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Etude mathématique et numérique de guides d'ondes ouverts non uniformes, par approche modale

Benjamin Goursaud 1 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This thesis deals with the theoretical and numerical study of the scattering of a time-harmonic wave by the junction between two open waveguides. We demonstrate that such a problem is well-posed. For this aim, we use modal radiating conditions, which are based on the representation of the solution in a straight waveguide thanks to the guided modes (which are linked to the point spectrum of the transverse operator) and the radiation modes (which are linked to the continuous spectrum of the transverse operator). This representation of the solution seems to be intractable in a numerical method, because of the presence of the continuum of the radiation modes. Alternatively, we use PMLs (Perfectly Matched Layers) in order to set the problem in a bounded domain in the transverse directions, which severely modifies the nature of the transverse operator: it loses its selfadjointness and its spectrum becomes exclusively discret. A new category of modes appears: the leaky modes, whose properties are studied. We explain that the loss of the selfadjointness implies that the calculation of the modes is intricate. These new modes (which form a discret set) are used into numerical methods for the junction between two open waveguides (transparent boundary conditions using Dirichlet-to-Neumann operators, multimodal method).
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Submitted on : Monday, December 13, 2010 - 4:07:58 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:04 PM
Long-term archiving on: : Monday, March 14, 2011 - 2:28:15 AM


  • HAL Id : pastel-00546093, version 1



Benjamin Goursaud. Etude mathématique et numérique de guides d'ondes ouverts non uniformes, par approche modale. Modélisation et simulation. Ecole Polytechnique X, 2010. Français. ⟨pastel-00546093⟩



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