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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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 35; no. 2; pp. B438 - B461
Main Author: Fliss, Sonia
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects:
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
line defect
spectral analysis
Dirichlet-to-Neumann operator
periodic media
guided waves
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary: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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ISSN:1064-8275
1095-7197
DOI:10.1137/12086697X