A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides
march, 2013
Publication type:
Paper in peer-reviewed journals
Journal:
SiAM J. Sci. Comp., vol. 35(2), pp. B438-B461
Download:
External link:
DOI:
HAL:
Keywords :
periodic media, line defect, guided waves, spectral analysis, Dirichlet-to-Neumann operator
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.
BibTeX:
@article{Fli-2013, author={Sonia Fliss }, title={A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides }, doi={10.1137/12086697X }, journal={SiAM J. Sci. Comp. }, year={2013 }, month={3}, volume={35(2) }, pages={B438--B461}, }