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

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

Mots clés: periodic media; line defect; guided waves; spectral analysis; Dirichlet-to-Neumann operator

Domaines: Equations aux dérivées partielles [math.AP]; Modélisation et simulation; Analyse numérique [math.NA]; Physique mathématique [math-ph]; Optimisation et contrôle [math.OC]; Théorie spectrale [math.SP]

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