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Theses

Simulation électromagnétique utilisant une méthode modale de décomposition en ondelettes

Abstract : 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.
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Ana Armeanu. Simulation électromagnétique utilisant une méthode modale de décomposition en ondelettes. Autre. Université de Grenoble, 2011. Français. ⟨NNT : 2011GRENT030⟩. ⟨tel-00721767⟩

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