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

july, 2011
Publication type:
Conference without proceedings
Workshop:
10th International Conference on Mathematical and Numerical Aspects of Waves, waves 2011, Vancouver
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 selfadjoint 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. Conversely 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:
@conference{Fli-2011,
    author={Sonia Fliss },
    title={A Dirichlet-to-Neumann approach for the exact computation of 
           guided modes in photonic crystal waveguides },
    publisher={10th International Conference on Mathematical and Numerical 
           Aspects of Waves, waves 2011, Vancouver },
    year={2011 },
    month={7},
}