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Linearization techniques for band structure calculations in absorbing photonic crystals

Effenberger, C. ; Kressner, D. and Engström, C. LU (2012) In International Journal for Numerical Methods in Engineering 89(2). p.180-191
Abstract

Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail.... (More)

Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques.

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author
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publishing date
type
Contribution to journal
publication status
published
subject
keywords
Band structure calculation, Krylov subspace method, Linearization, Lorentz model, Photonic crystal, Rational eigenvalue problem
in
International Journal for Numerical Methods in Engineering
volume
89
issue
2
pages
12 pages
publisher
John Wiley & Sons Inc.
external identifiers
  • scopus:84655167725
ISSN
0029-5981
DOI
10.1002/nme.3235
language
English
LU publication?
no
id
644f69cb-a82c-47aa-bf4b-3c84bfc48f89
date added to LUP
2023-03-24 11:12:06
date last changed
2023-03-24 14:29:19
@article{644f69cb-a82c-47aa-bf4b-3c84bfc48f89,
  abstract     = {{<p>Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques.</p>}},
  author       = {{Effenberger, C. and Kressner, D. and Engström, C.}},
  issn         = {{0029-5981}},
  keywords     = {{Band structure calculation; Krylov subspace method; Linearization; Lorentz model; Photonic crystal; Rational eigenvalue problem}},
  language     = {{eng}},
  month        = {{01}},
  number       = {{2}},
  pages        = {{180--191}},
  publisher    = {{John Wiley & Sons Inc.}},
  series       = {{International Journal for Numerical Methods in Engineering}},
  title        = {{Linearization techniques for band structure calculations in absorbing photonic crystals}},
  url          = {{http://dx.doi.org/10.1002/nme.3235}},
  doi          = {{10.1002/nme.3235}},
  volume       = {{89}},
  year         = {{2012}},
}