A Dirichlet-to-Neumann Approach for The Exact Computation of Guided Modes in Photonic Crystal Waveguides
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 e...
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| Vydané v: | SIAM journal on scientific computing Ročník 35; číslo 2; s. B438 - B461 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Philadelphia
Society for Industrial and Applied Mathematics
01.01.2013
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| ISSN: | 1064-8275, 1095-7197 |
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| Abstract | 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. [PUBLICATION ABSTRACT] |
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| AbstractList | 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 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. 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. [PUBLICATION ABSTRACT] |
| Author | Fliss, Sonia |
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| Keywords | line defect spectral analysis Dirichlet-to-Neumann operator periodic media guided waves |
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| SubjectTerms | Analysis of PDEs Applied mathematics Computation Computer Science Concentrates Crystal defects Eigenvalues Equivalence Mathematical Physics Mathematics Methods Modeling and Simulation Nonlinearity Numerical Analysis Optimization and Control Photonic crystals Spectral Theory Waveguides |
| Title | A Dirichlet-to-Neumann Approach for The Exact Computation of Guided Modes in Photonic Crystal Waveguides |
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