Publications

Titre : A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides
Année : 2011
Type : conférence sans actes
Auteurs : S. Fliss
Résumé : This works deals with one dimensional infinite perturbation - namely line defects - in periodic media. In optics, such defects are created to construct an (open) waveguide that concentrates light. The existence and the computation of the eigenmodes is a crucial issue. This is related to a selfadjoint eigenvalue problem associated to a PDE in an unbounded domain (in the directions orthogonal to the line defect), which makes both the analysis and the computations more complex. Using a Dirichlet-to-Neumann (DtN) approach, we show that this problem is equivalent to one set on a small neighborhood of the defect. Conversely to existing methods, this one is exact but there is a price to be paid : the reduction of the problem leads to a nonlinear eigenvalue problem of a fixed point nature.
Thèmes :
Référence : 10th International Conference on Mathematical and Numerical Aspects of Waves, waves 2011, Vancouver images/icons/doctype_pdf.gif