https://hal.inria.fr/hal-00937675Fliss, SoniaSoniaFlissPOEMS - Propagation des Ondes : Étude Mathématique et Simulation - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - UMA - Unité de Mathématiques Appliquées - ENSTA Paris - École Nationale Supérieure de Techniques Avancées - CNRS - Centre National de la Recherche ScientifiqueA Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguidesHAL CCSD2013periodic medialine defectguided wavesspectral analysisDirichlet-to-Neumann operator[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP][INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-SP] Mathematics [math]/Spectral Theory [math.SP]Vinoles, Valentin2014-01-28 17:06:012023-03-24 14:52:582014-01-28 17:06:08enJournal articles10.1137/12086697X1This 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