de diffraction. Le coût minimal de son calcul permet d’étudier l’influence des paramètres de contrôle et de les optimiser. Les modèles sont validés en comparant leurs prédictions avec des résultats numériques et expérimentaux de la littérature et des mesures faites au CETIM sur maquettes industrielles. Intégrés à la plate-forme CIVA, ils étendent les possibilités du module de simulation du CND par ondes guidées.

We address the problem of acoustic propagation in waveguides with wall impedance, or Robin, boundary condition. Two improved multimodal methods are developed to remedy the problem of the low convergence of the series in the standard modal approach. In the first improved method, the series is enriched with an additional mode, which is thought to be able to restore the right boundary condition. The second improved method consists in a reformulation of the expansions able to restore the right boundary conditions for any truncation, similar to polynomial subtraction technique. Surprisingly, the first improved method is found to be the most efficient. Notably, the convergence of the scattering properties is increased from N − 1 in the standard modal method to N − 3 in the reformulation and N − 5 in the formulation with a supplementary mode. The improved methods are shown to be of particular interest when surface waves are generated near the impedance wall.

International audience; Measuring machines gives a more and more accurate number of points in order to describe a surface. In a design process, we need to have a better description of geometry in order to assess all the behaviours involving interactions between material and it's environment. Focussing at the same time the infinite complexity of real objects and the simplification needed to make simple choices is a main goal of a metrologist. This is possible by the use of adapted geometric languages. A geometry parameterization has the challenge to have the following properties: - Unicity-inversibility: a unique set of parameters gives a unique shape. - Stability: continuous parameters. - Invariance: decoupling of parameters - Efficiency: ability to represent the measurement with a minimum number of parameters. - Exhaustiveness: to describe the complete measurement. - Complexity sorting: the first parameters are associated to the simplest shape. We had the idea to think about the natural vibrations of shapes in order to use all their very interesting properties corresponding to those properties. They form an automatic, natural, geometric vector space of shape descriptors. Fourier series that we all know is very useful, but limited to very simple shapes (line, circle for single Fourier series and square for double Fourier decomposition). If you remember that Fourier series are the modal solution of a vibrating rope, you understand that nature has given us a way to generalise what Fourier has discovered. We propose to use the modal eigen shapes of surfaces in order to describe them and we adapted this method called Discrete Modal Decomposition (DMD) to discrete surfaces. Recently we have made possible to compute this method to a huge number of points making possible to assess measurements of topographic machines. Now we can simplify the complexity of a measurement to different levels of geometry from the simplest one given by the global shape, through the "middle level" given by undulation to the finest level of roughness or a very local "geometric accident" using this new (but old, because natural) method of geometric filtering.

International audience; We study the time harmonic propagation of acoustic waves in a waveguide with varying cross section. This is done using a multimodal approach. The modal components are expressed thanks to an integral representation (Lipmann Schwinger representation) that is used to iterate the Born approximation. We compare the classical approach in which the infinite sum of modes is truncated in the practice to a new formalism in which the sum of modes is finite and an extra mode is artificially added. This method has been shown to ensure a better convergence because the additional mode allows a better approximation of the boundary condition at the walls. Numerical calculations are proposed and compared to direct finite element simulations to validate the iterated Born approximation. Analytical solutions are proposed in the first Born approximation and compared to classical results for the low frequency regime.

Structural health monitoring (SHM) using elastic guided waves is under study for the inspection of aircraft multilayered composite stiffened plates. Two simulation tools are developed to discuss its feasibility. The first predicts the wave propagation in the plates as a modal series by the semi-analytical finite element method (SAFE). The second tool is a hybrid computing predicting diffraction of guided waves in arbitrary incidence on a composite stiffener. The diffraction is calculated locally by finite element (FE), the global propagation by the SAFE method. The link between the two calculations is done through transparent boundaries of the FE domain avoiding artificial reflections, allowing the projection of the field in the stiffener on the modes of the plate and minimizing the FE computation domain. The tools are used in typical cases, the predictions are discussed in view of the industrial application of SHM., Un contrôle santé intégré (CSI) par ondes élastiques guidées est à l'étude, pour l'inspection des plaques aéronautiques raidies en composite multicouche. Deux outils de simulation sont développés permettant d'en discuter la faisabilité. Le premier prédit la propagation des ondes dans les plaques comme une série modale par la méthode des éléments finis semi-analytiques (SAFE). Le second outil est un calcul hybride prédisant la diffraction des ondes guidées en incidence quelconque sur un raidisseur. La diffraction est calculée localement par éléments finis (EF), la propagation globale par la méthode SAFE. Le lien entre les deux calculs se fait à travers des conditions transparentes aux frontières du domaine EF évitant les réflexions parasites, permettant la projection du champ dans le raidisseur sur les modes de la plaque et minimisant le domaine EF. Les outils sont utilisés dans des cas typiques, les prédictions sont discutées en vue de l'application industrielle du CSI.

The scatterometry requires calculating the optical response of periodic structures. Among the numerical methods for calculating electromagnetic diffraction by gratings, the most commonly used is the Fourier Modal Method (FMM). This seems to be ineffective for characterizing structures very isolated or very dense and can even fail. The objective of this thesis is to overcome the limitations of the FMM. We remain within the framework of modal methods but we are exploring new ways of using different bases of development that do not have the drawbacks of Fourier bases. First, we introduced the B-spline functions which are the first step towards multi-resolution analysis with wavelet splines. We formulated the problem of diffraction by a 1D grating as an eigenvalue problem that we solved numerically using the Galerkin method. We studied in detail the importance of the discretization compared to the discontinuities of permittivity function. Then we introduced the wavelet analysis at multiple levels of detail for the diffraction problem. The thesis contains a diversity of numerical examples concerning dielectric and metal gratings. We have carefully compared the convergence of our methods with that of other methods, especially with the FMM. We showed that multiresolution analysis can deal with cases where the FMM fails., La scattéromètrie requiert le calcul de la réponse optique de structures périodiques. Parmi les méthodes numériques de calcul électromagnétique de la diffraction par des réseaux, la méthode la plus couramment utilisée est la Méthode Modale de Fourier (FMM). Celle cis'avère peu efficace pour la caractérisation de structures très isolées ou très denses et peut même ne pas marcher du tout. L'objectif de cette thèse est de dépasser les limitations de la FMM. Nous restons dans le cadre des méthodes modales mais nous explorons de nouvelles voies en utilisant des bases de développement différentes qui ne présentent pas les inconvénients des bases de Fourier. Tout d'abord, nous avons introduit les fonctions B-spline qui sont le premier pas vers l'analyse multi-résolution avec les ondelettes splines. Nous avons formulé le problème de la diffraction par un réseau 1D comme un problème aux valeurs propres que nous avons résolu numériquement à l'aide de la méthode de Galerkin. Nous avons étudié en détail l'importance de la discrétisation par rapport aux discontinuités de la fonction permittivité. Ensuite, nous avons introduit les ondelettes et l'analyse à plusieurs niveaux de détails pour le problème de diffraction. La thèse contient une palette variée d'exemples numériques concernant des réseaux diélectriques et métalliques. Nous avons comparé soigneusement la convergence de nos méthodes avec celle d?autres méthodes, notamment avec la FMM. Nous avons montré que l'analyse multirésolution permet de traiter des cas pour lesquels la FMM échoue.

Structural health monitoring (SHM) using elastic guided waves is under study for the inspection of aircraft multilayered composite stiffened plates. Two simulation tools are developed to discuss its feasibility. The first predicts the wave propagation in the plates as a modal series by the semi-analytical finite element method (SAFE). The second tool is a hybrid computing predicting diffraction of guided waves in arbitrary incidence on a composite stiffener. The diffraction is calculated locally by finite element (FE), the global propagation by the SAFE method. The link between the two calculations is done through transparent boundaries of the FE domain avoiding artificial reflections, allowing the projection of the field in the stiffener on the modes of the plate and minimizing the FE computation domain. The tools are used in typical cases, the predictions are discussed in view of the industrial application of SHM., Un contrôle santé intégré (CSI) par ondes élastiques guidées est à l'étude, pour l'inspection des plaques aéronautiques raidies en composite multicouche. Deux outils de simulation sont développés permettant d'en discuter la faisabilité. Le premier prédit la propagation des ondes dans les plaques comme une série modale par la méthode des éléments finis semi-analytiques (SAFE). Le second outil est un calcul hybride prédisant la diffraction des ondes guidées en incidence quelconque sur un raidisseur. La diffraction est calculée localement par éléments finis (EF), la propagation globale par la méthode SAFE. Le lien entre les deux calculs se fait à travers des conditions transparentes aux frontières du domaine EF évitant les réflexions parasites, permettant la projection du champ dans le raidisseur sur les modes de la plaque et minimisant le domaine EF. Les outils sont utilisés dans des cas typiques, les prédictions sont discutées en vue de l'application industrielle du CSI.

International audience; We present two mode solvers applied to a very thin long-range plasmonic waveguide. We compare the guided mode complex effective index obtained either applying a Fourier modal method or calculating density of guided modes using the Green's dyad technique. We achieve good agreement for both effective indices and mode profiles. We also observe a different behaviour compared to long-range surface plasmon supported by thicker films.

International audience; This paper is devoted to a modal method for fast design of electrically large metal-plate lens structures. Themethod is based on Fourier Modal Method (FMM). Thelens consists of stacked parallel-plate waveguides. The lensis considered as a medium with discontinuities describedby Dirac Delta functions.

This thesis presents theoretical works based on a modal approach, about the optical properties of metallic surfaces with rectangular grooves whose dimensions are smaller than the wavelength of the incident light. These surfaces show reflection anomalies related to local enhancements of the electromagnetic field, due to, in particular, Fabry-Pérot like resonances inside the grooves.The problem of two near-field coupled sub-wavelength cavities is analysed. Hot spot phenomena occur, and we show how to control the localization of light at sub-wavelength scales. The results could find important applications: optical switching, quantitative light addressing, surface enhanced Raman scattering (SERS)... We also study the localization effects due to structural disorder: breaking the symmetry of periodic arrangements, different lighting configurations may appear, very sensitive to the excitation frequency. Some theoretical predictions are evidenced experimentally.Finally, we deal with the case of very sub-wavelength lamellar gratings, in connection with the Abnormal Optical Absorption and the SERS effect observed for some rough metallic films. Giant enhancements of the electric field, calculated inside nano-cavities with the exact modal method, in the visible region, are explained by the excitation of surface plasmons-polaritons whose wave vectors are much larger than those of light., Ce travail de thèse, essentiellement théorique et basé sur une approche modale, porte sur les propriétés optiques de surfaces métalliques comportant un certain nombre de gravures de profil rectangulaire dont les dimensions sont inférieures à la longueur d'onde de la lumière incidente.Ces surfaces présentent des anomalies de réflexion liées à des exaltations locales du champ électromagnétique, dues notamment à des résonances de type Fabry-Pérot à l'intérieur des sillons. L'analyse du problème d'un couple de cavités sub-longueur d'onde, couplées en champ proche, montre comment on peut générer des "points chauds" et contrôler la localisation de la lumière à l'échelle sub-longueur d'onde. Les applications sont de première importance: commutation optique, adressage quantitatif de la lumière, diffusion Raman exaltée ensurface (SERS)... On s'intéresse également aux effets de localisations liés au désordre structurel: la rupture de symétrie d'un arrangement périodique génère différents jeux d'allumage des cavités, très sensibles à la fréquence d'excitation. Certaines prédictions théoriques sont étayées expérimentalement.Enfin, le cas des réseaux lamellaires très fortement sub-longueur d'onde est examiné, en lien avec l'Absorption Optique Anormale et l'effet SERS observés sur certains films métalliques rugueux. Les exaltations géantes du champ électrique, calculées dans les nano-cavités par la méthode modale exacte, dans le domaine visible, s'expliquent par l'excitation de plasmons-polaritons de surface dont les vecteurs d'onde sont très supérieurs à ceux de la lumière.

We show that extraordinary light transmission of periodic subwavelength hole arrays, generally attributed to surface-plasmon resonances, is strongly influenced by the hole shape. Both experiments and calculations, based on a Fourier modal method, demonstrate that a shape change from circular to rectangular increases the normalized transmission by an order of magnitude while the hole area decreases. Moreover, the spectra exhibit large redshifts (approximately 2500 cm(-1)). A comparison with the transmission of isolated holes shows that shape resonances of the rectangular holes play a dominant role.

We have designed and fabricated a silicon grating which shows antireflection properties in the [4μm ; 6 μm] spectral region. It is shown both theoretically and experimentally that, even if the refractive index and the grating period are in the extend that a simple homogenization theory can not be used, a substantial broadband antireflection effect can be obtained. The grating was made using a wet anisotropic etching technique. The reflectance was calculated with a modal method and compared successfully with the experimental results. It is shown that the grating reduces the silicon substrate reflectance in the whole [4 μm ; 6 μm] spectral domain by a factor greater than 10.

International audience; The cooling loads of a building and the comfort its induces, depend on the local micro climate, the building, ist occupancy and its shape. The thermophysical and geometrical properties of a building can be described with static and dynamic parameters. These parameters represent the filter effect a building has between the environment and the occupant. The static parameters give an insight of the thermal state of a building in steady state conditions, the climate driving forces being constant. The other parameters are the dynamic ones as they represent the dynamic response of a building to variable driving forces. The modal form of the model for the thermal behaviour enables one to distinguish clearly the intrinsic dynamic parameters which are eigen modes and their corresponding eigenvalue. These parameters are independant of the nature of the outputs and inputs which are applied to the building. the thermal inertia of a building is therefore the physical entity defined as the set of all the eigenmodes and eigenvalues. The number of eigen modes in not a propoerty of the building; this number is related to the precision of the model (it is of the order of the nodes of the grid for finite difference method and is strictly infinite for a model continuous in space). However, simplified assumptions had to be done when elaborating physical and mathematical models. A coherent level of precision with these assumptions will make the best of an important reduction of the eigenmodes describing the interia. As a conslusion, the modal method allows one to strictly define the thermal inertia and it also provides tools for its analysis. Such an analysis will be roughly performed on a particulur example described later.