Title : A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides
Year : 2013
Type : article_acl
Authors : S. Fliss
Abstract : 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 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 (DtN) approach, we show that this problem is equivalent to one set on a small neighborhood of the defect. On 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.
Themes : Artificial boundaries
Wave guides
Reference : SiAM J. Sci. Comp. - vol. 35(2) (pp B438-B461 ) images/icons/doctype_link.gif