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A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides

Sonia Fliss 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : This work 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 computation of the eigenmodes is a crucial issue. This is related to a self-adjoint 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 approach, we show that this problem is equivalent to one set on a small neighborhood of the defect. Contrary 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. © 2013, Society for Industrial and Applied Mathematics
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https://hal.inria.fr/hal-00937675
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Submitted on : Tuesday, January 28, 2014 - 5:06:01 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM

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Sonia Fliss. A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2013, 35 (2), pp.B438 - B461. ⟨10.1137/12086697X⟩. ⟨hal-00937675⟩

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